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This is to certify that the

dissertation entitled

DETERMINATION OF A DISCRIMINANT FUNCTION
AS A PREDICTION MODEL FOR EFFECTIVENESS OF
SPEED ZONING IN URBAN AREAS

presented by

Fred Coleman, III

has been accepted towards fulfillment
of the requirements for

 

 

Ph.D. degree in Civil Engineering

Major professor :\

Date /////7//7$1

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MSU Is An Affirmative Action/Equal Opportunity Institution
mime-minnow

DETERMINATION OF A DISCRIMINANT FUNCTION AS A
PREDICTION MODEL FOR EFFECTIVENESS OF SPEED ZONING
IN URBAN AREAS
By

Fred Coleman, III

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

1994

ABSTRACT

DETERMINATION OF A DISCRIMINANT FUNCTION AS A
PREDICTION MODEL FOR EFFECTIVENESS OF SPEED ZONING
IN URBAN AREAS

By

Fred Coleman, III

The critical task of controlling the speed of drivers in order to create a safe, yet
efficient surface transportation system is found to be a mixture of policy,
human behavior, and the physics of vehicles in motion. Speed zoning is the
procedure utilized by traffic engineers to inform drivers of the required
balance between safety and Speed of travel apprOpriate for a specific section of
a road. The objective of speed zoning is to convey an understanding of these
factors in a manner consistent with environmental conditions and driver
expectancies such that the overall safest driving environment can be

achieved.

A review of the literature indicates traffic Speed variation, traffic speed
distributions, roadside friction, and human behavior are the primary factors

in accidents.

The problem is that where states have procedures which quantify and use
roadside development variables the empirical basis for their inclusion or
exclusion has not been validated. Furthermore, the type and level of
adjustment for these variables has not been substantiated as appropriate or

meaningful.

Because of these limitations in the Speed zoning procedure traffic engineers
have no way of predicting if their Speed zoning actions will result in better
compliance to speed limits and most importantly, make the driving
environment safer. AS a result, analyses of Speed zones have Shown mixed

results.

The hypotheses of this study is that a quantifiable relationship exists between
accident parameters, speed parameters, roadside friction, and

environmental / geometric variables such that it is possible to predict the
effectiveness of Speed zoning in urban areas. It iS hypothesized that there
exists specific variables which can serve as predictors of the effectiveness of

proposed Speed zoning actions.

In order to determine the effectiveness of speed zoning a set of treatment and
control zones from the Michigan Department of Transportation files were
matched in a before and after paired comparison experimental design. Those
zones determined to be effective based on statistical tests utilizing a
confidence coefficient of .95, in reducing accidents are analyzed. Discriminant
analysis is used to determine which variables distinguish effective from non--
effective speed zoning actions and therefore serve as predictors of the

effectiveness of Speed zoning actions.

Copyright by
FRED COLEMAN, HI
1994

Dedicated to
Jessie Mae Boyd Mack
1933-1971 (Mother)
and
Dillie James Boyd
1908-1989 (Grandmother)

ACKNOWLEDGMENTS

The support I have received over the years which has resulted in the
culmination of this effort is difficult to put into words. It always starts with
one's committee chair, my deepest appreciation is extended to William C.
Taylor, Ph.D., P.E. (Civil) for his enduring contributions to make this a
successful journey. I would also like to extend appreciation to Thomas L.
Maleck, Ph.D., P.E. (Civil) for his encouragement and thoughtfiil criticisms. I
also wish to thank my other committee members for their insightful comments
and assistance whenever called upon, John B. Kreer, Ph.D., P.E., (Electrical)
and Connie F. Page (Statistics). Also acknowledged is Herman D. Hughes
Ph.D., former Assistant Dean of the Graduate School whose support made it

possible to continue on.

A special recognition is merited for the staff who encouraged and
accommodated me so graciously at the Michigan Department of
Transportation, they are: Calvin Roberts, Jud Doyle, Jeanne Thomas, and
Trish Apere.

Friendship is itS’ own reward, B.D. Agrawal and Apurna Agrawal have been

there with love and support from the beginning.

Last and certainly not least, I wish to thank my wife Helen for her ongoing
encouragement, and my two children, Chike’ and Ayanna for all the joy and

love they have given me.

vi

TABLE OF CONTENTS

Page
List of Tables ............................................................................................................ xiv
List of Figures .......................................................................................................... xix
Chapter
1 Introduction ...................................................................................................... 1
1.1 Speed and Safety ...................................................................................... 1\"\?
1.2 Speed and Accident Types ...................... (4 >
1.3 Access Points and Roadside Development and Safety ................... 9
1.3.1 Driveways ..................................................................................... 10
1.3.2 Intersections ................................................................................. 12
1.3.3 Medians ......................................................................................... 13
1.4 Driver Judgement ................................................................................... 15
1.4.1 Driver Estimation of Speed of Travel .................................... 16
1.5 Human Factors ........................................................................................ 19

vii

1.6 Methods of Controlling Speed ................. . ........ ....... 22

 

1.6.1 Design Speed ................................................................................ "zj
1.6.2 Speed Laws ............................................. _ ...................................... 2 4

1.6.3 Speed Limits ................................................................................. 25

.V/
1.7 85th Percentile Speed ............................................................................. .. 26\
. . __,,I
1.8 Evaluation of Speed Zone Effectiveness ............................................ 28
1.9 Summary .................................................................................................. 29
1.10 Statement of the Problem ..................................................................... 31
1.10.1 Statement of the Hypotheses .................................................... 33
Methodology ..................................................................................................... 34
2.1 Introduction ............................................................................................. 34
2.2 Site Selection ............................................................................................ 34
2.3 File Building ............................................................................................ 35
2.4 Determination of Effective vs Non-Effective Speed Zones ........... 36

2.5 Individual Zone Effectiveness Leading to Effective and

Non-Effective Group Formation ......................................................... 38
2.6 Discriminant Analysis ........................................................................... 39
2.7 Speed Raised and Lowered Combined Effective Analysis ............. 4O

viii

2.8 Variable Selection--Speed Raised and Lowered Combined

Effective ..................................................................................................... 41
2.9 Discriminant Analysis on Specific Speed Zoning Actions ............ 42
Effectiveness of Speed Zones ......................................................................... 45
3.1 Background .............................................................................................. 45
3.2 Objectives .................................................................................................. 46
3.3 Matching of Test and Control Zones .................................................. 47
3.4 Data Preparation ...................................................................................... 48
3.5 Analysis of Dta ......................................................................................... 51

3.6 Determination of Effectiveness of Speed Zoning Action on
Accidents ................................................................................................... 53

3.6.1 Test of Comparability of Before Period Mean Accident
Rate ............................................................................................................ 53

3.6.2 Hypothesis-Comparability of Before Period Mean
Accident Rate ........................................................................................... 54

3.6.3 Findings ........................................................................................ 57

3.6.4 Significance of Findings: Comparability of Before Period
Mean Accident Rate ............................................................................... 58

3.7 Test of the Change in the Mean Accident Rate--Treatment
Compared to Control ............................................................................. 61

ix

3.7.1 Hypothesis--Test of the Difference in Before to After
Period Mean Accident Rate--Treatment Compared to Control....

3.7.2 Family Confidence Intervals for Speed Zoning
Actions ......................................................................................................

3.8 Test of Individual Zone Accident Reduction Effectiveness ..........

3.8.1 Discussion of Findings-Jndividual Zone Accident
Reduction Effectiveness ........................................................................

Combined Effective Speed Raised and Speed Lowered Analysis
vs Combined Non-Effective Speed Raised and Speed Lowered
Analysis ..............................................................................................................

4.1 Discriminant Analysis ...........................................................................
4.2 Variable Selection ...................................................................................
4.3 Analysis Categories .................................................................................
4.4 Initial Variables in Discriminant Analysis .......................................
4.5 Discussion--Before Period All and Rear End Accident Types .......
4.6 Speed Variables Included ......................................................................
4.7 Speed Variables Excluded ......................................................................
4.8 Validity of the Discriminant Means and their Distributions ........
4.9 Summary--Before Period All and Rear End Accident Types
with and without Speed Variables ......................................................
4.10 Discussion--After Period All Accident Types ...................................
4.11 Summary--After Period .........................................................................

61

66

67

69

77

77

77

80

82

91

91

93

95

98

99

104

5 Analysis of Speed Limit Raised - - _

5.1 Before Period Speed Limit Raised Zoning Action ...........................

5.2

Variable Selection -- -- ...........

 

 

5.3 Discriminant Analysis--Before Perod Effective All and
Effective Rear: All and Rear End Accidents ...........

5.4

5.3.1

5.3.2 Mean Values for Coded and Direct Variables

5.3.3 Coded Variables- - .................. - - -

5.3.4 Direct Variables ........ -

5.3.5 Summary Effective All and Rear End: All Accident
Types------ - . ..... -- - -- ................................... -

5.3.6 Before Period Raised Effective All and Effective Rear
End Analysis Rear End Accidents - ...... -

5.3.7 Coded Variables ...........................................................................

5.3.8 Direct Variables - - - -- - - u .....

5.3.9 Summary Effective All and Rear End: Rear End
Accident Types“--- ...... - ..........................

5.3.10 Summary--Before Period Raised .............................................

Analysis of After Period Speed Raised Zoning Action ...................

5.4.1 Comparison of the Change in Mean Values Between

5.4.2

 

Before Period Raised Effective All and Effective Rear

Analysis: All Accidents- - - - ..........

 

 

 

 

 

 

 

 

Time Periods for Location Sensitive Variables--Effective
All (All Accidents) .....

 

Summary--Change in Mean Values Between Time
Periods for Location Sensitive Variables--Effective

All (All Accidents)-- - - ......... - .....

 

xi

106

106

107

110

111

114

115

116

120

121

125

126

129

129

130

130

5. 4. 3 Summary--Analysis of After Period Speed Raised

 

 

Zoning Action -- - 133
6 Analysis of Speed Limit Lowered Zoning Actions ................................... 134-
6.1 Before Period Speed Limit Lowered Zoning Action- - 134

6.2 Variable Selection ................................................................................... 135

6.3 Discriminant Analysis--Before Period Effective All: All and

 

 

Rear End Accidents ................................................................................. 136
6.3.1 Measures of EffectiveneSS--Before Period Lowered

Effective All Analysis: All Accidents ...................................... 137
6.3.2 Coded Variables ....... ..... - -- - -- -- -- ............. . 140
6.3.3 Direct Variables ........................................................................... 142
6.3.4 Summary--Before Period Effective All Analysis:

All Accidents ................................................................................ 144
6.3.5 Before Period Effective All Analysis--Rear End

Accident Select ............. - - - -- -- - 144
6.3.6 Coded Variables ........................................................................... 147
6.3.7 Direct Variables ........................................................................... 149

6.3.8 Summary--Before Period Effective All Analysis: Rear

 

 

 

End Accidents--- --------- - - - - 150
6.4 Analysis of After Period Speed Lowered Zoning Action ............... 151
6.4.1 Comparison of the Change in Mean Values Between

Time Periods for Location Sensitive Variables .................... 151

7 Summary and Conclusions ........ ------- -- ......... 156
7.1 Basis and Objectives . ----- - - -- ...... 156
7.2 Conduct of the Research ........................................................................ 156
7.3 Summary and Conclusions of Each Phase of Research .................. 157

xii

Bibliography ............................................................................................................ 160

xiii

LIST OF TABLES

TABLE Page

3.1 Non-Matching Speed Limits in Before Period in Control

 

and Test Zones ........... -- - - - 48
3.2 Number of Zones by Zoning Action and Amount of Change ........... 49
3.3 Group Name and Associated Accident Years with Mean ................... 50

3.4 Before Period and After Period F Test of Treatment
vs Control by Speed Zoning -- -- ............ - 52

 

3.5 Test of Comparability in Before Period of Test Zone Mean
Accident Rate vs Control Zone Mean Accident Rate ........................... 56

3.6 Single Degree of Freedom Test Difference in Before to
After Period Accident Rate Treatment vs Control ............................... 64

3.7 Family Confidence Intervals for Speed Zoning Actions,
All Accident Types ..................................................................................... 67

3.8 Individual Zone Effectiveness by Type of Zone and

Accident Categories .................................................................................... 70
3.9 Zoning Action and Accident Categories ................................................ 71
3.10 Zoning Action by Land Use and Accident Categories ........................ 72
3.11 Comparison of Zoning Action and Accident Categories .................... 74

xiv

3.12 Listing of Effective Zones by Zoning Action and

3.13

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Accident Categories .................................................................................... 75

Number of Effective Zones versus Non-Effective Zones by
Speed Zoning Action--All and Rear End Accident Types .................. 76

Identification and Description of Variables in the
Discriminant Analysis ............................................................................... 82

Before Period Raised and Lowered Effective All and Rear End
Accidents vs Before Period Raised and Lowered Non-Effective
All and Rear End Accidents Measures of Effectiveness ..................... 86

Before Period Raised and Lowered Effective Structure
Coefficients and Standardized Coefficients with Speed Variables,
Accident Type: All and Rear End ............................................................ 87

Before Period Raised and Lowered Effective Structure
Coefficients and Standardized Coefficients without Speed Variables,
Accident Type: All and Rear End ............................................................ 89

Before Period Raised and Lowered Effective Means with Speed
Variables vs Before Period Raised and Lowered Non-Effective
Means w/Speed Variables, Accident Type: All and Rear ................... 90

Before Period Raised and Lowered Effective Means without Speed
Variables vs Before Period Raised and Lowered Non-Effective
Means without Speed Variables, Accident Type: All and Rear ........ 90

Percentage of Cases Utilized in Discriminant Analysis Per
Data Set ......................................................................................................... 96

Comparison of Selected Before Period Variables Population
Means vs Discriminant Data Set Means with Results for

Null Hypothesis (on = .05) .......................................................................... 97

4.9

4.10

4.11

4.12

5.1

5.2

5.3

5.4

5.5

5.6

5.7

Comparison of Selected After Period Variables Population
Means vs Discriminant Data Set Means with Results for

Null Hypothesis (or = .05) - -- -- ................

 

After Period Raised and Lowered Effective All and Rear End
Accidents vs After Period Raised and Lowered Non-Effective All
and Rear End Accidents Measures of Effectiveness ----------------

 

After Period Raised and Lowered Effective Structure
Coefficients and Standardized Coefficients without Speed
Variables, Accident Type: All and Rear End“ -- - - - -- . ----------------

 

After Period Raised and Lowered Effective Means without Speed
Variables vs After Period Raised and Lowered Non-Effective

Means without Speed Variables, Accident Type: All and Rear
End ........................... .............. - -

 

Listing of Speed Limit Raised Effective Zones .....................................

Before Period Raised Variable Identification ....... - .....

 

Before Period Raised Variable Identification Coded and
Direct Variables ..........................................................................................

Before Period Effective All and Rear End Comparison of
Measures of Effectiveness: All Accidents - -- - -

 

Before Period Raised Effective All and Rear End Variable
Correlations with respective Discriminant Functions, All
Accidents ......................................................................................................

Mean Values of the Variables in the Before Period Raised
Effective All and Rear End vs Before Period Raised Non-Effective
All and Rear End, All Accidents -------- - --------------- -

 

Before Period Raised Effective All--All Accidents Comparison
Coefficient Sign and the Magnitude of the Effective and Non-
Effective Means - - --------------- - - . .............

 

xvi

102

106

108

109

112

113

5.8

5.9

5.10

5.11

5.12

5.13

5.14

5.15

6.1

6.2

6.3

Before Period Raised Effective Rear End--All Accidents
Comparison of Coefficient Sign and the Magnitude of the
Effective and Non-Effective Means

 

Before Period Effective All and Rear Comparison of Measures of
Effectiveness, Rear End Accidents -

 

Before Period Effective All and Rear End Variable Correlations
with respective Discriminant Functions, Rear End Accidents ...........

Before Period Raised Effective All and Rear End vs Before
Period Raised Non-Effective All and Rear End, Rear End
Accidents ......... -

 

Before Period Raised Effective All--Rear End Accident Select
Comparison of Coefficient Sign and the Magnitude of the
Effective and Non-Effective Means ........................................................

Before Period Raised Effective Rear--Rear End Accident
Comparison of Coefficient Sign and the Magnitude of the
Effective and Non-Effective Means - - -

 

Comparison of the After Period Means with Before Period Means
of Location Sensitive Variables in Discriminant Analysis, Effective
All Data Set--All Accidents ------------------------------------------

 

Comparison of the After Period Means with Before Period Means
of Location Sensitive Variables in Discriminant Analysis, Effective
All Data Set--Rear End Accidents --------- -- - - ------

 

Listing of Speed Limit Raised Effective Zones .....................................

Before Period Lowered Variable Identification ...................................

Before Period Effective A11 Comparison of Measures of
Effectiveness: All Accidents - -- - ............... .

 

xvii

119

121

123

125

127

128

131

132

134

136

138

6.4

6.5

6.6

6.7

6.8

6.9

6.10

6.11

6.12

Before Period Lowered Effective All Structure Coefficients and
Standardized Coefficients - ---------- 139

 

Mean Values of the Variables in the Before Period Lowered
Effective All vs Before Period Lowered Non-Effective
--All Accidents ............................................................................................. 139

Before Period Lowered Effective All--All Accidents Comparison
of Coefficient Sign and the Magnitude of the Effective vs Non-
Effective Means .... - - - -- --------- -- ......... 143

 

Before Period Effective All Comparison of Measures of
Effectiveness: Rear End Accident Type Selection ................................ 145

Before Period Lowered Effective All Structure Coefficients and
Standardized Coefficients: Rear End Accidents ................................... 146

Before Period Lowered Effective All vs before Period Lowered
Non-Effective--Rear End Accidents ........................................................ 147

Before Period Lowered Effective All--Rear End Accident
Selected Comparison of Coefficient Signs and the Magnitude of
the Effective and N on-Effective Means .................................................. 147

Comparison of the After Period Means with Before Period Means
of Location Sensitive Variables in Discriminant Analysis,
Effective All Data Set--All Accidents ..................................................... 152

Comparison of the After Period Means with Before Period Means
of Location Sensitive Variables in Discriminant Analysis,
Effective All Data Set--Rear End Accidents .......................................... 154

xviii

LIST OF FIGURES

FIGURE Page

1. Accident Involvement Rate by Deviation from Average Speed .......... 3

. Percentage of Rear End and Angle Involvements Day vs. Night
with Travel Speed ............................................................................................ 6

. Percentage of Single Vehicle Involvements Day vs. Night
with Travel Speed ............................................................................................ 7

. Variation of Accident Type with Speed ...................................................... 9

. Number of Intersections Per Mile on Two Lane Highways
Related to Type Of Collision .......................................................................... 15

. Percentage of Error of Final Speed as a Function of
Initial Speed, R < 1 ........................................................................................... 18

. Percentage Error of Final Speed as a Function of
Initial Speed, R >1 ............................................................................................ 18

xix

Chapter 1

Introduction

1.1 Speed and Safety

The relationship between speed and safety is characterized by the physics of
vehicles in motion. Transportation Research Board Special Report 204 [1984]
identified the following four reasons why reduced speeds are likely to yield safer
driving:

1. When traveling at a higher Speed, a car moves a greater distance
during the fixed period of time that it takes for the driver to react to a
perceived problem;

2. On highways lacking adequate superelevation, a driver's ability to steer
safely around curves diminishes with speed;

3. The distance required to stop a vehicle by braking increases with speed;
and,

4. Crash severity increases disproportionately with speed at impact.

Another factor in the speed-safety relationship is that concerning variation in
speeds on the same highway segment. AS reported by Solomon [1964] and
Cirillo [1968] a wider variability in Speeds increases the frequency of motorists
passing one another which, in turn, increases the opportunities for multi-vehicle

accidents to occur.

The authors of TRB 204 [1984] in discussing this topic add "speed variability
contributes to the front-to-rear accidents prevalent on Interstate highways. These
accidents are most common near intersections as motorists who Slow down and

change lanes to exit mix with motorists traveling at much higher speeds."

This relationship was also illustrated in West and Dunn's [1971] study. West and
Dunn's data consisted primarily of rural two lane highway segments. Their
study was able to identify the exact Speed of travel for a large proportion of
vehicles involved in accidents on the study segments. This is in contrast to police
traffic investigators who estimate speed data from Skidmarks and eyewitnesses
to the accident. The ability to accurately pinpoint the travel speed of at least one
of the vehicles as reported by West and Dunn [1971] just prior to the accident has
provided the most accurate portrayal of the accident involvement rate by the

deviation from average Speed . Figure 1 illustrates these findings.

 

100

 

  

 

 

W

 

    

 

 

 

   

R

< 15.5 -15.5

 

Involvement Rate per Million Vehicle Mlles

15.5 >15.5

Speed deviation in miles per hour

Figure 1. Accident Involvement Rate by Deviation from
Average Speed

Source: West and Dunn [1971]

A key finding of West and Dunn [1971] was that slow drivers had higher
accident involvement rates than fast drivers. Warren in a FHWA [1982] report on
West and Dunn's findings, indicates when turning accidents were excluded the
involvement rates for high and low speed drivers were very close and
approximately six times higher than those of drivers close to the mean traffic
speed. Warren explained the difference by noting the fact that cars stopping to
turn or enter a road are naturally going to be deviating significantly from the

mean traffic speed.

However it is not only vehicles stopping to turn that deviate from the average
speed as documented in research conducted by CC. Denton [1967]. His

experiment on drivers directed to attain a series of pre-determined speeds

l

 

4
without use of a Speedometer yielded results of substantial over and

underestimation. DentonS' prior research on drivers use of a speedometer to
monitor and control their Speed indicated that drivers did not use the
speedometer but evaluated their speed via sensory motion. His 1967 study

concluded their ability to accurately select a speed by this technique was limited.

In summary, the relationship between Speed and safety is one characterized by
the physics of vehicles in motion. The speed at which it is safest for drivers to
travel is within approximately (i) one standard deviation of the mean travel
speed of the traffic stream. Low speed and high Speed drivers are the most
likely to become involved in accidents. The faster the speed of vehicles involved

in accidents the greater is the likelihood of injury.

1.2 Speed and Accident Types

The relationship of speed to accidents by type is documented by Solomon's
[1964] work. Using data from his study, figures 2, 3, and 4 represent his
findings. Essentially, at low speeds the predominant accident types are rear end
and angle. Figure 2 illustrates the similar trend in day and night occurrences of

rear end and angle involvements as travel speed increases.

The overall pattern for rear end involvements is a high proportion of
involvements at low Speeds declining as Speed increases. Rear end accidents as a
percentage of total accidents range between 50% and 40% at speeds less than 22
mph up to 47 mph for both day and night occurrences. From 48 mph to 72 mph
rear end accidents decline as a percentage of total accidents in both day and night

to Slightly above 20%. This trend indicates that rear end accidents as observed in

5
this study are related to Speed, however in a less significant manner as Speed

increases above 42 mph.

The substantially higher rear end involvements at low to moderate speeds are
explained by Solomon in comparing the speed difference between the normal
travel speed between pairs of vehicles and that of the two colliding vehicles.
Solomon [1964] states "In summary, passenger car drivers involved in rear end
collisions were more likely to have been traveling at a Speed difference much
greater than that for pairs of vehicles in normal traffic." Beatty [1972] studying
similar mainline highway segments categorized as urban and rural locations
found that 84 percent of two-vehicle accidents were reported as rear-end
collisions or same-direction sideswipe. Beatty [1972] found that "40 percent of
the two-vehicle accidents were in urban areas and only 27 percent of Single-
vehicle accidents occurred in these same areas. This would certainly imply the
congested traffic conditions more typical of the urban areas." Beatty also
confirmed Solomon's findings of speed difference and accident involvement.
Beatty [1972] found "speed differences for two vehicles involved in an accident is,
on the average 11.4 mph greater than for two randomly selected vehicles. The
magnitude of the excess is almost twice the standard error even for single

observations."

    
 

._»;---.._‘_' ,-,. —--------------
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"- .\'~T\‘\.‘, '.'.
I ...«‘ ._._I ._...

.-.\;\'-_-.
- 2::-

' '.'. . 4"I’ ."' ...........................

Percentage
of Accident-
Involvements
N
o
I
I
I
l
I
I
I
I
I
i
I
l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
l

 

 

STAN <22 22- 33- 38- 43- >73
DING 32 37 42 47

Travel Speed, MPH

Figure 2. Percentage of Rear End and Angle Involvements
Day vs. Night with Travel Speed

 

“'3' REAR END-DAY “" REAR END-NIGHT ”A“ ANGLE-DAY ”I“ ANGLE-NIGHT

 

 

 

Source : D. Solomon [1964]

Angle accident involvements peak at a travel speed of less than 22 mph at about
38 percent for day and 33 percent for night. Angle accidents for both day and
night range from 16% to 7%(day) to 14% to 4%(night) for the remainder of the
speed categories. This leads to the conclusion that angle accidents as a
percentage of total accident involvements are not related to increasing speed.
Solomon's data indicates that at low Speeds (5—25 mph) angle accidents are a
significant share of accident involvements. Solomon points out "This is the Speed
of many vehicles at crossroads, driveways, and other points of access. However,
the study sections were selected so that crossroads were at a minimum, and the
data shown are typical of main rural highways having little roadside
development. Main rural highways having considerable roadside development
or many more intersections would have a higher proportion of angle collisions

than shown here."

7
Figure 3 compares the same relationship of involvement for single vehicle

accidents (day and night) with travel speed. A Slightly increasing trend over the
speed range from 33 to 72 mph is Observed for daytime accident involvements.
The lower end of the Speed range for daytime occurrences constitutes a very low
percentage of accident involvements. The range greater than 73 mph Shows a

moderate increase over the Speed range of 33-72 mph.

35 ---------------------------------------------------------
3o i------~--

mxfl! .----.--------_._--

        

..._'--' """u-----------XB'P?‘J;¥T=°3:'_, x
. . mmxmxwxr‘swxmxmn , __ _ _ __ X

Percentage
0f Accident-
Involvements

I I I I I I I l
I I 1 I

33- 38- 43- 48- 53- 58- 63- >73

37 42 47 52 57 62 72
Travel Speed, MPH

Figure 3. Percentage of Single Vehicle Involvements Day vs.
Night with Travel Speed

 

“at: SINGLE VEHICLE-DAY =51!- SINGLE VEHICLE-NIGHT

 

 

 

Source : D. Solomon [1964]

The pattern is similar for night time occurrences with a higher percentage of
involvements in the standing Speed range. From less than 22 mph to 37 mph the
Clay and night percentage of occurrences are mirrored. Beyond 37 mph night
time occurrences are double the percentage in daytime over the speed range 38 to
52 mph. This disparity in accident involvements continues from 53 mph to 72
mph but at a reduced difference. At greater than 73 mph the night time

percentage dips Slightly below the daytime percentage accident involvement.

8
This data leads to the conclusion that night time single vehicle accident

involvements are more likely to occur at speeds in the range from 37 mph to 72
mph in comparison to daytime single vehicle accident involvements in the same
speed range. The rate of occurrence increases substantially between 38 and 52
mph, indicating a Speed range where these accidents are increasing relative to
daytime accident involvements of this type. This is in contrast to rear end and
angle accidents which are declining as Speed increases. This finding indicates a
positive relationship between night time single vehicle accidents and increasing

Speed over a defined Speed range.

Figure 4 derived from Solomon's data and re-compiled by Warren in a FHWA
[1982] report represents the change in daytime percentage of accident
involvements over various Speed ranges. The data provides evidence that rear
end and single vehicle accident types are related to Speed of travel at the time of
the accident. The percentage of accident involvements for rear ends decrease as
speed increases. However, the percentage of accident involvements for single

vehicle accidents increase as speed increases.

 
   
  

   
   
  

 

 

   

 

 

 

 

 

 
 
    
     

 

 

 

   

100 '
90_ "”4““ IIIIII ”Wm
V
80 ' F k 14\ngle l3 ‘
. 7 ’
a, 3 70 k A //ISiHead-Onl4
m *J c 60 ‘ 7 A — — __ __ _
s a =—
§ g g 40 - = E RearEn
a g fi = e—
20 ' — —
0 _ 5 17 Single Vehicle
<32

32-42 43-52 53-62 63-72 >73
Travel Speed, MPH
Figure 4. Variation of Accident Type with Speed

Source: D. Solomon [1 964]

The predominance of rear end accidents in certain speed ranges is explained by
Solomon [1964] as follows:
"Pairs of passenger-car drivers involved in two-car rear end
collisions were much more likely to be traveling at speed
differences greatly in excess of those observed for pairs of cars in
normal traffic. For example, fully one-third of accident-involved
pairs of drivers were traveling at speed differences of 30 mph or

more, compared to only 1 percent of pairs of cars in normal
traffic."

1 .3 Access Points and Roadside Development and Safety

The environmental conditions drivers face in navigating urban and rural
roadways produces conflicts, some of which are a direct result of the access
points available. The greater the intensity of access points the greater the

likelihood of accidents resulting from these conflicts.

10
1.3.1 Driveways

Studies by the National Safety Council [1970], Marks [1961], Michael and Petty
[1966], Box [1969], Box [1970], and Cribbins et al. [1967] indicate access points in
the form of driveways contribute to a high percentage of accidents in both urban

and rural settings.

Box [1970] conducted a study of driveway accidents in Skokie, Ill. by type of
maneuver and collision. His statistics Show that 58% of the total involve entering
vehicles and 70% involve left turns. Of those involving entering vehicles rear
ends were 65% of the accident type. Of those involving left turns, rear ends were

37%, right-angles were 34%, and head-on were 21%.

Glennon and Azzeh [1976] describe four types of accidents which they indicate
are hard to identify and they believe are underrepresented in most if not all

accident statistics concerning driveways:

(1) The rear end accident which happens upstream from the driveway
because Of a vehicle Slowing down to enter the driveway;

(2) The sideswipe accident caused by vehicles changing lanes behind a
vehicle preparing to enter a driveway;

(3) The rear end accident that happens downstream from the driveway
involving a vehicle from the driveway that has not yet gained enough
Speed; and

(4) Collisions involving two vehicles using closely Spaced adjacent
driveways and collisions of driveway vehicles with intersection
vehicles when the driveway is close to the intersection.

Glennon and Azzeh [1976] report that the most critical factor relevant to
driveway accidents is relative Speed. ”Large Speed differentials between through

vehicles and maneuvering driveway vehicles create traffic inefficiency and its by-

11
product, increased accident potential.” Stover et a1. [1970] in their study found a

distinct relation between driveway entrance speed and the efficiency and safety
of driveway operations. They found that as driveway entrance Speed increased
from 2 mph-10 mph the traffic interference falls off rapidly. For the increase
from 10 mph-15 mph some additional reduction is realized, but for higher

entrance Speeds, the additional change is small.

Glennon and Azzeh [1976] argue that for rural roadways and some urban
roadways entrance speeds of 15 mph may be too low. Referring to Solomon
[1964] they point to the "strong correlation between the involvement rate for
two-car rear end collisions and Speed difference for main rural highways. His
findings indicate that for minimizing rear end collisions, a differential of less

than 10 mph between through speed and driveway speed is desirable."

Stover et al. [1970] reports that " the kind and amount of medial and marginal
access control bear heavily on the kind and amount of roadside development. In
addition, the kind and amount of roadside development determine the kind and
amount of vehicle traffic entering the traffic stream at any particular access point.
The number of access points and the traffic entering the traffic stream at these
points determines, in some measure, the over-all accident rate for any particular

length of highway."

Kipp [1952] in his Minnesota study found no significant difference in accident
rates for road sections having no access points and those having access points
serving non-commercial purposes. Stover et al. [1970] summarized these
findings as "this would seem to indicate that access points which are used

relatively infrequently do not make a major contribution to the accident potential

12
of a road section." The rate for sections with access points serving commercial

activities was twice as great as the rates in the other two categories (no access
points and non-commercial access points). When road sections were analyzed by
traffic volume groups, correlation was found between the number of access
points per mile and the accident rate. Road sections with commercial activities
on abutting lands had relatively high accident rates. The rate for these sections
was between two and three times the rate found on sections having no
commercial development and nearly four times as great as the rate for strictly

rural sections With few intersections.

Major and Buckley [1962] in their study of access point spacing along an arterial
stream of traffic considered the problem from the abutting property viewpoint in
evaluating arrangements to provide for minimum delay to and maximum
capacity for entering traffic. In their study they found " a multiplicity of
driveways or access points at close intervals produced undue conflict with the
arterial and mutual conflict with each other, resulting in lower capacity and

increased delays for traffic from abutting property entering the highway."

1.3.2 Intersections

Peterson and Michael [1965] in their Indiana study report that intersection

accidents per 100 million vehicle-miles increased when:

(1) Percent green time on the bypass decreased

(2) Bypass or cross-street ADT increased

(3) Percent left turns from the bypass increased

(4) Maximum approach Speed increased

(5) Number of intersection approaches increased

(6) Total Width of driveways within 200 ft. of the intersection increased.

13
In their same study they found that for non-intersection study sections, accidents

per 100 million vehicle-miles increased when:

(1) Total number of establishments per mile increased

(2) Total number of driveways per mile increased

(3) Total number of low volume intersections per mile increased
(4) Geometric modulus increased

(5) ADT increased

(6) Operating Speed increased

(7) Total width of driveways per mile increased

(8) Length of intersection turning lanes in the section increased

1.3.3 Medians

Cribbins [1967] study in North Carolina of median openings, accidents and
roadside development found that "as traffic volumes increase, use of median
openings rapidly become more hazardous. "When combined with intensive
roadside development, use of median openings under high-volume conditions
becomes more hazardous. Signalization of median openings does not necessarily
reduce the hazard Of using openings under high-volume conditions; rather, it
tends to make the traffic flow in a more orderly way by offering a more equitable
time distribution for movements. Also as roadside development increases and
crossovers of any type are permitted, accidents will increase." With regard to
speed limit reduction, high volumes and roadside development the authors state:
" the mere reduction in Speed limit, when volumes are high and roadside
development is intense, does not suffice to keep the accident rate at a low level.
The increased hazards associated with turning movements under high volume

conditions far exceed the benefits occasioned by reducing the speed limit."

14
Safety on a road is determined largely by freedom of interference with the free

flow of traffic. Therefore highways with full access control are expected to have
the lowest rate of accidents with partial and unlimited access being higher.
Mulinazzi and Michael [1967] verified this in their study. They found " accident
rates are lowest for highways with full access control and highest for no access
control. On the other hand, the number of fatalities was highest under partial

access control."

Essentially, the conclusions are that there is a strong relationship between
roadside development and access points for accidents in general and accidents
by type. Faithful [1959] has found a "definite correlation between accidents and
ribbon development." Flaherty [1959] found a similar result in his Minnesota
study between lineal feet of highway oriented uses and traffic volume. His

analysis showed a correlation coefficient of .81.

Solomon [1964] presented data in a table format indicating type of accident
involvement by day and night related to number of intersections per mile. This
same data is presented here as Figure 5. Rear end accidents occurring during
day and night indicate a trend of increasing frequency as the density of access
increases. This relationship iS also documented for angle accidents, with those
occurring in the day showing the sharpest rate of increase as access density
intensifies. Access points provide increased opportunity for variability in the
speeds of vehicles in the form of entry and exit as well as crossing the traffic
stream. The distance traveled when traveling at a higher speed and the distance
required for braking increases with Speed. The frequency of access points, the

volume of traffic served by a variety of access points, and the

15
acceleration / deceleration of through and merging traffic creates situations where

constant evaluation of Speed and distance are required by the driver.

 

 

 

 

 

 

 

 

a 50 --""""""----------—-—-----.--
5 “‘— 3 '0' REAR END-DAY
'U
‘8 .9
S 5 "" REAR END-NIGHT
w E
O I»
u '2‘ "'3" ANGLE-DAY
°° o
.8 >
5 ’5 "" ANGLE-NIGHT
t
a. 0 . : 1 "°" HEAD-ON-DAY
0.0—0.9 1-1.9 > 2.0 _._
Number of Intersections Per Mile HEAD ON NIGHT

 

 

 

Figure 5. Number of Intersections Per Mile on Two Lane
Highways Related to Type Of Collision

Source : D. Solomon [1964]

1.4 Driver Judgment

The prevalence of certain accident types(i.e. rear ends, angles, sideswipes) can be
partially explained by known factors under which these involvements take place.
Conditions such as the type of maneuver, traffic control (or lack thereof), and

geometric conditions all provide meaningful clues to understanding the basis for

certain accident types.

What is harder to ascertain is the judgment of drivers immediately before the
accident. Seldom does a driver state the use of poor judgment to an investigating
officer, probably because of the trauma of the accident as well as financial

consequences if the driver is at fault. From a research perspective knowing the

16
behavior exhibited by the driver and an accurate travel Speed immediately prior

to the accident is very important. Headways maintained between vehicles
traveling in the same direction in the traffic stream provide one measurable
variable to understand vehicle behavior. This variable along with travel speed

provide the most direct measurements of driver judgment.

Police officers investigating an accident are required to take statements from both
parties involved. Where a fatality or serious injury has occurred, this is also
supplemented in many states with an on-scene accident investigation where
physical evidence such as skid marks, brake function, etc. are checked to
determine how the accident occurred. One of the questions routinely asked by
investigating officers to involved drivers is the speed they were traveling
immediately prior to the accident. This Speed can also be determined from skid
marks if they are present. In property-damage or minor injury accidents
evidence which would provide accurate information on the Speed of vehicles
involved in accidents is seldom collected. In most cases, the officer has to rely on
the speed estimated by one or both of the involved drivers. Under the
circumstances of stress and shock the accuracy of their statements concerning

travel Speed is questionable.

1.4.1 Driver Estimation of Speed of Travel

A more basic question is whether drivers can estimate their Speed of travel or
velocity in an automobile accurately. Denton [1965] in his research reports that
"drivers tend not to use the speedometer as an aid to driving when carrying out
maneuvers." Denton [1967] and Snider [1967] separately conducted experiments

on drivers to determine how accurately they could estimate their driving Speed.

17
Both experimenters used different approaches but arrived at the same

conclusion. Drivers tend to underestimate their travel Speed below 30-40 mph

and overestimate it above this same range.

Denton [1967] found that "in a driving situation Speed estimation by the driver is
affected by initial speed of the vehicle and by the extent and direction of speed
change." Denton found that in deceleration tests the initial speed (S) had little
effect on the ability to achieve a certain speed, but rather the change in speed (R)
was the dominant factor in achieving a desired final Speed. Denton tested
drivers required to decelerate to 1 / 4 to 1 /2 to I (retain initial speed) of their
initial Speed. The results indicate that drivers consistently drove faster than the
prescribed speed change requested in the test. Denton [1967] suggests the
implication on actual driving is the following : " drivers on a motorway traveling
at 80 mph and wishing to decelerate to exit at a speed of 20 mph, if judging
subjectively would enter the ramp at 48 mph believing the sensation to be that of
20 mph. In other words he has committed a positive error of judgment of 140%."
At 40 mph with a final speed objective of 20 mph Denton reported the error in

judgment is approximately 40%.

The results for acceleration (R> 1) in contrast to deceleration indicate subjective
error is significantly affected by both initial Speed (S) and change in Speed (R).
Denton states "the subjective error is seen to be significantly affected by both (S)
and (R), in such a way as to suggest that drivers accelerating from sliproads
(ramps ) onto the motorways will tend to think that they are traveling faster than

they really are."

18

Figure 6 and 7 represent a graphical representation of the relationship between
initial speed S, and change in speed R, for the deceleration and acceleration data

respectively expressed as percentage error in final speed.

  
  

140
120

1 00
Overestimation

Range
60 """"""'

4o 1

A

A__.'____ ...:‘.!".-.:-.-.-.--—I

R < I = Decelergtion

80 III—.---—---——.--——.—-—--_--_.-___.____-_-__-.....

.--.----.:---.----.-.

A

 

Percentage Error
of Final Speed

 

 

“1.- ——-x.\
20 II— - ——-—-——--—----—----——----—--—-——-————-—-
o I I I I

 

20 30 4O 50
Initial Speed, mile / h

60

 

 

"' R=I /4

'fi' R=1/2

 

 

Figure 6. Percentage Error of Final Speed as a Function of

Initial Speed, R< 1
Source : G.G. Denton [I 967]

30 -----------------------------------------

20 Overestimation-----_-_-.--_---_--.-_-

o .

“A

Percentage Error
of final Speed
8

-20 ---—----------.---------. .-----_-_._-_
_3o -—.--—- l.-..........................._.____.__
-40 --.--_-._- -._-_-.---- --_-...-..-.--_-.---

-50 -- - - - -- - - ' "ufide'réétumatibfi'fl'a'nse
'60 : 1L5 .0 2.5
5 10 Initial Speed 8, (mileih)

Figure 7. Percentage Error of Final Speed as a Function of

Initial Speed, R > 1

Source : G.G. Denton [I 967]

R > 1 = Acceleration

 

"' R=I
'9' R=2

Q" R=4

 

 

 

19
1.5 Human Factors

The driving task is a combination of interactions between humans, vehicles, and
the roadway. Auditory, visual and perceptual cues are used by drivers to assist
them in performing this task. The ability of drivers to see a change in distance in
a car-following Situation and apply the brakes to avoid a potential accident
involves the drivers ability to judge distance and maintain a safe headway as
well as sufficient brake reaction time. Colbourn et a1. [1984] conducted a study to
assess the headways drivers would choose to maintain a safe driving distance
between vehicles at three different Speeds: 30, 40, and 50 mph. Using three
different driver experience levels tested under (1) improbable conditions of
sudden deceleration and (2) highly probable conditions of deceleration, results
on a closed test track yielded values very close to the "two second rule of thum "
which generates a distance that enables drivers to detect and react to drastic
changes in the Speed of a lead vehicle in a car-following Situation. However,
Colbourn [1984] reports "kinematically the critical distance separating vehicles
varies with the square of the speed. As a result, drivers will maintain headways
greater than necessary at low Speeds but will tend to follow too closely at higher
Speeds." Colbourn took his drivers through a third set of conditions which
focused on random unannounced panic stops to measure the length of headways
maintained before and after the stop. His findings were that "drivers used
headways which did allow them to stop safely behind the leading vehicle in an
emergency situation and with a respectable margin." Colbourn reflected on these
findings in regard to the real-world Situation drivers find themselves in by
stating:

"On average, some 40% of the initial headway was lost during
rapid braking. These conditions were fairly extreme in terms of

20

severity of braking and optimal in terms of vehicle performance
and road surfaces. Also the task was much Simpler than that
required on the road; subjects being fully aware of what would
happen. Hence, it may not be surprising that performance was
good. On the road there is a wealth of other information to
process and reaction times will inevitably not be as fast as in a
simple Situation used experimentally.

Thus, while it was observed here that drivers seemed to be
using adequate headways in order to stop in an emergency
situation, that situation was perhaps unrepresentative of
highway driving conditions."

Being fully aware of the anticipated action was felt to have biased these results
regarding maintenance of headways and headway choice in an experimental
situation. One other impact of the anticipation effect was the measurement of
brake reaction times. The range in the Colbourn [1984] data was .5 to 1.5
seconds. Using a correction factor developed by Johanssen and Rumar [1971] to
estimate reaction times to an unexpected compared with an anticipated demand
the corrected median reaction time was 0.9 seconds. Colbourn [1984] comments
"again the Situation considered was simple reaction, which is often radically

different from that occurring on the road."

Colbourn [1984] concludes that "these findings suggest that under Optimal
conditions at least, and irrespective of their traffic experience, drivers can judge
safe distances for vehicle following without perceptual-motor support devices.
However, it is clear that such performance will rapidly deteriorate under

conditions of poor visibility, bad weather, etc."

Probst et a1. [1984] in his work on perceived self-motion and impairment of
vehicular guidance also tested drivers brake reaction times. In an experiment

involving vehicle following at different distances and Speed while trying to

21
maintain a constant gap he found that "reaction times were extremely Slow,

almost two seconds for a gap of 40 meters when the cars were traveling at 70
kilometers per hour." Using this data and other data from laboratory Simulations
Probst [1984] argues that additional reaction time over and above the normal
reaction time range of .6 seconds to 1.0 seconds is needed in driving Situations in
the real world. Probst recommends that an additional .3 seconds be added
because of the difficulty of determining the perception of motion while moving.
In addition, .25 seconds if one is not already viewing the object and .15 seconds if
ones' glance overshoots the object. Adding these values to the normal range
leads to 1.30 seconds to 1.70 seconds for brake reaction times if all conditions are
present. The upper value is approximately equal to values determined by

Colbourn [1984].

Sivak [1982] conducted an experiment on drivers brake reaction times similar to
Colbourn [1984], however with a data set of 1,644 data points. Taoka [1989] in
estimating the statistical distribution of the Sivak [1982] data set postulates that
"the measured reaction times published by Sivak and colleagues probably more
closely estimates the true brake reaction time distribution of drivers than do the
other three investigations. A car-following driver has less of an opportunity to
anticipate the actions of the car ahead than a driver approaching a green signal at
an intersection has in anticipating when the Signal will turn to yellow." The 50th
percentile (median) brake reaction time estimated by Taoka [1989] from Sivak
[1982] is 1.07 seconds, 85th percentile is 1.78 seconds and 95th percentile is 2.40

seconds.

Data from Colbourn [1984] under optimal conditions suggest a brake reaction

time between 1.8 and 2.0 seconds. Probst [1984] suggests a brake reaction time in

22
the real world of 1.30 to 1.70 seconds. Taoka [1989] using data from Sivak [1982]

suggests a brake reaction time of 1.78 seconds. All of these values provide an
adequate safety cushion if drivers observe a two second headway rule of thumb
if traveling at low to moderate speeds. In Colbourn [1984] the following is

addressed to this "critical distance" :

However, kinematically the critical distance separating vehicles
varies with the square of the speed. AS a result, drivers will
maintain headways greater than necessary at low Speeds but
will tend to follow too closely at higher Speeds.

Rockwell's [1972] field studies showed that normal car-
following results in a separation of 3—4 seconds between
vehicles; 6 seconds was considered by most drivers to be
appropriate for open-road driving. Minimum safe separations
averaged 1-2 seconds, and headways preparatory to overtaking
was about .5-1.0 seconds. British observational studies by
Harms [1966] have shown that the percentage of vehicles close
following (separations of less than 1 second) increases linearly
with increasing traffic flow; from 5% at 150 vehicles per hour, to
25% at 1000 vehicles per hour.

Therefore if these observations and studies are correct it iS possible to suggest
that in general, under fairly optimal conditions most people drive at a reasonably
safe distance in car-following situations. However, under increasing traffic
density, poor visibility, or weather conditions, the Optimal conditions under
which drivers detect speed and distance changes is altered, and therefore place

themselves at increased risk of accident involvement.

1.6 Methods of Controlling Speed

Methods for controlling Speeds of drivers are achieved through three different

means, design Speed, speed laws, and Speed limits. Design Speed is a speed

23
selected for a functional class of streets and roads to control the geometric design

of the facility for basic safe operation. Speed laws are the legal definitions of
laws regarding the type of speed limit which is implemented in a jurisdiction.
While speed limits are the posted vehicle Speeds determined through an

engineering study of existing conditions and accident rates.

1.6.1 Design Speed

Design Speed as defined by the American Association of State Highway and
Transportation Officials (AASHTO) [1984] is "the maximum safe speed that can
be maintained over a specified section of highway when conditions are so

favorable that the design features of the highway govern."

Relative to arterial streets AASHTO states :

"On arterial streets the design Speed control applies to a lesser degree
than on other high type highways. On rural highways or on high-type
urban facilities, a certain percentage of vehicles are able to travel at or near
the safe Speed determined by geometric design elements, but on arterial
streets the top speeds for several hours of the day are limited or regulated
to that at which the recurring peak volume can be handled. Speeds are
governed by the presence of other vehicles traveling en masse both in and
across the through lanes and by traffic control devices rather than the
physical characteristics of the street. During periods of low-to-moderate
volume, speeds are governed by such factors as Speed limits, midblock
frictions, and intersectional frictions."

AASHTO [1984] recommends that arterial streets "be designed and regulated by
control devices, where feasible, to permit running speeds of 20 to 45 mph." The
lower range for local and collector streets through residential areas and the
higher Speeds for high-type arterials in outlying suburbs. Recognizing the

transition from urban to suburban areas, AASHTO recommends the adoption of

24
some form of speed zoning or control to prevent hazards associated with high

speeds. The AASHTO basis is stated as follows: "although through traffic
should be expedited to the extent feasible, it may be equally important to

establish a ceiling speed to reduce hazard and serve local traffic."

1.6.2 Speed Laws

Speed control is implemented through three basic types of speed laws. The

following are definitions from a FHW A [1985] report on speed zoning practices:

0 Basic Speed Rule--specifies that regardless of any other Speed limit that

may be applicable at the time and place, the driver shall operate at a Speed
that is reasonable and prudent for existing conditions, taking into account

actual and potential hazards encountered.

"g, Prima Facie LimitS--any vehicles speed in excess of the established
numerical limit is prima facie evidence that the driver is not operating at a
reasonable and prudent speed. The law permits the driver the right to
provide proof that the speed was not improper under existing conditions.
Prima facie limits recognize the fact that no Specific speed is particularly
safe or unsafe at all times.

0 Absolute limits--Absolute or fixed speed limits are always illegal to
exceed regardless of whether the driver's speed was safe or reasonable
and prudent for conditiOns.

The State of Michigan and many of it's municipalities use Prima Facie and
Absolute Limits as the speed laws under which to govern vehicle Speeds on
designated sections of the road and street network. Based on these laws traffic
engineers are required to perform an engineering study to determine the

numerical Speed limit that will apply to the road segment in question.

25

1.6.3 Speed Limits

Traffic engineers during the period from 1950-1970 gradually refined techniques
utilized to determine a safe and reasonable Speed limit (often in conjunction with
police enforcement agencies) for motorists to travel on local, state and federal
roadways. These techniques consist of measurements of traffic characteristics,
land use, speed, and geometric factors existing at the time of the traffic
engineering study. Their application and practice is oriented to the setting of

Speed limits in speed zones as opposed to speed limits on limited access facilities.

Accident frequency, severity, and accident type are the measures by which the
safety of a roadway is determined. Accident statistics often serve as the variable
of interest when a change is applied to a roadway (such as speed limits,
Signalization, or geometrics). Usually a "before and after" analysis is performed
if other influencing variables such as traffic volume, land use characteristics, or

construction have not independently altered the traffic characteristics of interest.

State and local transportation officials and the traffic engineering profession have
practiced two Similar procedures in determining a speed limit in a Speed zone.
The primary basis for both is the 85th percentile speed Obtained in a spot speed
sample. The major difference is to use "engineering judgment" to recognize and
include other environmental and geometric factors ostensibly to reduce the limit
below the 85th percentile speed if deemed necessary. In contrast, a small number
of states and municipalities have adopted a policy which replaces engineering
judgment with some form of quantification of environmental and geometric

variables to reduce the speed limit below the 85th percentile speed.

26

A debate in the traffic engineering profession is underway fueled by recent state
and federal research which seeks to determine which of the two policies of speed

zoning leads to a safer driving environment for motorists.
1.7 85th Percentile Speed

Throughout the literature on speed zoning there is varied discussion as to which
factors should be utilized in determining speed limits in speed zones. Carter
[1949] may have been the first to suggest the value between the 80th and 90th
percentile of the free-flowing speed plotted on a cumulative frequency curve.

Matson, Smith and Hurd [1955] in their traffic engineering book state:

"For any given road there is an optimum speed limit which will have the
greatest effect on spot Speed. This value is usually between the 80 and 90
percentile of the free-flowing speed as plotted on a cumulative frequency
curve."

Johnston [1956] also suggested the 85th percentile. Baerwald [1957], Kessler
[1959], andevery [1960]; provided additional support for the 85th percentile as
the primary value to be used in setting speed limits. Kessler stated the
justification as follows: "The 85th percentile speed is based upon the theory that
the majority of motorists traveling upon a city street or highway are competent
drivers and possess the ability to determine and judge the speed at which they
may operate safely; further, that motorists are responsible and prudent persons
who do not want to become involved in an accident and desire to reach their

destinations in the shortest possible time."

27
In 1961, the Institute of Transportation Engineers Technical Committee 3-C

published an article on "a valid statement of speed zoning principles and of the
factors to be recognized in their application." The article "An Informational
Report on Speed Zoning" suggests that speed limits should be based on
prevailing vehicle speeds, physical features, accident experience, and traffic

characteristics and control.

The institutionalization of the 85th percentile Speed as the primary factor in the
setting of Speed limits in a speed zone was undertaken in 1969 by "Resolution of
the Annual Meeting of the American Association of State Highway Officials"

which states:

"The review of existing practice revealed that most of the member
departments use, primarily, the 85th percentile Speed. Some agencies use
the 90th percentile Speed, and of secondary consideration are such factors
as design speed, geometric characteristics, accident experience, test run
speed, pace, traffic volumes, development along the roadway, frequency
of intersections, etc."

"On the basis of the foregoing review, the Subcommittee on Speed Zoning
recommends to the AASHO Operating Committee on Traffic for
consideration as an AASHO Policy on Speed Zoning that:

The 85th percentile Speed is to be given primary consideration in Speed
zones below 50 miles per hour, and the 90th percentile speed is to be given
primary consideration in establishing speed zones of 50 miles per hour or
above. To achieve the optimum in safety, it is desirable to secure a Speed
distribution with a skewness index approaching unity."

Further support of the 85th percentile criterion was provided by Research

Triangle Institute [1969] stating:

"The standard deviation of the Speed distribution is from 5 to 7 mph.
Approximately 85% of the drivers drive below the mean plus one
standard deviation. The drivers having speeds between the mean and one
standard deviation above the mean are definitely in a low involvement

28

group. The region between one and two standard deviations above the
mean Speed encompasses approximately 10 percent of the drivers and
does not have a Significantly greater involvement rate than at mean Speed.
This region from the end of the first to the end of the second standard
deviation is approximately the tolerance level allowed by police agencies."

Thus the 85th percentile Speed is seen to be within one to two standard
deviations of the mean speed which was found by Solomon [1964] and Cirillo

[1968] to be the point at which there was the lowest accident involvement rates.

1.8 Evaluations of Speed Zone Effectiveness

A survey of highway officials on Speed zoning practices was conducted in 1984
by the AASHTO Task Force on Speed Zoning and Control. ItS' results along with
a literature review were included in a report by Parker [1985]. The majority of
respondents (82%) identified the highest priority research area as "determine the
effects of altering the speed limits on Speed and accidents." Kessler [1959] in his
evaluation of 30 locations where speed limits were raised found the 85th
percentile Speeds unchanged, however, accidents decreased from 62 to 40.
Parker [1992a] reports that Wenger [1960] examined accident experience at 25
locations in St. Paul, Minnesota and found that raising speed limits from 30 to 35
or 40 mph adversely affected accidents. Avery [1960] examined speed
compliance in the same city at 18 locations where Speed limits were raised from
30 to 35 or 40 mph and found no change in mean speed or 85th percentile speed.
Dudek and Ullman [1987] examined Six sites in rapidly developing urban fringe
areas where speed limits previously posted at 55 mph were reduced to 45 mph.
This change was not in accordance with prevailing 85th percentile speeds. They

found no significant changes in Speeds, speed distribution, or accident rates.

29
Parker [1992a] using 99 experimental and comparison Sites in 22 states found

where Speed limits were raised accidents were reduced by 6.7 percent after
implementation. Sites where speed limits were lowered, accidents increased by
5.4 percent. In both cases the change in accidents was not statistically Significant.
Also, Parker [1992a] found little change in the speed distribution as a result of
raising or lowering the speed limits on urban and rural nonlimited access

highways.

Parker [1992] in his study for the State of Michigan found that the 68 Sites where
speed limits changed, the overall reduction in accidents was 2.21 percent. He
noted that before and after speed data were not collected at the Michigan
experimental and comparison Sites. Consequently, the effects of the posted

speeds on driver behavior at the Michigan sites are not known.

1.9 Summary

The critical task of controlling the Speed of drivers in order to create a safe, yet
efficient surface transportation system iS found to be a mixture of policy, human
behavior, and the physics of vehicles in motion. Speed zoning is the procedure
utilized by traffic engineers to inform drivers of the required balance between

safety and speed of travel appropriate for functional classes of roads.

The literature review details the history of speed control, the apparent safe
operating Speeds, environmental conditions, as well as human decision-making

which leads to safe operation at various Speeds.

30
In summary, traffic Speed variation, traffic speed distributions, roadside friction,

and human behavior are found to be the primary factors in achieving effective
speed control. The objective of speed zoning is to understand and apply these
factors in a manner consistent with environmental conditions and driver
expectancies such that the overall safest driving environment can be achieved

with respect to the functional facility designated.

Michigan speed zoning procedure [1987, 1981] is based primarily on the 85th
percentile speed with consideration for accident experience. Operating
procedures agreed to in 1987 and prior draft procedures in 1981 confirm this
practice. With a lack of empirical evidence to support a relationship to a speed
limit change, the accident factor is relegated to subjective engineering judgment.
Therefore, the results for the sites in this study reflect the variability of

application of this factor in determining speed limits.

Parker [1992] in a study for the Michigan Department of Transportation (MDOT)
found that while department policy suggested posting limits within 5 mi / h of
the 85th percentile speed, due to political and community pressures and other
nonquantitative considerations, this guideline is often waived. It was found in
this study Speed limits posted at nearly 31 percent of the experimental Sites (21)
and 23 percent of the comparison Sites (20) were not within the 5 mi/ h guideline.
In nearly all [these] cases the limits were posted less than the 85th percentile

speed.

In the same report Parker investigated errors associated with Speed data
collection. At a small sample of Sites where data collected by the state was

compared with automated equipment, he found the MDOT estimate of the 85th

31
percentile speed is approximately 3 mi / h less than the speeds recorded by the

automated equipment.

The errors found in speed data collection by the MDOT along with a significant
lack of adherence to the suggested guidelines suggest that a number of Sites have
artificially low Speed limits, which when compared to sites where this is not the
case, the accident experience may be aberrant in comparison to Similar Signed

ZOIIGS.

Also, since typically little to no understanding of the empirically proven
relationship demonstrated by Taylor [1965, 1965a] between speed distribution
parameters such as skewness and accidents is employed in their Speed zoning
procedures, an opportunity is overlooked for setting consistent safe speed zone

limits.

The results of the research conducted in Speed zoning effectiveness indicate the
results are mixed in regards to the relationship between setting Speed limits at
the 85th percentile Speed and accident improvement. The purpose of this
research is to identify additional factors involved and clarify their relationship to
raising or lowering the Speed limit based on generally accepted traffic

engineering principles.
1.10 Statement of the Problem
In a 1985 Federal Highway Administration survey of state and local

transportation officials four factors received the highest frequency response as

part of their speed zoning procedure. In descending order they are : 85th

32
percentile Speed, accidents and pace speed tied for second, type and amount of

roadside development was fourth. These four factors are measurable in
quantitative units and are utilized by a number of states as part of a procedure to

adjust the speed limit.

The problem is that where states have procedures which quantify and use
roadside development variables the empirical basis for their inclusion or
exclusion has not been validated. Furthermore, the type and level of adjustment
of a variable in a procedure has not been substantiated as appropriate or

meaningful.

Along with these limitations in the speed zoning procedure is the fact that traffic
engineers have no way of predicting if their Speed zoning actions will result in
better compliance to speed limits and most importantly, make the driving
environment safer resulting in a reduction in accidents. AS a result, analyses of

Speed zones have Shown mixed results.

In the Parker [1992] study of Speed zones in Michigan he reported that 46 of the
zones resulted in an increase in accidents while 19 resulted in a decrease. Taylor
and Coleman [1988] report similar results for a study of Speed zones in
Muskegon County, Michigan. They found that 16 Sites exhibited an increase in
accidents following implementation of a speed limit, while 16 exhibited a

reduction in accidents.

33
1.10.1 Statement of the Hypothesis

The hypotheses iS that a quantifiable relationship exists between accident
parameters, speed parameters, roadside friction, and environmental / geometric
variables such that it is possible to predict the effectiveness of Speed zoning in
urban areas. It is hypothesized that there exists specific variables which can

serve as predictors of effectiveness of proposed Speed zoning actions.

CHAPTER 2

Methodology

2.1 Introduction

The literature review illuminated a number of factors that might be used to
determine if Speed zoning will be effective. In general, these were prior
accidents, geometric and environmental conditions, Speed parameters, and

driver behavior.

The premise of this analysis is that it is possible to discriminate between effective
speed zones and non-effective Speed zones based on an accident analysis, by

identifying the significant variables and characteristics of these road segments.

2.2 Site Selection

Several data bases were accessed to build the files used to conduct this analysis.
MDOT staff provided a combined accident / geometric file for each Speed zone
for each year pre and post Speed zoning action for all candidate Sites. Candidate
Sites were selected based on an implemented Traffic Control Order (TCO)

and/ or a request for a Traffic Survey for an existing Speed zone. The inventory

of implemented zones was used to select candidate treatment (test) zones and the

34

35
non-implemented zones resulting from a no change in speed limits decision were

used to select control zones.

Zone matching of test and control zones for comparability was based on the
criteria of speed limits (prior to change), volume, laneage, type (i.e. urban or
transition to urban), and length. TCO maps for each speed zone were utilized

along with the aforementioned data bases to assist in this process.

2.3 File Building

The Specific technique to accomplish the merging of each accident in relation to
environmental and geometric data, as well as Speed data is to combine with each
accident the respective variables that describe those conditions at the Site of the
accident. This was accomplished by utilizing the Michigan Department of
Transportation (MDOT) Accident Master file for accidents, MDOT MIDAS 111
Road Segment file for geometric data, and MDOT Traffic Survey Request Speed
file. In addition, to supplement the level of detail proposed for this analysis and
capture conditions as close as possible to the time of accidents, the MDOT Photo-
Log file for each speed zone was utilized to build a coded land use, laneage,
driveway frequency, Signal, and other geometric/ environmental condition

inventory for each tenth of a mile segment.

Using the ADD and MATCH commands in Statistical Package for the Social
Sciences (SPSS) in each of the unique data sets, a record with accident, speed, and
geometric data for each tenth of a mile that contained an accident in a speed zone
was created. A Single record for each accident including all the variables from

each database is built. This created a new record which contained the accident

36
data, geometric data provided by MDOT and manually collected photo—log data,

and speed data. Spot Speed data from Speed data collection stations within each
zone were utilized and is assumed to be representative of speeds throughout the
segment in question. Typically MDOT chooses speed data stations free of

interference from traffic signals and where free-flow speeds could be obtained.

In most cases the names of variables utilized by MDOT were used directly in the
analysis. In some cases, names were Slightly altered due to length restrictions. In
order to utilize those variables which were qualitative as opposed to quantitative
in nature, the researcher created codes and labels to identify them. These types
of variables were identified as "coded" variables in the analysis and where
appropriate will be identified as such. Typically, they were associated with data
obtained from the photo-logs, such as land use types, laneage types, shoulder
types, fixed objects, etc.

2.4 Determination of Effective vs N on-Effective Speed Zones

The experimental design utilized to determine effective versus non-effective
Speed zones is Before and After with comparison groups. Utilizing this design,
the strength of findings and conclusions are improved if the comparison groups
are shown to be comparable on those variables of interest in the before period.
This analysis is performed on the accident variable Since safety, aS measured by

accidents, is the primary measure of effectiveness (MOE).

Prior to complete accident/ geometric/ speed individual record-building, an
analysis of the effectiveness of the Speed zones was undertaken. The procedure

involved converting accident frequencies to accidents per million vehicle miles

37
(acc/MVM) for each year pre and post zoning action for each test and control

zone. The year of the zoning action was excluded for both test and control zones.
Each zone then had an accident rate per year pre and post Speed zoning action
calculated. The test and control zones were then identified by Specific speed
zoning action with a code, indicating test Speed raised 5, test speed raised 10,
control speed raised 5, etc. This code also included reference to a time period,
before or after Speed limit change. Therefore, in each zone an analysis record for
each year pre and post Speed zoning action was built which included accident
rates. The groupings from the Speed zoning action resulted in 16 unique groups,
related to speed zoning action and time period. They are: Raised 10 Before,
Raised 10 After, Raised 10 Control Before, Raised 10 Control After, Raised 5
Before, Raised 5 After, Raised 5 Control Before, Raised 5 Control After, Lowered
10 Before, Lowered 10 After, Lowered 10 Control Before, Lowered 10 Control
After, Lowered 5 Before, Lowered 5 After, Lowered 5 Control Before, and

Lowered 5 Control After.

One way Analysis of Variance (ANOVA) was performed to determine if there
was a statistically Significant difference in the change in the mean accident rate
between the treatment groups and the control groups. If no difference is
detected, this indicates the treatment (i.e. speed zoning action) had no effect on
mean accident rates. The implication is that this Specific change in speed limits

had no effect on accident rate(S), and therefore did not improve safety.

Continuing the analysis of the Speed zoning groups, comparison (i.e. contrasts)
between two or more factor level means is conducted. The difference in mean
accident rate between before to after periods is compared between treatment and

control groups. The analysis determines if Specific Speed zoning actions have

38
resulted in a statistically Significant decrease in accident rates for treatment

groups relative to their matched control counterparts. The Single degree of
freedom test is performed to make this determination. A finding of no difference
(i.e. equality) indicates that the change in accident rates over time between
treatment and control groups iS not statistically different. This finding leads to
the conclusion that the treatment groups performed the same as their control
counterparts, and that accidents as a measure of safety was not improved by the

speed zoning action.

2.5 Individual Zone Effectiveness Leading to Effective and Non-Effective

Group Formation

The analysis of the effectiveness of speed zoning thus far has involved the overall
effectiveness of Speed zoning actions (ANOVA), and the effectiveness of specific
speed zoning actions (contrasts). AS a basis for determining if the individual
treatment zone compared to its’ matched control counterpart is effective in
reducing accidents, accident frequencies are compared. The percentage
reductions in accident frequency before to after for each treatment and control
zone are calculated and these values are used to determine if a statistically
Significant reduction has occurred utilizing the Poisson test for accident
reduction. The results of this analysis leads to identification of individual

effective and non-effective treatment zones.

Each treatment zone iS a specific Speed zoning action, and with the
determination of effective versus non-effective, the creation of specific groupings

by Speed zoning action is formed. These groupings by effective Speed zoning

39
action or non-effective speed zoning action forms the basis for the analysis

groups to be utilized in discriminant analysis.

Accident type in the form of all accidents and rear end accidents was also
conducted for each individual zone. This created two distinct data sets within
each speed zone action grouping-effective all by respective Speed zoning action

and effective rear by respective speed zoning action.

2.6 Discriminant Analysis

Discriminant analysis is a multivariate statistical procedure which analyzes
differences between mutually exclusive groups through linear relationships
between variables to create the largest orthogonal Space or distance between
groups. It is employed on the effective speed zoning action groups and non-
effective speed zoning action groups to determine how the effective groups differ
from the non-effective. The analysis of the groups employing discriminant

analysis is utilized to meet the following objectives:

(1) identify those variables that contribute to distinguishing between the
groups,

(2) analyze the differences between these mutually exclusive groups, and

(3) develop a model to predict group membership for new cases whose group
membership is desired, but unknown.

The limitation of no Speed data for zones in the after period prevent the direct
comparison of speed variables in the discriminant analysis between the before
and after period. Motorists improved compliance with Speed distribution

parameters such as 85th percentile Speed, mean Speed, and skewness are often

40
utilized as measures of effectiveness for speed zoning. However findings

regarding their effectiveness are mixed when accidents after a speed zoning
change are considered [Parker 1992a, Dudek and Ullman 1987, Taylor 1965,
Avery 1960, Kessler 1959].

The determination of a procedure to predict speed zoning effectiveness is the
overall objective of this effort. The variables identified, analyzed, and proposed
for a procedure to predict group membership using the before period data for

each Specific Speed zoning action is presented.

2.7 Speed Raised and Lowered Combined Effective Analysis

The merged records (i.e. cases) for each analysis group is the input data utilized
in discriminant analysis. The initial approach is to analyze all effective groups
combined versus their non-effective counterparts. The analysis is undertaken in
two stages. The first being to examine the before period between effective versus
non-effective, initially with all accident types and then rear end accidents. The
analysis of the before period is expected to identify variables that characterize the
conditions present before a speed zoning change is implemented which may
allow the prediction of whether the intended change will be effective. The
utilization of the combined speed raised and lowered effective groups in
comparison with control counterparts is to determine what variables (regardless
of Speed zoning action) distinguish effective zones from non-effective zones.
Analysis by all and rear accident type is conducted to determine whether

variables change based on the accident type investigated.

41
The second stage analyzes the after period data. This analysis is conducted to

determine if there had been a migration or Shift in accident locations.

2.8 Variable Selection--Speed Raised and Lowered Combined Effective

Since over two hundred variables were created through the merging of data
bases previously described, variable selection prior to beginning discriminant
analysis was conducted. Correlation analysis was employed to eliminate highly
correlated variables. Crosstabulation analysis was also utilized to discern
relationships between ”global” variables such as weather and lighting in relation
to accident type, land use, laneage, and other variables expected to play a critical
role in the discriminant function. These procedures identified 32 variables which
met the criteria of not being highly correlated and providing insight into the

relationships between variables.

Several measures of effectiveness (MOES) are utilized to determine the best
discriminant function. These are eigenvalue, Wilks’ lambda, and percent
correctly classified of those cases(i.e. records) for effective and non-effective
groups. In terms of overall Significance as an MOE, WilkS’ lambda is generally
considered superior. Its’ range is between ”1.0” and ”0.0”, with values close to
zero indicating a function providing the best separation between groups. Thus,
the minimization of WilkS’ lambda, along with percent correctly classified

become key determinants in the evaluation of discriminant functions.

Forward stepwise variable selection was then used to identify an initial set of

variables which minimized Wilks’ lambda in each comparison. Further analysis

42
revealed that it was possible to identify a smaller number of variables which

contributed approximately 80-85% of the total reduction in Wilks’ lambda.

This set of variables was used to determine a discriminant function for each
analyses based on stepwise variable selection. The discriminant functions and
variables selected in this manner, along with the variable means and MOES are
indicated. Discussion of the difference in mean values between the effective and
non-effective groups forms the characterization of effective speed zones by

period and accident type.

Using speed zoning action and the determination of effective vs non-effective
speed zone groups, the following group comparisons were utilized to determine

those variables which produced a discriminant function which minimized Wilks'

lambda:

Before Period Raised and Lowered Effective vs Before Period Raised and
Lowered Non-Effective

Before Period Raised and Lowered Effective {Rear Ends} vs Before Period
Raised and Lowered Non-Effective {Rear Ends}

After Period Raised and Lowered Effective vs After Period Raised and
Lowered Non-Effective

After Period Raised and Lowered Effective {Rear Ends} vs After Period
Raised and Lowered Non-Effective {Rear Ends}

2.9 Discriminant Analysis on Specific Speed Zoning Actions

The analysis of each primary Speed zoning action--Speed raised and Speed

lowered, begins by a variable selection process similar to the combined effective

43
discriminant analysis. Correlation analysis and crosstabulation analysis were

employed to eliminate highly correlated variables and understand the
relationship of "global" variables in the data sets. Specifically it was determined
that the before period and after period included many of the same variables. For
Specific Speed zoning action analysis, each period was analyzed by the
discriminant analysis forward variable selection process, identifying those
variables which minimized 80-85% of Wilks’ lambda. The before period data set
variables and after period data set variables are then scrutinized for the same
variables, as well as different variables. The question of how variables from the
two time periods should be combined is resolved through consideration of the
type of variable (i.e. direct or coded), its’ potential role in determining an
effective discriminant function, and the time period (one or both) in which the
variable occurred. Based on this the following approach was used to generate

four discriminant functions:

All Direct Variables common to before period and after period,
All Direct Variables common to before period and after period and in
either the before period or after period,

0 All Direct and Coded Variables common to before period and after
period and,

0 All Direct and Coded Variables common to before period and after
period and in either the before period or after period

Each effective Speed zoning data set by accident type was analyzed--yielding

discriminant functions for all accidents and rear end accidents based on this

typology.

The analysis at this point follows the same format as the combined effective
analysis, first examining the before period with the same intent, and then the

after period. A key difference from the combined effective analysis is that

44
specific effective groupings as defined by accident type was also analyzed. This

analysis was conducted for speed raised data sets (before and after). The speed
lowered data sets was found not to have any differences from the total accident

type effective data set(S).

As before, with the combined effective versus non-effective analysis, the primary
MOES to evaluate the resulting discriminant functions are minimization of Wilks’

lambda and percent correctly classified.

After determination of the most effective discriminant function, evaluation of the
variables remaining in this function occurs. This was conducted by: (1) assessing
the degree of correlation between the pooled within-groups structure coefficients
and the discriminant function, and (2) analyzing the difference in means between

the effective group and non-effective group.

The evaluation of the variables in the discriminant function in this manner
provides a characterization of how the effective zones are different than the non-
effective zones. Utilizing the comparisons between before time periods for each
primary speed zoning action allows conclusions to be reached regarding the

conditions characteristic of effective Speed zones.

Comparing results and characterizations between before and after time periods
for primary speed zoning actions describes the shift in accident locations for each
primary zoning action. More important, however, is that as a result of this
analysis, Speed zoning procedures which quantify and use roadside
development variables now have evidence that suggests this approach is

appropriate.

CHAPTER 3

Effectiveness of Speed Zones

3.1 Background

Speed zoning actions of raising or lowering the speed limit are undertaken with
the expectation that accidents will be reduced in frequency after the zoning
action has been in effect over some period of time. Normally this period of time
for analysis purposes is no less than two years and may range as high as ten. In
this analysis, the minimum range is two years before or after the zoning action

and the maximum is seven years after.

Initially, in preparing the proposal and conducting the analysis, a zone-by-zone
analysis of Speed zoning effectiveness was to be undertaken. Chi-Square for
Poisson Frequencies was to be the statistical method utilized. However, this
procedure requires that each site or location have the same time period in the
pre-zoning term and yet a different (but equal) time period (zone to zone) in the
post zoning action term. This constraint could not be met at all Sites. Also, the
need to group the individual zoning actions later into homogeneous groups,
such as limit lowered, limit raised etc., would not have been feasible under this
procedure because of the different lengths of before and after time periods of

analysis in numerous zones.

45

46

Since at this stage of the analysis, effectiveness of zoning action was of primary
interest, using ONEWAY ANOVA as the statistical procedure was determined as
a viable alternative. The objective of this test is to determine if there are
Significant differences in the group means under study. This technique permits
the testing of all the groups at once through a calculated F statistic. The
procedure also allows multiple comparisons between selected groups or
combinations of groups. Both of these analyses were performed on the accident
data set. ANOVA allows groups to be formed based on coding and a dependent
and independent variable identification. In this case, ACC_RATE became the
dependent variable and ZON_ACT became the independent variable.
ACC_RATE is a numeric variable and ZON_ACT is an integer variable which

identifies the zoning action.

3.2 Objectives

In general, the objective in performing statistical analysis on groups of speed
zones based on the zoning action undertaken was to determine if, as expected,
the zoning action resulted in a statistically significant reduction in accidents
when compared to comparable matched control zones. Additionally, the
statistical analysis was repeated for rear end accidents and the remaining
accident types labeled "non-rear ends". The basic experimental design is
Before/ After with comparison group. While it is recognized that this design has
serious threats to validity from local history, regression to the mean, and
maturation, its strength is considerably improved if the comparability of the test
and control groups are demonstrated. The matching process to address the

comparability of the groups iS discussed in the methodology section.

47

3.3 Matching of Test and Control Zones

The matching of test / control pairs was undertaken with the following variables
as the key determinants: laneage, ADT, type of Speed zone, one-way or bi-
directional traffic, curvature and Speed limit. Data on fixed objects, number of
driveways, and other roadside or environmental factors were not used in
matching, since a primary focus of this study is to determine their role in
predicting the type and number of accidents. Thus these variables will be
independent of the matching process in order to determine their contribution to

the effectiveness of Speed zones.

The control zones were matched on the before speed limit of the test zone in
most cases. However, where there were constraints to matching based on the
before period speed limit, the control zones were matched on the after period
speed limit. Table 1 identifies these exceptions and their deviation from the

preferred methodology.

48

Table 3.1

N on-Matching Speed Limits in Before Period in Control and Test Zones

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

District Test Zone Speed Change Control Zone Speed Limit
5 41-030—88T R-10, 25 TO 35 41-030-88C 35
6 25—007-85T R—5, 30 TO 35 25-007—85C 35
7 NONE N / A N/ A N/ A
8 33-001-84TC L-10, 45 TO 35 11-024-73C 35
8 81-023-84 L-10, 45 TO 35 81-023-84C 35
9 77-015-85T L-5, 50 TO 45 77-015-85C 45
9 82-017-85T R-5, 35 TO 40 82-017-85C 40

 

Note: N / A indicates ”not applicable”.

3.4 Data Preparation

Accident data received from the Michigan Department of Transportation

(MDOT) were converted to Spreadsheet format from a database format. The

accident data contained basic information on accident type, time of day, ADT,

hazardous action codes, etc. The accident data set for each zone were extracted

from MDOT files for each year of interest, pre and post the zoning action. The

set would range from 1981 to 1990, with the year of zoning action excluded from

the accident analysis.

 

49
This data set was built for each test zone under study and its matching control

zone. The zoning action which defines the major categories are Speed limit
raised and Speed limit lowered, with further sub-categorization by the amount of
change--5 or 10 miles per hour (mph). The final number of zones for each sub
categorization is : 5 MPH Raised--9, 10 MPH Raised--4, 5 MPH Lowered--8, and
10 MPH Lowered-5. Resulting in a total of twenty—Six test zones and twenty-six

control zones. Table 2 provides a more informative breakdown by speed limits.

Table 3.2
Number of Zones by Zoning Action and Amount of Change

 

 

 

 

 

 

 

 

 

 

Lowered Count Lowered Count Raised 5 Count Raised Count
5 MPH 10 MPH MPH 10 MPH
40 to 35 2 35 to 25 1 25 to 30 1 25 to 35 1
45 to 40 3 40 to 30 1 30 to 35 2 30 to 40 3
50 to 45 3 45 to 35 2 35 to 40 4
50 to 40 0 45 to 50 2
55 to 45 1
Total 8 5 9 4

 

 

 

 

 

 

 

 

 

Statistical Package for the Social Sciences (SPSS) was used to read the
Spreadsheet files and produce a summary of total accidents, accidents per million
vehicle miles (MVM) and accident type for each year pre and post zoning action.

These accident rates were then compiled into a Single spreadsheet composed of

50
the columns: District, TCO Number, ZON_ACT, Year, REAR_END, ACC_RATE,

NON_REAR, INIT_SPD and FIN_SPD. The rows are the accident rates for each
year for each test zone and matching control zone, starting with district 5 and
proceeding through district 9. The codes in the column ZON_ACT reflect the
zoning action and status of the zone associated with that zone for each year.
Table 3 lists the specific categorization(i.e. group) and its abbreviated name in the

SPSS output.

Table 3.3
Group Name and Associated Accident Years with Mean

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mean--All Acc.
Categorization Count SPSS Output Types
Name (Acc / MVM)
Raised 10 Before 18 RA 10 BEF 6.57
Raised 10 After 18 RA 10 AFT 8.55
Raised 10 Control 18 NC 10 RBEF 8.31
Before
Raised 10 Control 18 NC 10 RAFT 13.38
After
Raised 5 Before 39 RA 5 BEF 7.42
Raised 5 After 41 RA 5 AFT 6.81
Raised 5 Control 39 NC5 RA BEF 10.27
Before
Raised 5 Control 41 NC5 RA AFT 9.04
After
Lowered 10 Before 26 LOW 10BEF 7.98
Lowered 10 After 19 LOW 10AFT 5.28
Lowered 10 26 NC 10LOBE 5.47
Control Before

 

 

51

 

 

 

 

 

 

 

Table 3.3 (continued)
Lowered 10 19 NC 10LOAF 8.16
Control After

Lowered 5 Before 29 L0 5BEF 6.79

Lowered 5 After 35 LO 5AFT 6.90

Lowered 5 Control 29 NC 5 LOBE 4.38
Before

Lowered 5 Control 35 NC 5 LOAF 5.33
After

TOTAL 450 7.46

 

 

 

 

 

3.5 Analysis of Data

SPSS reads the file and performs those commands and subcommands assigned
by the user to operate on the data. In this analysis, a oneway analysis of variance
was performed on the accident rate data as the dependent variable and zoning
action as the independent variable. The particular analysis undertaken on the
accident data is a single factor study with Sixteen treatment levels. The
conclusions will extend only to the factor levels under study, and thus this type
of analysis of variance model is a fixed effects model or Model I. The analysis of
variance (ANOVA) is undertaken to analyze the effects of the independent
variable, zoning action, on the dependent variable, accident rate. The factor level
means are compared to each other to determine if they are equal. If they are
found equal, the implication is that there is no relation between the factor
(grouping of independent variables) and the dependent variable. Conversely, a
finding of unequal factor level means indicates there is a relationship between
the factor (treatment) and dependent variable. The F test is used to check for the

equality of factor level means.

presented in Table 3.4.

52

contained in the output from an ANOVA table.

Table 3.4

In order to determine if the factor level means are the same, the calculated F (F *)
is compared to a table value with the appropriate degrees of freedom, in this case
K (number of groups) -1 and N (number of observations) -K. The calculated F is

the ratio of Between Groups Mean Squares and Within Groups Mean Squares

The procedure conducted was to compare the treatments by speed zoning action
group for each period to their control counterparts. The table values for the F
distribution at .95 confidence coefficient with appropriate degrees of freedom

were compared to F" values obtained from ANOVA output. Results are

Before Period and After Period F Test of Treatment vs Control by Speed Zoning
Action (CL = .05)

 

 

 

 

 

 

 

 

 

Before After
Zoning Action
Speed Raised 10 Accept HO Reject H0
Speed Raised 5 Reject HO Reject HO
Speed Lowered 10 Reject Ho Reject Ho
Speed Lowered 5 Reject Ho Accept H0

 

With the exception of Speed Raised 10 in the before period and Speed Lowered 5

in the after period, the mean accident rates are found to not be equal to their

 

53
control counterparts. An additional comparison between Speed Raised 10 and

Speed Raised 5 combined for the before period with their control counterpart

(combined) also yielded rejection of Ho.

Examination of whether the change in mean accident rates before to after for
treatment zones are statistically significantly different than their control

counterparts, was conducted and follows.
3.6 Determination of Effectiveness of Speed Zoning Action on Accidents

There are several tests which can be employed in the Before and After with

comparison groups experimental design. The two most relevant here are:

(1) A test of the before period group mean (i.e. treatment vs control) values to
determine how comparable the treatment (test) group is to the control group,
and

(2) A test of the difference in mean accident rates from the before to after
period, treatment compared to control.

3.6.1 Test of Comparability of Before Period Mean Accident Rate

The first test determines whether there are statistically significant differences in
the before period mean accident rates for the treatment and control groups. The
strength of the experimental design is improved if it can be demonstrated that
the comparison locations are approximately equal before treatment. At this point
with accidents as the variable under consideration, a finding of no difference
would indicate that both treatment and control groups would be candidates for
speed zoning action if no other variables were considered. Also, at least on this

variable, it would indicate that both test and control groups belong to the same

54
pool of zones. Thus, they Should behave Similarly over time to all internal

threats to validity, as well as any treatment or lack thereof. Council [1980] states:

"the strength of the (Before and After with comparison groups) design is
directly proportional to how Similar the treatment and control groups are.
Thus in using this design, the evaluator should always carefully compare the
measures for the two groups in the before period".

Using ANOVA the comparison of the test group means to their control group
means addresses the issue of comparability and also the strength of the design.
All the zones analyzed in this research were categorized as having undergone a
zoning action (treatment) or no zoning action (control). The basis for inclusion
in the test group may have been a procedural review (conducted every ten
years), which produced a zoning action, or a series of complaints which may
have led agency officials to a review and zoning action. Under either premise,
agency policies and procedures Should have led to Speed zoning changes only if
the change was supported by the data. Therefore, any speed zoning changes
should be substantiated by the following data elements utilized by MDOT listed
in approximate order of importance: 85th percentile speed, total accident history
for previous 3-4 years, volume, number of driveways, existing speed limit,
laneage, shoulders, width of lanes, adjacent land use, and functional

classification of the facility.
3.6.2 Hypotheses--Comparability of Before Period Mean Accident Rate

The hypothesis for this test is the following: H01 u1 = u2 vs. Ha: III at Hz

Critical Region: -t(1-0</2), n1 + n2 - 2 < < t(1-or/2), n1 + 112 - 2, (on: .05)

S_

_Y

7—T
X

55

This is a two-tailed t-test which determines if the before period mean accident

rate is approximately equal between the treatment and control groups.

Table 3.5 presents results of the test for total accidents, rear end accidents, and
non-rear end accidents. The data set was grouped by speed zoning action. The
analysis of variance was performed on the treatment and control group of each
speed zoning action separately, thus the pooled standard deviation of the
variance is only for the specific groups analyzed. In addition to the outcome of
the t-test, labeled as "Outcome" in the top half of Table 3.5, the results of the F-
Test for the treatment means is also indicated. In this case, the F-test and t-test

are equivalent, if the t-test statistic is squared.

For comparison purposes, a non-parametric test, Wilcoxon Signed-Rank Test was
also performed on the same data set using accident frequencies as opposed to
accident rates per million vehicle mile. The results of this analysis is presented in
the bottom half of Table 3.5. Both the analysis of variance and Wilcoxon Signed-

Ranks Test utilize a confidence limit coefficient of .95.

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57
3.6.3 Findings

The Raised 10 Before results for the t-test involving total, rear, and non-rear
accidents lead to the conclusion that the treatment and control accident rates are
not significantly different. The results of the F-test indicate that the factor level
treatment means have no significant effect on the dependent variable, accident

rate.

The Raised 5 Before results for the t-test involving total and rear end accidents
indicate that the accident rates are Significantly higher in the test section than
they were in the control sections. The opposite is found for non-rear accidents.

The results of the F-test reflect the findings in the t-test by accident type.

The Lowered 10 Before results for the t-test indicate total and non-rear end
accidents are also significantly higher in the treatment sections. This finding was
not observed for the rear end accident type. The F—test results follow the pattern

of the t-test.

The Lowered 5 Before results for the t-test also indicate total, rear end, and non-
rear accidents are significantly higher in the treatment sections. Again, the F-test

results reflect the findings in the t-test by accident type.

The findings from the non-parametric test reflect those from the analysis of

variance. This is to be expected. Conover [1980] states:

"the assumptions of the Wilcoxon test are easier to justify than the assumption
of normality. If the data are discrete, we know right away that the
distribution is nonnormal because the normal distribution is continuous. If
the data have an occasional very large or very small observation called

58

"outliers", the power of the t-test drops considerably and should not be used.
Unfortunately, this type of nonnormality is difficult to detect. If the normal
distribution is required of the differences between the pairs, the asymptotic
relative efficiency of the Wilcoxon test to the t-test is .955"-

The Wilcoxon Signed-Rank test is applicable to the Before and After with

comparison groups design which is essentially paired observations.

3.6.4 Significance of Findings: Comparability of Before Period Mean Accident
Rate

The Raised 10 Before acceptance of the null hypothesis across all accident
categories would indicate that the accident rates are the same between treatment
and control zones in the before period. However, the Sign of the difference
between the means for all three accident types is negative indicating that the
mean accident rates are less in the treatment group than the control group. A
conclusion would be that, in comparison to their control counterparts, there may
not be a priori justification for speed zoning based on the before period accident

history.

The Raised 5 Before mixed results indicate that some of the accident rates are
significantly different between treatment and control groups. The Sign of the
difference between the means for all three accident types is negative indicating
that the treatment zone rate was less than the control zones. The mixed results
may indicate that rear end accidents are more frequent in the control zones than

the test zones, and is Significant enough to influence the total accident finding.

The rejection of the null hypotheses for two out of three accident type categories

when the treatment group mean accident rate is lower than the control group

59
means that (1) either the control group is not appropriately matched to the

treatment group, or (2) the treatment group may not have needed the speed
zoning action relative to the matched control zones (at least based on accident

experience).

The Lowered 10 Before findings are also mixed with acceptance of the null
hypothesis on rear end accident types with all others rejecting the null
hypothesis. This may indicate that the non-rear accident types influenced the
total accident type outcome more than the rear ends in this case. It may also
indicate that rear end accident types are at least not the primary problem for
zones considered for this Speed zoning action. The Sign of the difference
between the means for all three accident types is positive, indicating that the
treatment zone rate was more than the control zone rate. This taken with the
results of the t-test may indicate that this zoning action for the treatment group
compared to the control group on the accident variable, identified a need for a

change in the Speed limit.

The Lowered 5 Before findings indicate that treatment accident rates for all
accident types were larger than the control groups, meaning that relative to this
comparison group there is a priori evidence for speed zoning action on the

treatment zones.

Overall, the Speed limit raised zones means were less than their control
counterparts in the before period. For the Raised 10 grouping this led to
acceptance of the null hypothesis across all accident types. Conversely, the
Raised 5 grouping rejected on two of the three accident categories. However,

since the difference in mean values were negative, it would appear that based on

60
accident rates there was little justification for the zoning action. This finding iS

not surprising, as raising the speed limit often results from observing that the
prevailing speed is higher than the speed limit then in effect, rather than an

attempt to decrease accidents.

The pattern of findings was the opposite for the speed limit lowered category,
with the treatment zones means greater than their control counterparts. The
consistent findings of rejection of the null hypothesis in the Wilcoxon test results
coupled with a positive difference in mean accident values, indicate for this
speed zoning action there was an accident based a priori justification for speed

zoning action.

The basic question addressed by this particular analysis was whether the
treatment and control groups were similar in the before period at a confidence
coefficient of .95 on one variable, accident rates. It is found that generally they

are not, with one exception, Speed Limit Raised 10.

Although the remaining groups were generally determined not to be similar at
the confidence level specified, the higher mean accident rates for accident types
within treatment groups suggests that the accident experience may have been a
factor leading to the speed limit change. Therefore, as one of the primary
criterion leading to a Speed zoning change, the higher rates compared to control
groups is reasonable. The finding of non-comparability in the before period on

the accident variable is not unjustified in this case.

61

3.7 Test of the Change in the Mean Accident Rate--Treatment Compared to
Control

The results from Table 3.5 indicate that for a number of the treatment actions
across all accident types there is an effect of the action on the dependent variable,
accident rates. The principal question of interest here is to determine if the
specific actions have resulted in a decrease in accident rates relative to their
control groups. In order to test this hypothesis, the difference between the before
to after period accident rates for treatment and control factors for each speed
zoning action were compared. The null hypothesis is that the diffm for the

treatment and control groups are equal, indicating no effect by treatment.

3.7.1 Hypothesis-Test of the Difference in Before to After Period Mean
Accident Rate--Treatment Compared to Control

The hypothesis for the second test to be performed at OI = 0.05 is:

HO =(l-11—l12)—(l13"l14)= 0 VS Ha=(li1—ll2) —(l~l3—l~l4) $0

alternatively: HO : 2 Gilli = C vs. Hat 2 Citli at c

where: ui = factor level means (i.e. Raised 5 Before, Raised 5 After)
ci = constants associated with the factor level means(i.e. in this case 1 / 2)
2C1 = O

Neter, Wasserman, and Kutner [1985] indicate that to test the alternatives the t*

test statistic is:

62
29F? i ' C

C-2
MSE Z—i-
ni

which follows the t distribution with nT - r degrees of freedom when HO holds.

 

 

t*=

Where: ni = number of items in each group
r = number of groups
nT = total items in all groups
l\_/I_SE = Mean Square Error

Y; = sample mean of the factor levels.

The test expressed in the t* statistic involves the linear combination of factor level
means in the analysis. The test is called a single degree of freedom test. The
question of interest is the comparison of the before period to after period
difference in the treatment zone means compared to the before period to after
period difference in matched control zones. Depending on the Sign of the

difference, the treatment may be considered effective in reducing accidents.

The single degree of freedom test is implemented here as a two-tailed test. Table
3.6 presents the results of this analysis with the respective speed zoning action
groups further demarcated based on location of the zone in the urban
environment. Transition, abbreviated to "Trans." in the table refers to speed
zones on the city periphery which have an urban setting. However, because of
both their Speed reducing function (from a 50 or 55 mph limit to 45 or 40 mph
limit) and their not being entirely in a residential, commercial, or industrial area ,
they are so categorized. Urban zones are just the opposite and normally have
speed limits in the 25 to 40 mph range and are generally contained in areas with

one or more typically urban land uses. The degrees of freedom Shown for each

63
speed zoning action represent the accident years in total for the before to after

period comparison between the treatment and control groups involved for that
speed zoning action. Only two groups, "Transition Raise 10" and "Transition
Lower 10" which consisted of one treatment and control zone and no zones
respectively, were not included in this analysis. All other zones were included in

one of the groups.

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65
The results from Table 3.6 indicate that only one group, "Lower 10" and it's single

related sub-group, "Urban Lower 10" reject the null hypothesis of equal
differences in accident rate reduction for all accident types between the before to
after periods, treatment compared to control. An observation is that the two
groups are composed of the same zones, as reflected in the results and the lack of
zones in the Transition Lower 10 category. The results of the F test for rear end
accidents indicate that the factor level means are equivalent at the confidence
coefficient of .95. Meaning that there is very small chance that there is a
relationship between the treatment levels and the dependent variable rear end
accident rate. The t" test results for Lower 10 means that the absolute reduction
in accident rates for the test zones when compared to the control zones were

found to be significantly greater at the .95 confidence level.

The results of Table 3.6 for "Lower 10" is significant given that Table 3.5 results
indicate that the rejection of the null hypothesis for the t* test took place on both
the total and non-rear accident types, and was accepted on rear ends. All three
accident types had positive differences in mean accident rates in the before
period, indicating the treatment zones had higher accident rates than the control
zones. Table 3.6, however, indicates that the difference in rates between before to
after periods were significant. A review of the means for total, rear end and non-
rear indicate a trend toward lower accident rates in the treatment after period
compared to the before period. This finding for "Lower 10" indicates that for all
accident groupings, the action of lowering the speed limit is shown to be

statistically Significant in reducing accident rates.

The results of Table 3.6 are significant also for the remaining Speed zoning

actions. Cumulatively, a conclusion is that speed zoning was not effective in the

66
aggregate in reducing accidents at the .05 level of significance, for most types of

speed zones.

These results are consistent with past experience which also Show mixed results
from speed zoning. In Michigan as in other locations, Simply changing the speed

limit does not always result in a decrease in accidents.

3.7.2 Family Confidence Intervals for Speed Zoning Actions

The individual tests in Table 3.6 use a confidence coefficient of .95. In order to
draw conclusions about the major speed zoning actions with an overall

confidence level, multiple comparison procedures are employed.

Utilizing Scheffe’ and Bonferroni multiple comparison procedures creates a
confidence coefficient that assures in (1- 0L) x 100 repetitions the same
approximate range of confidence intervals would be found for the family of
statements. Both methods were used to construct confidence intervals with a

family confidence level of 95 percent with the following results in Table 3.7:

67

 

 

 

 

 

 

 

 

 

T bl 3.7
Family Confidence Intervals for Spire: Zoning Actions, All Accident Types
(a = .05)
Speed Zoning Action Scheffe’ Bonferroni
Raised 10 All -1.622 3 L1 5 4.718 —1.211 5 L1 5 4.308
Raised 5 All -2.574 _<_ L2 3 1.952 -2.340 5 L2 5 1.718
Lowered 10 All 1.194 5 L3 5 4.198 1.349 _<_ L3 5 4.043
Lowered 5 All -1.200 5 L4 5 2.043 -1.033 5 L4 5 1.8759

 

 

 

 

 

Note: The values in the table are accidents per million vehicle miles. Negative values
denote an increase in accidents, while positive values indicate a decrease in accidents.

The conclusion from both techniques is : (1) There is no overall effect for the
Speed zoning actions of Raised 10, Raised 5, and Lowered 5 on the accident rate,
Since the confidence intervals contain zero; (2) For Lower 10, the effect at the .95
confidence level is that the accident rate decreased between 1 and 4 accidents per
million vehicle miles (acc/ mvm) in the treatment zones relative to the control

zones.

3.8 Test of Individual Zone Accident Reduction Effectiveness

Each speed zone was analyzed for its' effectiveness in reducing accidents after

treatment, in this case a speed zoning change of raising or lowering the speed

limit. The methodology was to use the treatment and control zones before and

68
after accident frequencies, along with the number of years in the treatment after

period to produce an expected accident frequency for the treatment zones. A
percentage improvement was derived based on the difference between the
expected and actual divided by the actual, multiplied by 100. This percentage
improvement (if positive) reflects a decrease in accidents. Poisson curves [Box
and Oppenlander 1976] based on expected after accident frequencies without
treatment and percentage improvement were used to determine a significance
level. This procedure was applied to each zone and groups of zones based on
speed zoning action and type of zone. The primary focus of this effort was to
determine which zones were individually effective in comparison to their
matched control zone in reducing accident frequencies. The results of this
analysis is presented in Table 3.8--Individual Zone Effectiveness by Type of Zone
and Accident Categories, Table 3.9-~Zoning Action and Accident Categories,
Table 3.10--Zoning Action by Land Use and Accident Categories, Table 3.11-
Comparison of Zoning Action and Accident Categories, and Table 3.12--Listing

of Effective Zones by Zoning Action and Accident Categories.

The selection of zones for the effective zones listing in Table 3.12 is based on the
All Accidents and Rear End Accidents at the 85% level of significance.

Normally a 95% level of significance would be utilized as the level of
significance, however Since the total number of zones in this study was small
(total 26) and the majority of effective Sites were greater than 95% level of
significance, it was concluded that the additional two Sites this change allowed
would not jeopardize the results. N on-Rear End accident category was not used
in the selection of effective zones, since they are not a primary focus of this study.

However, their data is provided in all three tables for comparison purposes.

69

3.8.1 Discussion of Findings-Individual Zone Accident Reduction Effectiveness

Table 3.8 presents a listing of the accident data for all the test and treatment
zones. Negative values under the "% Difference" column indicate there were
more accidents in the after period than would be expected. Collectively, the set
of zones in this study are shown to have achieved a reduction in accident
frequencies at the 99% level of significance. This result was also obtained for
these zones when only rear end accidents were identified and analyzed. Only an
80% level of Significance was achieved when non—rear end accidents were

analyzed.

A conclusion is that the zoning actions undertaken individually may vary,
however aS a total group they are effective at the 99% level of significance for
total and rear end accidents. The matching of test and control zones and the
general finding of their comparability on the accident variable further

strengthens these results.

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73
Table 3.9 groups the zones by zoning action and accident categories. The analysis

was used to determine how individual zones grouped by common zoning
actions were or were not effective in reducing accident frequencies. The values
in parentheses behind each group name indicates the number of zones in that
group. Another important consideration related to the strength of the findings is
the comparability of each group with its' control group. Using the results from
Table 3.5 and the data from Table 3.9, a comparison of results is shown in Table

3.11.

The results indicate that in the zones where the speed limit was raised or lowered
by 10 mph the before period accident rate was comparable to the control zone.
However this is not true where the speed limit was raised or lowered by 5 mph.
It would appear that the majority of the inconsistency is in the 5 mph lowered
category. Keep in mind that the data in Table 3.5 is only for before period

comparability and not zoning category effectiveness.

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76
Table 3.12 provides a listing of those zones with a significance level of _>_ 85% for

the accident categories of total and rear end. In Table 3.9, the data is demarcated
by zoning action of raising or lowering the speed limit. These zones form the
grouping of "effective zones". They are to be analyzed in comparison to their
non-effective counterparts to determine the contribution and significance of
roadside friction and speed variables to their effectiveness. Table 3.13 below
presents the number of effective zones and non-effective zones by speed zoning

action based on the listing in Table 3.12.

Table 3.13
Number of Effective Zones versus Non-Effective Zones
by Speed Zoning Action--All and Rear End Accident Types

Zoning No. 0 ' No. 0 Non-
Action Zones Effective Zones
Rear Rear
5 4 5
Raised 10

1 3
Low 5 3 5
1O 3 2

Total 11

 

CHAPTER 4

Combined Effective Speed Raised and Speed Lowered Analysis vs
Combined Non-Effective Speed Raised and Speed Lowered Analysis

4.1 Discriminant Analysis

The process of determining mutually exclusive groups is the primary
methodological requirement for discriminant analysis. The determination of
effective speed zones versus non-effective as previously indicated is now utilized
to form the groups for discriminant analysis. The primary intent of this effort is

to:

(1) identify those variables that contribute to distinguishing between
the groups,
(2) analyze the differences between these mutually exclusive groups.

Since both lowering and raising the speed limit are combined in this section of
the report, the development of a model to predict group membership is reserved

for a later section.

4.2 Variable Selection

The literature review identified a number of speed parameters such as 85th

percentile speed, skewness, percentile in the pace, upper and lower limit of the

77

78
pace, etc., used to establish speed limits. The literature also identified roadside

friction variables, such as driveway density, land use type, and fixed objects as
parameters to be considered in establishing speed zone limits. Driver behavior
variables which can also be considered because they are represented in the data
set are hazardous action codes identified by accident investigators as well as

circumstances such as weather, other contributing circumstances, lighting, etc.

A single data base including these variables was built for each speed zoning
action and its control counterpart combining the accident, speed, and geometric
files. Using the ADD and MATCH commands in SPSS, and matching on each
tenth of a mile in each of the unique data sets, a record with accident, speed, and
geometric data for each tenth of a mile that contained an accident was created.
These data were then used to create speed zoning action(i.e. Speed Raised)
effective and non-effective groups. Through appropriate utilization of the ADD
files procedures, larger groups were built such as Before Period Effective Speed
1:555 and Lowered. Appropriate counterparts were also developed in this

same manner.

The analysis of these newly formed groups involved determining frequencies of
direct and coded variables. "Direct" variables are those where their values are
directly interpretable, such as SKEWNESS or KURTOSIS. "Coded" variables are
those where a value has been assigned to a qualitative level, and thus are not
directly interpretable from their numerical values. Examples would be FIXOB_E,
where values were developed for the number of utility poles, trees, fire hydrants,

etc.

79
The coded variable and direct variable frequencies are a combination of the

accident milepoint they occurred at and the frequency of accidents which
occurred at that milepoint. Each group is therefore composed of the matching of
the accidents at milepoint occurrences with the features of the geometric, speed,
and environmental conditions present in the approximate timeframe and in the

one tenth mile section where the accident occurred.

Correlation analysis and crosstabulation analysis were techniques used to select
variables for discriminant analysis. The procedure employed was to use
correlation analysis to identify and eliminate highly correlated variables.
Crosstabulation analysis was used to identify and understand the distribution of
variables within ubiquitous or "global" variables such as road type as well as

specific variables such as hazardous action or land use.

Using both techniques allowed identification of variables which were minimally
correlated and were distributed throughout the data set. This second point is
important from the perspective of understanding the relationship and
distribution of "coded" variables such as land use, laneage, and hazardous

actions across accident types within locations and environments.

This core set of variables identified in this manner were then used in all initial
discriminant analyses in a stepwise variable selection process. The specific
criteria for variable selection was the minimization of Wilks' lambda. While
other methods such as Rao's V and Mahalanobis' Distance were available, Wilks'
lambda was selected due to its' close theoretical underpinnings to Analysis of
Variance, using the ratio of the within-groups sum of squares to the total groups

sum of squares. As such, it is the proportion of the total variance in the

80
discriminant scores not explained by differences among groups. Norusis [1990]

indicates "Small values of lambda are associated with discriminant functions that
have much variability between groups and little variability within groups". This
characteristic builds cohesive groups while still measuring the separation
between groups. Thus, in a variable selection technique, one is able to select
variables which improve group cohesiveness while maintaining good group
separation over a variable which reduces group cohesiveness while also
maintaining good group separation. Wilks' lambda has a range with a maximum
value of 1.0 which indicates poor performance, to a value close to 0.00 which
indicates very good performance. The ability to convert Wilks’ lambda to a Chi-
Square distribution and obtain a multivariate F statistic and a partial F statistic as

each variable is entered facilitates the analysis of variable selection.

Proceeding in this manner, and using parameter settings for partial F-statistics
for entry and exit of variables into the discriminant function, as well as a

tolerance level which prevents linear combinations of variables to be included
above a minimum, analyses were performed on combinations of effective and

non-effective speed zone groups.

4.3 Analysis Categories

Using speed zoning action and the listing of effective vs non-effective speed zone
groups, the following group comparisons were utilized to determine those
variables which produced a discriminant function which minimized Wilks'

lambda:

Before Period Raised and Lowered Effective vs Before Period Raised and
Lowered Non-Effective (BP2 RAISLOW EFF ALL vs BPZ RAISLOW NON-
EFF ALL)

81

Before Period Raised and Lowered Effective {Rear Ends} vs Before Period
Raised and Lowered Non-Effective {Rear Ends} (BP2 RAISLOW EFF ALL vs
BP2 RAISLOW NON-EFF ALL--REAR END ACCIDENTS ONLY)

After Period Raised and Lowered Effective vs After Period Raised and
Lowered Non-Effective (AP2 RAISLOW EFF ALL vs AP2 RAISLOW NON-
EFF ALL)

After Period Raised and Lowered Effective {Rear Ends} vs After Period
Raised and Lowered Non-Effective {Rear Ends} (AP2 RAISLOW EFF ALL vs
AP2 RAISLOW NON-EFF ALL-~REAR END ACCIDENTS ONLY).

The before period effective vs non-effective comparisons identify those variables
which separate effective and non-effective groups prior to changing the speed
limit. Thus, if statistical measures of the discriminant function and the function
itself are reasonably significant, information needed to predict whether speed
zoning actions would be effective based on the characterization of the zone is

available.

The after period analysis provides another opportunity to characterize the
effective vs non-effective speed zoning groups by comparing variables
differentiating the effective vs non-effective speed zones after the speed limit
change. Through the variables selected, the agency establishing the speed zone
can predict the success (or lack of success) in reducing accidents through the
implementation of the speed zone. If there is a change in variables selected from
the before period to the after period this would indicate a shift in accident

locations within the zone.

Variables selected and the value of their means provide an overall

characterization of how the effective and non-effective groups differ.

82
Segmentation of the comparison files by all accidents and rear end accidents was

performed to determine if major accident types significantly changed the

selection of variables and therefore the characterization of how the groups differ.

4.4 Initial Variables in Discriminant Analysis

Thirty-two variables were identified from the output of the correlation analysis
and crosstabulation analysis and are presented as follows: ADT AREA_COZ
CONT_CIl CONT_C12 DRYWAYE DRYWAYW DST_CRS EIGHT5_P FD(OB_E
FIXOB_W HAZ_ACT1 HAZ_ACT2 HWY _TYPE KURTOSIS LANEAG_E
LANEAG_W LANUSE_E LANUSE_W LIGHTING OB]_HIT1 OB]_HIT2
PERC_IN_ PRK_LEFT PRK_RIGH RDSIDE_D ROAD_CON ROAD_TYP
SIGNAL_E SIGNAL_W SKEW SKEWNESS TRAF_CON. Their meaning is
described in Table 4.1 which follows:

Table 4.1
Identification and Description of Variables in the Discriminant Analysis

 

 

 

 

 

Variable Name Variable Meaning Variable Name Variable Meaning
ADT Average Daily LANUSE_E Type of land use in
Traffic eastbound"
direction
AREA_COZ Highway Area LANUSE_W Type of land use in
Code and Highway westbound
Type Combined direction
CONT_CI1 Contributing LIGHTING Type of light under
Circumstances, which the accident
Vehicle 1 occurred
CONT_C12 Contributing OB]_H1T1 Object hit by
Circumstances, vehicle 1
Vehicle 2

 

 

 

 

 

83

Table 4.1 continued

 

 

 

 

 

 

 

 

 

 

 

 

DRYWAYE Number of OB]_H1T2 Object hit by
driveways vehicle 2
eastbound direction

DRYWAYW Number of PERC_IN_ Percentile of vehicle
driveways speeds in the 10
westbound mph pace range
direction

DST_CRS Distance from PRK_LEFT On-street parking
accident location to on the left side
nearest crossroad

EIGHT5_P 85th percentile PRK_RIGH On-street parking
speed on the right side

FD(OB_E Number and type RDSIDE_D Roadside
of fixed objects in Development Code
eastbound direction

FD(OB_W Number and type ROAD_CON Road Surface
of fixed objects in Condition
westbound
direction

HAZ_ACT1 Violation ROAD_TYP Roadway type
(Hazardous
Action), Driver 1

HAZ_ACT2 Violation SIGNAL_E Number and type
(Hazardous of traffic signals in

q{ Action), Driver 2 eastbound direction

HWY_TYPE Specific highway SIGNAL_W Number and type

area type of traffic signals in
westbound
direction

KURTOSIS Measure of SKEW Measure of
distribution distribution

distortion, in
comparison to the
normal distribution,
there is an over or
under
concentration of
observations at the
center in relation to

 

the tails

 

distortion, in
comparison to the
normal distribution,
there is a shift of the
central value to the
right or to the left

 

 

84

Table 4.1 continued
LANEAG_E Type and width of SKEWNESS Same as skew,

 

laneage in however the

eastbound direction skewness index
uses a value of 1.0,
as opposed to 0.0 to

indicate normality
LANEAG_W Type and width of TRAF_CON Type of traffic

 

laneage in control, including
westbound signage, if any.
direction

 

 

 

 

 

ote: * Where eastbound and westbound are specified this can also represent northbound and
southbound as well.

Stepwise variable selection was used to identify an initial set of variables which
minimized Wilks’ lambda within each test section. Further analysis was then
conducted to identify a smaller number of variables which contributed
approximately 80-85% of the total reduction in Wilks' lambda. Each separate test

situation was processed in this manner.

The use of the eigenvalue as a measure of the effectiveness of the discriminant
function has no direct scalar interpretation. It is the ratio of the between group
Sum of Squares divided by the within group Sum of Squares. Since discriminant
analysis is based on creating the largest difference between groups from the
linear combinations of independent variables, the larger the numerator and
smaller the denominator, the better (in a general sense) is the discriminant
function. Therefore, in general, large eigenvalues are associated with good
functions. However since no scale exists, the comparison is relative. The
eigenvalue is used to gain an understanding of which variables best distinguish

between effective and non-effective speed zones.

 

85
The discussion of each speed zoning comparison will focus initially on the

variable values determined for the before period. The measures of effectiveness
(MOES), the relationship between the discriminant function and its variables, and

means and distribution of variables will be presented and discussed.

The results of the before period analysis by accident type with and without speed
variables is presented in Table 4.2.

86
Table 4.2

Before Period Raised and Lowered Effective All and Rear End Accidents

Before Period Raised and Lowered Non-Effective A11 and Rear End Accidents

VS

Measures of Effectiveness

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effective All Accident Type:

Actions ALL

Analysis WILKS Correct Correct

Type EIGENVALUE Lambda Classification Classification
FINAL Group 1 Group 2

Analysis

W /Speed 1.44 .41 88.8% 84.2%

Variables

Analysis

w/o Speed .57 .64 90.4% 67.6%

Variables

Effective All Accident Type:

Actions REAR END

Analysis WILKS Correct Correct

Type EIGENVALUE Lambda Classification Classification
FINAL Group 1 Group 2

Analysis

w/Speed 1.57 .39 94.4% 87.0%

Variables

Analysis

w/o Speed .71 .59 93.2% 73.7%

Variables

 

 

 

The findings indicate that for both accident groupings inclusion of speed
variables improves all the measures of effectiveness with the exception of Correct
Classification for Group 1, which is the effective zones grouping. The

significance of this finding is that: 1) The importance of speed variables in

distinguishing between effective and non-effective zones is confirmed, and 2)

Even without speed variables, the models correctly classify a high percentage of

the zones.

Tables 4.3 and 4.4 contain the correlation coefficients also known as pooled

within-group structure coefficients. These structure coefficients are simple

bivariate correlations with the discriminant function and are unaffected by

relationships with other variables. Also included in these tables are standardized

coefficients. These coefficients indicate the relative importance of the variable

and its contribution to the discriminant score.

 

 

 

Table 4.3
Before Period Raised and Lowered Effective Structure Coefficients and

Standardized Coefficients with Speed Variables
Accident Type: All and Rear End

 

 

 

 

 

 

 

 

 

 

 

 

 

Accident: All Accident:
Rear End
w/ Speed w/ Speed
Variables Variables
Structure Standardized Structure Standardized
Coefficients Coefficients Coefficients Coefficients
SKEWNESS .42 .93 .44 .33 SIGNAL_W
SIGNAL_W .41 .29 -.43 -.12 DRYWAYE
DRYWAYE -.38 -.12 .42 .90 SKEWNESS
EIGHT5_P .36 .60 .34 .55 EIGHT5_P
ADT .21 .63 .25 .73 ADT
RDSIDE_D .16 .49 .16 .27 SIGNAL_E
KURTOSIS .04 .48 .03 .55 KURTOSIS

 

 

 

 

 

 

 

88
Unlike structure coefficients, Klecka [1980] states "standardized coefficients take

into consideration the simultaneous contributions of other variables". Norusis
[1990] also regarding standardized coefficients adds "the actual signs of the
coefficients are arbitrary. The negative coefficients...could just as well be positive
if the signs of the other coefficients were reversed". Klecka [1980] indicates that
in discriminant analysis "structure coefficients are a better guide to the meaning
of the canonical discriminant functions than the standardized coefficients are".
Where the sign of the structure coefficients are concerned, Norusis [1990]
indicates "exercise care when attempting to interpret the coefficients, since
correlations between variables affects the magnitudes and signs of the

coefficients".

Starting with Table 4.3 the structure coefficient sizes indicate weak correlations
with the discriminant function. The groupings of variables based on the
magnitude of the structure coefficients indicates that four of the variables have
the most significant role in analyzing all and rear end accident types. They are
SKEWNESS, SIGNAL_W, DRYWAYE, and EIGHT5_P. While their order
changes based on accident type their magnitude remains approximately the

same.

 

 

 

89

Table 4.4

Before Period Raised and Lowered Effective Structure Coefficients and

Standardized Coefficients without Speed Variables
Accident Type: All and Rear End

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Accident: All Accident:
Rear End
w/o Speed w/o Speed
Variables Variables
Structure Standardized Structure Standardized
Coefficients Coefficients Coefficients Coefficients
SIGNAL_W .65 .45 -.66 .33 SIGNAL_W
DRYWAYE -.60 -.57 .64 .68 DRYWAYE
LANUSE_E .37 .36 --38 -.29 ADT
ADT .34 .14 .24 .18 LANUSE_W
LANUSE_W -.27 -.22 .17 .38 PRK_RIGH
RDSIDE_D .25 .37 .03 -.40 PRK_LEFT
FD(OB_E -.20 -.14

 

 

 

 

 

Results shown in Table 4.4 where speed variables are not included in the analysis
finds slightly stronger correlations, although still considered weak, for
SIGNAL_W and DRYWAYE. There is a sizable reduction in magnitude
compared to SIGN AL_W and DRYWAYE for other variables included in the
function. The size of the correlations of these two variables with the discriminant
function creates a distinctive grouping containing these two variables and the
remainder of the variables. This pattern occurs across all and rear end accidents.
A reversal of signs occurs on‘ SIGNAL_W, DRYWAYE, and ADT between the all
accident and rear end accident grouping. This is attributed to the difference in
variables included for rear end accidents, PRK_RIGH and PRK_LEFT. A check
for correlations in the variable sets by each accident type found no highly

correlated values.

 

90

Table 4.5
Before Period Raised and Lowered Effective Means with Speed Variables

VS

Before Period Raised and Lowered Non-Effective Means with Speed Variables,
Accident Type: All and Rear End

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

All Rear End
Effective Non- Effective Non-
, w / S eed Effective w / S eed Effective .
Variables (M e :1) (Mean) (M e ah) (Mean) Variables
SIGNAL_W 5.7 17.7 6.5 20.3 SIGNAL_W
DRYWAYE 3.1 1.03 3.2 .80 DRYWAYE
SKEWNESS .56 1.03 .52 1.02 SKEWNESS
EIGHT5_P 42.2 46.3 42.2 46.1 EIGHT5_P
ADT 23907 27815 24753 29286 ADT
RDSIDE_D 2.8 3.00 12.3 17.9 SIGNAL_E
KURTOSIS 3.14 3.19 3.13 3.17 KURTOSIS

 

 

 

Table 4.6
Before Period Raised and Lowered Effective Means without Speed Variables

VS

Before Period Raised and Lowered Non-Effective Means without Speed
Variables, Accident Type: All and Rear

 

 

 

 

 

 

 

 

 

 

 

 

 

 

All Rear End
Effective Non- Effective Non-
, w / o S eed Effective w / o S eed Effective .
Variables (M e an}; (Mean) (M e an}; (Mean) Variables
SI GNAL_W 5.7 17.7 6.5 20.3 SIGNAL_W
DRYWAYE 3.1 1.03 3.2 .80 DRYWAYE
LAN USE_E 19.2 28.1 24753 29286 ADT
ADT 23907 27815 20.5 14.9 LAN USE_W
LAN USE_W 20.3 14.8 .22 0.0 PRK_RIGH
RDSIDE_D 2.8 3.00 .13 .10 PRK_LEFT
PIXOB_E 14.7 10.5

 

 

 

91
4.5 Discussion--Before Period All and Rear End Accident Types

The mean values for the variables shown in Table 4.5 are a weighted value,
composed of the value of the variable multiplied by the frequency of accidents.
Thus, a road section with a large value for one of the variables and a moderate
accident frequency will contribute equally to the mean value as a section with

moderate variable values and a high accident frequency.
4.6 Speed Variables Included

Starting with the review of data in Table 4.5 where speed variables are in the
discriminant function, and analyzing the all accidents and rear end grouping
together, the two coded variables [of significance] are SIGNAL_W and
RDSIDE_D. For RDSIDE_D, there are three variable levels, rural(1), strip-
fringe(2), and urban(3). Both data sets are composed primarily of urban sites,
thus the value of this variable is 2.79 and 3.00 respectively. The SIGNAL_W
variable represent(s) the frequency of accidents which took place at or near
signalized intersections in the westbound direction. The non-effective zones for
all accidents and rear end accidents had 62% and 63% of their accidents
respectively near signalized intersections, while effective zones had 26% and 23%
of their accidents respectively near signalized intersections. This finding
indicates that candidate locations which have most of their accidents at or near

signalized intersections are not good candidates for speed zoning.

The DRYWAYE mean values indicate that in non-effective zones for both
accident categories, over two-thirds of the accidents were at locations where no

driveways were in the immediate vicinity. The effective zones accidents were

92
distributed throughout the range of driveway frequencies with two drive and

five drive locations having the largest proportion. Therefore, locations with a

high frequency of driveway accidents are good candidates for speed zoning.

The mean SKEWNESS value is an average of the skewness index values for the
speed distribution nearest to each accident in the respective data sets. The mean
value for effective zones is negatively skewed, indicating that a majority of
drivers are driving faster than the mean speed. A normal curve would contain
about 50% of the drivers above and below the mean speed. Since fewer drivers
(percentage-wise) are traveling below the mean speed, there is less deviation in

the speed profile, possibly leading to a safer driving environment.

The mean skewness value for the non-effective zones in both accident categories
indicate a normal curve. Approximately 33% of the values for all accidents and
27% for rear ends are negatively skewed, with the remainder in the normal range

between 1.0 and 1.17.

These findings indicate that speed zoning is found to be effective where the
speed distribution prior to implementing the speed zone has a negative skewed
distribution. This indicates that locations with an existing negative skewness

index are good sites for speed zoning.

Mean values for ADT are lower in the effective zones for both accident categories
than non-effective zones. The difference is about 5,000 vehicles per day. A
review of the frequency values for effective zones found groupings in the 12,000,
19,000, and 29,800 values. For non—effective zones groupings were found at

13,500 and 35,500. The range for the effective zones was between 7,000 and

93
29,800 compared to 6,200 to 37,590 for the non-effective. Because of the overlap

of ranges in ADT, it is not considered to be a good predictor of success in speed

zoning.

Kurtosis for both data sets were mesokurtic, and thus this does not appear to be a

good ”predictor” variable.

The effective zones 85th percentile speed was approximately 4 miles per hour
less than the non-effective zones. The difference is substantial from a speed limit
setting perspective, allowing a change of 5 miles per hour higher or lower, since
both speed raised and speed lowered zones comprise the data set. However,
because of the overlap of ranges in 85th percentile speed, it is not considered to

be a good predictor of success in speed zoning.

4.7 Speed Variables Excluded

Review of Table 4.4 and Table 4.6 indicates that the only variables which have
not been discussed and have a structure coefficient of note is LANUSE_E for all
accidents and LANUSE_W for rear ends. Starting with LANUSE_W the accident
distribution for effective zones is characterized by two land use types. One is a
retail-oriented land use with high vehicular interaction such as gasoline stations,
malls, and sit-down style restaurants, and the second is single family residential
development. The retail land use accident distribution (percentage-wise) for
accidents in effective zones is 43% and 46% for all and rear end accidents
respectively. For residential land use the distribution of accidents by all and rear
end accidents is 30% and 33% respectively. The distribution of accidents for the

two land uses in combination is 73% and 79% for all accidents and rear ends

94
respectively. For non-effective zones LANUSE_W is dominated by retail land

uses, with 82% and 88% for all and rear end accidents respectively.

Similar to the westbound land use, the accident distribution for LANUSE_E is
also characterized by retail-oriented land use and single family residential
development. The distribution of accidents at or near retail land uses in effective
zones is 48% and 54% for all and rear end accidents respectively. Similarly the
distribution of all accidents and rear end accidents at or near single family
residential land uses in effective zones is 36% and 32% respectively. These two
land uses in combination total 84% and 86% for all and rear end accidents

respectively.

For LANUSE_E in non-effective zones, residential land use comprises a very low
percentage of accident locations for all and rear end accidents. The distribution
of accidents in non-effective zones is dominated by retail land uses and
undeveloped land use. For retail the distribution of accidents is 44% and 42% for
all and rear end accidents respectively. For undeveloped land use the

distribution is 33% and 38% for all and rear end accidents respectively.

These findings for LANUSE_E indicates that retail land uses and undeveloped
land use are not good sites for speed zoning to be effective. However, zones with
retail land uses mixed with single family residential development are good

candidates for speed zoning.

The findings for LANUSE_W are similar to those for LANUSE_E. However the

accident distribution is found to be more highly concentrated at retail land use

95
sites. Retail land uses mixed with single family residential are once again found

to be good candidates for speed zoning.

4.8 Validity of the Discriminant Means and their Distributions

Unfortunately discriminant analysis procedures do not allow a frequency
distribution to be generated from the cases used to generate the discriminant
function. The discriminant analysis procedure also drops any case with a

missing value on a variable chosen to be in the discriminant function.

A reasonable question is how representative are the discriminant function data
sets compared to the total data sets used to generate the frequency distributions.
To minimize any possible difference, traffic volume (ADT), laneage, and segment
length were matched as close as possible for each test and control zone. The
percentage of the available accidents utilized by the discriminant analysis

procedure for each data set is indicated in Table 4.7.

96

Table 4.7
Percentage of Cases Utilized in Discriminant Analysis Per Data Set

 

 

 

 

 

 

 

 

 

 

 

 

Data Set Percent Utilized
BP RAISLOW EFF ALL 85%
BP RAISLOW N ON-EFF ALL 71%
BP RAISLOW EFF REAR 59%
BP RAISLOW NON-EFF REAR END 45%
AP RAISLOW EFF ALL 80%
AP RAISLOW NON-EFF ALL 63%
AP RAISLOW EFF REAR END 58%
AP RAISLOW NON-EFF REAR END 39%

 

 

 

 

A t-test was performed on the means for the variables with the largest difference
between the complete data set and the data set used to produce the discriminant
values. Those variables from discriminant data sets which use a high proportion
of cases from the all inclusive data sets were found to have no difference from the
population means at the .95 confidence limit. The differences became
increasingly more significant as the proportion of accidents decreased. These

results are shown in Table(s) 4.8 and 4.9.

Based on the results in Table(s) 4.7, 4.8, and 4.9, it appears that the mean value of
variables in the all accident data sets are equal at the .95 confidence limit

coefficient. This does not hold for the mean values in the rear end accident data

97

sets. The variable distributions described for rear end accidents therefore may be

different than the distributions used in the discriminant analysis. However, the

mean values provide a perspective on the differences between effective versus

non-effective groups.

Table 4.8

Comparison of Selected Before Period Variables Population Means vs
Discriminant Data Set Means with Results for Null Hypothesis (CL = .05)

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable BP RAISLOW BP RAISLOW BP RAISLOW BP RAISLOW
EFF ALL NON-EFF EFF REAR NON-EFF
ALL END REAR END

ADT ACCEPT REJECT REJECT REIECT
DRYWAYE ACCEPT ACCEPT ACCEPT REJECT
EIGHT5_P ACCEPT ACCEPT REJECT ACCEPT
LANEAG_E ACCEPT ACCEPT REJECT REJECT
LANEAG_W ACCEPT ACCEPT REIECT REJECT
SKEWNESS ACCEPT ACCEPT REJECT REJECT
SIGNAL_E ACCEPT REIECT REJECT REJECT
SIGNAL_W ACCEPT REJECT REJECT REJECT

 

 

 

98
Table 4.9

Comparison of Selected After Period Variables Population Means vs
Discriminant Data Set Means with Results for Null Hypothesis (0L : .05)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable AP RAISLOW AP RAISLOW AP RAISLOW AP RAISLOW
EFF ALL NON-EFF EFF REAR NON-EFF
ALL END REAR END
DRYWAYE ACCEPT ACCEPT ACCEPT REJECT
EIGHT5_P ACCEPT ACCEPT REJECT ACCEPT
LANEAG_E ACCEPT ACCEPT REJECT ACCEPT
LANEAG_W ACCEPT ACCEPT REIECT ACCEPT
SKEWNESS ACCEPT ACCEPT REJECT ACCEPT
SIGNAL_E ACCEPT ACCEPT REJECT ACCEPT
SIGN AL_W REIECT ACCEPT REJECT REJECT
4.9 Summary--Before Period All and Rear End Accident Types with and

without Speed Variables

Analysis of the combined effective data sets found SIGNAL_W and DRYWAYE

to be the most important discriminating variables. They appeared in the

discriminant functions for all and rear end accidents with and without speed

variables in the discriminant function. When speed variables were included,

SKEWNESS and EIGHT5_P had structure coefficients with a magnitude that

indicated a significant correlation to the discriminant function.

When speed variables were not included LANUSE_E (all accidents) and

LANUSE_W (rear end accidents) were identified as additional significant

variables.

 

99

The conclusion from this analysis is that speed zoning can be expected to be

effective where:

0 most accidents do not occur at or near signalized intersections,
0 the frequency of driveways is high (ranging from two to five per .1 mile

segment),
0 the skewness index is negatively skewed, and

0 land use is a mixture of retail and single family residential

Based on the findings and conclusions, if the objective was to determine where
speed zoning would be effective in reducing accidents prior to a speed limit

change, the sites would contain these characteristics.

4.10 Discussion--After Period All Accident Types

The analysis of after period data is undertaken to determine if there is a shift in
the location of accidents after the speed limit is changed. Starting with the
comparison of MOES between the after period and the before period, the MOES
in Table 4.10 (after period) compare favorably with those in Table 4.2 (before
period).

100

Table 4.10
After Period Raised and Lowered Effective All and Rear End Accidents
vs
After Period Raised and Lowered Non-Effective All and Rear End Accidents
Measures of Effectiveness

 

Effective All Accident Type:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ALL
Analysis WILKS Correct Correct
Type EIGENVALUE Lambda Classification Classification
FINAL Group 1 Group 2
Analysis
w/o Speed .62 .62 85.2% 80.0%
Variables
Effective All Accident Type:
REAR END
Analysis WILKS Correct Correct
Type EIGENVALUE Lambda Classification Classification
FINAL Group 1 Group 2
Analysis
w/o Speed .80 .55 88.4% 79.5%
Variables

 

 

 

 

Eigenvalues and Wilks lambda are also comparable, and the percentage of cases
classified correctly is similar. The ability of the discriminant functions to classify

the effective zones (Group 1) and non-effective zones (Group 2) is noteworthy.

101

Table 4.11
After Period Raised and Lowered Effective Structure Coefficients and

Standardized Coefficients without Speed Variables
Accident Type: All and Rear End

Rear End
w o

Coefficients Coefficients Coefficients Coefficients

 

Table 4.11 presents the structure and standardized coefficients from the
combined effective zones vs non-effective zones without speed variables. The
magnitude of the structure coefficients for all and rear end accidents are Close,
with almost the same variable lists. Therefore, for all and rear end accidents, the
variables most highly correlated with the discriminant function are LANEAG_W,
LANEAG_E, and DRYWAYE.

Comparing the results to Table 4.4 for the before period, SIGNAL_W
(Signalization westbound) has the largest structure coefficient with both accident
types. In the after period it is replaced by LANEAG_W and LANEAG_E under

both accident types.

102
DRYWAYE in the before period has the second largest structure coefficient after

SIGNAL_W. The magnitude of the structure coefficient in the after period is
slightly smaller than in the before period, the decrease is attributed to the
inclusion of the LANEAG_E variable.

LANUSE_E (all accidents) and LANUSE_W (rear end accidents) ranked third
and fourth respectively in the before period based on the magnitude of their
structure coefficients. In the after period, LANUSE_W is included in the
discriminant function, however, the magnitude of the structure coefficient is

small causing it to rank fourth with rear ends and fifth in all accidents.

Table 4.12
After Period Raised and Lowered Effective Means without Speed Variables
vs
After Period Raised and Lowered Non-Effective Means without Speed Variables,

Accident Type: All and Rear End

Effective w / 0 Effective

 

103
Table 4.12 lists the mean values for those variables retained in the discriminant

function without speed variables. LANEAG_W, LANEAG_E and DRYWAYE

were determined to have the largest correlations with the discriminant function.

LANEAG_E and LAN EAG_W accident distributions are within one or two
percentage points of each other for both effective and non-effective groups and
by accident type. The after period combined effective zones finds that the
accident distribution occurs primarily on 5 LN 2 WAY 12 FT LNS with 74% for
all accidents and 65% for rear ends. The after period combined non-effective
accident distribution for all accidents occurs primarily on 4 LN 1 WAY 12 FT
LNS with 44%, and the remainder distributed approximately equally between 5
LN 2 WAY 12 FT LNS and 4 LN 2 WAY 12 FT LNS. The distribution for rear
ends for non-effective finds 58% in the 4 LN 1 WAY 12 FT LNS category, with the

remainder distributed equally between the same two categories for all accidents.

These findings indicate that 5 lane highways are good candidates for speed

zoning to be effective, while 4 lane highways are not good candidates.

Laneage variables were not selected for the discriminant function in the before
period. However, a large number of accidents in the combined before period
effective occur on 5 LN 2 WAY 12 FT LNS. This finding further substantiates

that speed zoning will be effective at 5 lane sites.

In the after period the presence of driveways near the accident location was
noted for effective zones. Non—effective zones accidents occur where there were
no driveways, with 73% for all accidents and 74% for rear end accidents

respectively.

104

The after period combined effective distribution was found to have the same
type of accident distribution as the before period. The consistency of the findings
for DRYWAYE in the before and after period indicates that driveway frequency
is a good predictor of speed zoning effectiveness, but the location of accidents

relative to driveway location is not altered by changing the speed limit.

Accident distribution based on land use follows the same pattern as was found in

the before period for effective zones.

4.11 Summary--After Period

The analysis of discriminant functions and their variables in the after period is

found not to be significantly different than findings in the before period.

0 Driveway frequency was found to be a consistent roadside friction variable
indicating that the presence of driveways is a good indicator that speed
zoning will be effective.

0 Specific laneage types are found to distinguish where speed zoning is
effective. The facility associated with effective speed zoning is 5 LN 2 WAY
12 FT LNS, and 4 LN 1 WAY 12 FT LN S where speed zoning is not effective.

0 A mixture of retail and residential land uses were found to provide the
environment where speed zoning is effective.

These findings for combined effective raised and lowered speed zones in
comparison to combined non-effective zones characterize effective speed zoning
in an urban environment. Importantly, the role of skewness (index) as a

predictor variable for speed zoning effectiveness is confirmed, and the specific

105 .
characteristics and role of laneage type, driveway frequency, and land use

characteristics which determine where speed zoning will be effective are

identified.

CHAPTER 5

Analysis of Speed Limit Raised Zoning Actions

5.1 Before Period Speed Limit Raised Zoning Action

There are eight zones out of a total of thirteen that were found to be effective in
reducing accident rates after their speed limits were raised. The type of zone and

the amount which the speed limit was raised is presented in Table 5.1 below.

Table 5.1
Listing of Speed Limit Raised Effective Zones

 

106

107

These eight zones formed the speed limit raised effective group and were
analyzed in comparison to the five speed limit raised non-effective zones. A
subset of these eight zones were also effective in reducing rear end accidents.
Those identified with an asterisk (*) comprised this set. This set of zones was

analyzed with the same procedures utilized on the all accident list.

5.2 Variable Selection

Similar to the combined effective speed raised and lowered analysis, correlation
analysis and crosstabulation analysis were conducted on the two data sets to

select variables for discriminant analysis.

A compilation of the variables for the before period and accident type are shown
in Table 5.2. Those variables which are italicized indicate they are "coded"
variables, meaning that their values are not directly interpretable from the

discriminant integer output because of their qualitative nature.

108

Table 5.2

Before Period Raised Variable Identification

 

BP RAISED EFF ALL

BP RAISED EFF ALL

 

ACCIDENT TYPE: NO SELECT

ACCIDENT TYPE: REAR END

 

DATA SET: ALL DATA SET: ALL
LANEA G_ W LANEA G_ W
PERC_IN_ KURTOSIS
KURTOSIS PERC_IN_
EIGHT5_P

 

BP RAISED EFF REAR
ENDS

BP RAISED EFF REAR
ENDS

 

ACCIDENT TYPE: NO SELECT
DATA SET: REAR

ACCIDENT TYPE: REAR
DATA SET: REAR

 

 

ADT
KURTOSIS
DR YWA YE
FIXOB_ W
SKEWNESS
PRK_RIGH
SIGNAL_E
PRK_LEFT
DR YWA YW

ADT
KURTOSIS
DR YWA YE
FIXOB_ W
HAZ_ACT2
SKEWNESS
LANEAG_E

 

 

 

Table 5.3 combines the variables from both accident type analyses for the before
time period and separates the "direct" and "coded" variables. The double listing
of variables in Table 5.3 identifies the variable as being selected in both the all

zones effective and rear end zones effective data sets.

109

Table 5.3

Before Period Raised Variable Identification
Coded and Direct Variables

 

BP ALL 8: REAR

BP ALL & REAR

 

 

 

DIRECT VARIABLES DIRECT VARIABLES
ACCIDENT TYPE: NO SELECT ACCIDENT TYPE: REAR END
ADT ADT

EIGHT5_P KURTOSIS

KURTOSIS PERC_IN_

PERC_IN_ SKEWNESS

SKEWNESS

 

BP ALL & REAR

BP ALL 8: REAR

 

CODED VARIABLES
ACCIDENT TYPE: NO SELECT

CODED VARIABLES
ACCIDENT TYPE: REAR END

 

 

 

DR YWA YE
DR YWA YW
FIXOB_ W
LANEA G_ W
PRK_LEFT
PRK_ RIGH
SIGNAL_E

DR YWA YE
FIXOB_ W
HAZ_AC T2
LANEA G_E
LANEA G_ W

 

 

Various combinations of these variables were tested to determine how they
performed on discriminating between the effective zones and non-effective
zones. Wilks' lambda, eigenvalues, and the classification of the effective and
non-effective cases were the measures of effectiveness used to determine if a
combination of values had high discriminating power. The determination of
combinations with high discriminating power provides an indication of which
variables may be used to determine if a speed zone will be effective in carrying

out its' intended purpose, which is a safer driving environment.

110
5.3 Discriminant AnalysisuBefore Period Effective All and Effective Rear: All

and Rear End Accidents

The analysis was carried out on both effective all and effective rear data sets. The

variable groupings consisted of the following typology:

0 All Direct Variables common to the before period and after period,

0 All Direct Variables common to the before period and after period or
appearing in either the before period or after period,

0 All Direct and Coded Variables common to the before period and after
period and,

0 All Direct and Coded Variables common to the before period and after

period or appearing in either the before period or after period

As an example, the variable list for the before period effective all and effective

rear are as follows:

Analysis 1: KURTOSIS, PERC_IN_, SKEWNESS

Analysis 2: ADT, KURTOSIS, PERC_IN_, DRYWAYE, DRYWAYW, SKEWNESS,
and EIGHT5_P

Analysis 3: KURTOSIS, PERC_IN_, FIXOB_W, LANEAG_W, PRK_RIGH,
SKEWNESS

Analysis 4: KURTOSIS, PERC_IN_, SKEWNESS, FIXOB_W, LANEAG_W,
PRK_RIGH, ADT, DRYWAYE, DRYWAYW, EIGHT5_P, PRK_LEFT,

and SIGNAL_E

111
Discriminant analysis operations between the effective zones and non-effective

zones were repeated through each of the variable sets and discriminant functions

along with associated statistics were obtained for each analysis.

5.3.1 Before Period Raised Effective All and Effective Rear Analysis: All

Accidents

Since the same sets of variables defined the effective all and effective rear data
sets, a comparison of the measures of effectiveness was undertaken to determine
how the variable groupings performed in discriminating between the effective

and non-effective zones. The results are presented in Table 5.4.

112
Table 5.4

Before Period Effective All and Rear End Comparison of

Measures of Effectiveness: All Accidents

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effective Accident Type:
All ALL

ACCIDENTS

Eigenvalue Wilks' Correct Correct

Lambda Classification Classification
Group 1 Group 2

Analysis 1 .16 .86 57.8% 76.1%
Analysis 2 5.72 .15 100.0% 100.0%
Analysis 3 3.30 .23 94.5% 92.7%
Analysis 4 11.47 .08 100.0% 100.0%
Effective Accident Type:
Rear End ALL

ACCIDENTS

Eigenvalue Wilks' Correct Correct

Lambda Classification Classification
Group 1 Group 2

Analysis 1 .43 .70 57.2% 93.3%
Analysis 2 2.69 .27 100.0% 82.0%
Analysis 3 4.28 .19 93.4% 98.1%
Analysis 4 6.69 .13 97.5% 99.2%

 

 

 

 

 

Based on the eigenvalue, Wilks' lambda, and correct group classification for the
cases used in the analysis, the variables used to form Analysis 4 were most
effective on both the before period effective all data and effective rear data sets.
However, each of the analyses except Analysis 1 was successful in discriminating

between the two categories (successful and non-successful).

113

Table 5.5 which follows, contains the correlation coefficients and standardized

coefficients of variables for the discriminant function in Analysis 4.

Table 5.5
Before Period Raised Effective All and Rear End Variable Correlations

with respective Discriminant Functions, All Accidents

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effective All Effective Rear
End
Variable Correlation Standardized Variable Correlation Standardized
Value Coefficient Value Coefficient
LANEAG_W .29 -.39 ADT .42 .63
PRK_RIGH -.27 -.82 EIGHT5_P .39 .50
EIGHT5_P .26 2.92 LANEAG_W .38 .35
PERC_IN_ .06 .89 SKEWNESS .23 1.15
DRYWAYE -.04 .38 KURTOSIS .15 .30
FD(OB_W -.04 -.64 PRK_RIGH -.11 —1.71
KURTOSIS .03 1.87 DRYWAYE -.08 .59
SIGNAL_E .01 .14 PRK_LEFT -.05 .60
DRYWAYW —.04 .13
PERC_IN_ -.O4 .14
SIGNAL_E -.O4 .39
FD(OB_W -.O2 -.77

 

 

 

 

The effective all data set utilizes eight of the possible twelve variables to build its
discriminant function. The effective rear end utilizes all twelve variables. The
effective all correlations indicate weak association with the discriminant function.
This means no single variable or small set of variables represents a large

proportion of the power of the discriminant function.

114
The effective rear end data set variable correlations are slightly larger than the

effective all. However they too are generally considered weak. The sign of the
largest correlations are all positive indicating they are acting in concert with the
discriminant function. The conclusion is that although the individual
correlations are weak, the discriminant function is strengthened through the
breadth of variables. Their positive correlation indicate that ADT, 85th percentile
speed, laneage, and skewness can be used to distinguish between effective and

non-effective zones.

This was not the case for the effective all variables where the correlations were
weaker, there were fewer variables, and a negatively correlated variable was
among the largest. A significant finding is that 85th percentile speed is among
the top three variables in both groups. This indicates that this speed parameter is
important as a predictor variable. The same appears to be true for the coded
geometric variable, laneage westbound which appears in both lists with one of

the larger correlations with the discriminant function.

5.3.2 Mean Values for Coded and Direct Variables

Table 5.6 contains the mean values of variables used in the before period raised
effective all and rear end analysis, compared with the non-effective data set. The
mean values for the coded variables and direct variables are a weighted value,
composed of the value representing the characteristics of each analysis zones .10
mile segment and the frequency of accidents occurring in that segment. Thus, a
variable with a large value and moderate accident frequency may have a
considerable influence on the mean value. This would also be true of the

opposite situation.

115

Table 5.6

Mean Values of the Variables in the Before Period Raised
Effective All and Rear End vs
Before Period Raised Non-Effective All and Rear End,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

All Accidents

All Rear End

Variables Effective Non- Effective Non-
(Mean) Effective (Mean) Effective
(Mean) (Mean)

KURTOSIS 3.6 3.8 3.2 3.8
PERC_IN_ 75.5 77.1 78.3 77.1
SKEWNESS 1.08 1.03 .41 1.03
FIXOB_W 22.0 17.3 18.5 17.3
LANEAG_W 26.9 61.6 32.6 61.6
PRK_RIGH 2.09 0.00 .70 0.00
ADT 14485 26864 12714 26864
DRYWAYE 2.2 1.6 2.3 1.6
DRYWAYW 3.5 2.7 3.4 2.7
EIGHT5_P 38.9 44.9 34.6 44.9
PRK_LEFT 1.04 .29 .61 .29
SIGNAL_E 2.6 3.1 1.5 3.1

 

 

 

 

 

 

 

5.3.3 Coded Variables

The coded variables which were determined to be most highly correlated with
the discriminant function will be the primary focus of discussion. Referring to
Table 5.6, for the effective all and effective rear data set, for LANEAG_W the only
distinguishing characteristic is that one way streets represent a higher percentage
of non-effective zones than effective zones. However, this characteristic does not

dominate this category.

 

116
PRK_RIGH in the effective all data set had parking availability distributed on a

60/40 basis with exclusive parking comprising the higher value. Conversely,
100% of the streets in the non-effective data set had no parking allowed. It
appears speed zoning is more effective where on street parking is allowed than
on streets where it is prohibited. Generally, parking is not allowed on state

trunklines except in the central business district.

5.3.4 Direct Variables

The direct variables found to be the most highly correlated with the discriminant

function for each effective data set will be the focus of this discussion.

Referring to Table 5.6, the EIGHT5_P speed variable was identified in both the
effective data sets as a significant variable in the discriminant function. For
effective all, the mode of this variable is 38 mph, with a median of 39 mph. The
mode and median for non-effective was 48 mph. For effective rear, the mode
was 34 mph and the median 34 mph. A difference of approximately 10-14 mph
exists between the mode and median of the effective zones versus the non-

effective zones.

SKEWNESS (skewness index) for the effective all zones and non-effective zones
indicates a positive value. Effective rear exhibits a negatively skewed value with
a median of 0.00 and a mode of 0.00. A normal distribution would have a skew
value of approximately 1.0 and one standard deviation above the mean would be
very close to the 85th percentile speed. A negatively skewed distribution
indicates the majority of drivers are traveling above the mean and grouped close

to the 85th percentile speed. This also means there are a number of drivers

 

117
traveling below the mean, and thus there is potentially a large speed difference

between successive vehicles in the traffic stream.

This analysis leads to the conclusion that a negatively skewed speed distribution
in the before condition may be an indication that the speed zone will be effective
in reducing rear end accidents. Given the laneage, parking, and 85th percentile
speed values for effective rear data sets, this finding would seem to indicate that
skewness may be an important variable in determining the predicted

effectiveness of raising the speed limit.

ADT is one of the direct variables playing a role in defining the best discriminant
function for the effective rear data set. The correlation with the function was not
strong, however it was the strongest of all the direct variables. The primary
difference between the effective and non-effective data sets is the mean value.
Median and mode values also reflect this large difference, contributing to the
selection of ADT as a significant discriminating variable.

A conclusion is that streets with low to moderate ADT are more likely to realize a

reduction in accidents when the speed limit is raised.

 

 

118

Table 5.7

Before Period Raised Effective All-All Accidents
Comparison of Coefficient Sign and the Magnitude
of the Effective and Non-Effective Means

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Structure Standardized Effective Non- Larger Mean- Sign of
VARIABLE Coefficient Coefficient Mean Effective Effective vs Structure and
Mean Non-Effective Standardized
Coefficient
LANEAG_W .29 -.39 26.9 61.6 Non-Effective Mixed
EIGHT5_P .26 2.92 38.9 44.9 Non-Effective Positive
PERC_IN_ .06 .89 75.5 77.1 Non-Effective Positive
KURTOSIS .03 1.87 3.6 3.8 Non-Effective Positive
SIGNAL_E .01 .14 2.6 3.1 Non-Effective Positive
PRK_RIGH -.27 -.82 2.09 0.00 Effective Negative
DRYWAYE -.04 .38 2.2 1.6 Effective Mixed
FD(OB_W -.O4 -.64 22.0 17.3 Effective Negative

 

 

 

 

 

 

 

 

119

Table 5.8
Before Period Raised Effective Rear End--All Accidents

Comparison of Coefficient Sign and the Magnitude
of the Effective and Non-Effective Means

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Structure Standardized Effective Non- Larger Mean- Sign of
VARIABLE Coefficient Coefficient Mean Effective Effective vs Structure and
Mean N on-Effective Standardized
Coefficient
ADT .42 .63 12714 26864 Non-Effective Positive
EIGHT5_P .39 .50 34.6 44.9 Non-Effective Positive
LANEAG_W .38 .35 32.6 61.6 Non-Effective Positive
SKEWNESS .23 1.15 .41 1.03 Non-Effective Positive
KURTOSIS .15 .30 3.2 3.8 N on-Effective Positive
PRK_RIGH -.11 -1.71 .70 0.00 Effective Negative
DRYWAYE -.08 .59 2.3 1.6 Effective Mixed
PRK_LEFT -.05 .60 .61 .29 Effective Mixed
DRYWAYW -.04 .13 3.4 2.7 Effective Mixed
PERC_IN_ -.O4 .14 22.0 17.3 Effective Mixed
SIGNAL_E -.04 .39 1.5 3.1 Non-Effective Mixed
FD(OB_W -.02 -.77 18.5 17.3 Effective Negative

 

 

 

 

 

 

 

In regards to Table(s) 5.7 and 5.8, the finding is that when the structure

coefficient is signed positive, the mean values of the variable is larger in the non-

effective zones than in the effective zones. The opposite is true when the

structure coefficient is signed negative.

 

120

Thus, in the operation of the discriminant function, increasing the value of
variables (holding all other variables constant ) when their structure coefficients
are signed positive would tend to increase the separation between the effective
and non-effective groups. The opposite would hold true for variables with their
structure coefficients signed negative. Therefore, a direct interpretation of the
discriminant function for all accidents would be that lower values of the 85th
percentile speed, increased parking (higher values), and a high frequency of

driveways would be good predictors of effective speed zoning.

5.3.5 Summary Effective All and Rear End: All Accident Types

Using the size of the structure coefficients and the difference in mean values
between effective and non-effective data sets, variables were identified for in-
depth analysis. For effective all, the coded variables were LANEAG_W and
PRK_RIGH. The direct variables were ADT, EIGHT5_P, and SKEWNESS.

The effective all data set was characterized by two lane and four lane facilities
with travel in both directions. Parking was available in both directions where
accidents occurred. The volume characteristics were low to moderate, skewness

values were negative, and the 85th percentile speeds were slightly below 40 mph.

The non-effective data set was characterized by a single direction multi—lane
facility. Parking was not available, the volume levels were double those of the
effective zones, skewness values were normal, and 85th percentile speeds were a

6-10 mph higher.

121
5.3.6 Before Period Raised Effective All and Effective Rear End Analysis Rear

End Accidents

In Table 5.9, a screening procedure is used in the discriminant analysis to select
only rear end accident records. The variables determined for this analysis were
those associated with rear end accidents through the variable selection

procedures described earlier. Therefore, the variables are highly specific to rear

end accidents.

Table 5.9

Before Period Effective All and Rear Comparison of

Measures of Effectiveness,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rear End Accidents
Effective Accident Type:
All REAR END
Eigenvalue Wilks' Correct Correct
Lambda Classification Classification
Group 1 Group 2
Analysis 1 .35 .74 66.3% 82.4%
Analysis 2 1.74 .36 95.9% 82.9%
Analysis 3 2.53 .28 95.9% 90.2%
Analysis 4 3.22 .24 95.9% 92.7%
Effective Accident Type:
Rear REAR END
Eigenvalue Wilks' Correct Correct
Lambda Classification Classification
Group 1 Group 2
Analysis 1 .55 .64 63.6% 94.5%
Analysis 2 3.60 .22 99.5% 82.9%
Analysis 3 5.93 .14 97.2% 97.6%
Analysis 4 9.99 .09 99.1% 100.0%

 

 

 

 

 

 

 

122
Variables utilized in each analysis are as follows:

Analysis 1: KURTOSIS, PERC_IN_, SKEWNESS

Analysis 2: ADT, PERC_IN_, SKEWNESS, DRYWAYE, and
KURTOSIS

Analysis 3: SKEWNESS, PERC_IN_, KURTOSIS, FIXOB_W,
LANEAG_E, and LAN EAG_W

Analysis 4: DRYWAYE, PERC_IN_, SKEWNESS, FIXOB_W, ADT,
LANEAG_E, LANEAG_W, SKEW, KURTOSIS, and
HAZ_ACT2

Analysis 4 (based on the measures of effectiveness previously identified) defines
the discriminant function which performs best in distinguishing effective zones
from non-effective zones. It is not surprising that when each effective data set is
constrained to rear end accidents, the effective rear data set discriminant output
are superior to the effective all data set for rear end accidents. As in the previous
section, all of the analyses except Analysis 1 classify nearly all of the zones

correctly.

Referring to Table 5.10, seven of the possible ten variables for Analysis 4 were
utilized in determining the discriminant function for the effective all grouping.
The two laneage variables have the strongest correlations with the discriminant
function. However, the strength of the correlation for these two variables is still

considered weak.

 

 

 

 

123

Table 5.10
Before Period Effective All and Rear End Variable Correlations
with respective Discriminant Functions, Rear End Accidents

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effective All Effective Rear
End
Variable Correlation Standardized Variable Correlation Standardized
Value Coefficient Value Coefficient
LANEAG_W .52 2.77 ADT .35 2.58
LANEAG_E .32 -1.33 LANEAG_W 31 1.23
PERC_IN_ .20 .19 LAN EAG__E .22 -2.94
FD(OB_W -.10 -.22 SKEWNESS .22 1.62
DRYWAYE -.08 .56 KURTOSIS .14 .30
SKEW -.04 .76 DRYWAYE -.07 .31
HAZ_ACT2 -.O4 -.22 SKEW -.05 .49
HAZ_ACT2 -.05 -.24
FD(OB_W -.01 -.56

 

 

 

Analysis 4 contained nine of the ten possible variables for determining the

 

discriminant function for the effective rear end grouping. ADT and LANEAG_W
have the largest correlations with the discriminant function. LANEAG_E and

SKEWNESS tie for third with a smaller correlation value.

The geometric variables of laneage in both eastbound and westbound directions
are prominent in both data sets. Speed variables continue to play a role,
although they differ for each data set. This seems to indicate that speed variables

are important to the discriminant function.

124
Again, the effective rear end data set involved more variables than the effective

all data set. In both cases, the sign of the correlations were positive for the most

highly correlated variables.

To characterize the effective zones in comparison to the non-effective zones,
analysis of the variables which determined the best overall discriminant

functions were undertaken.

The same process utilized in the all accident analysis was employed here. The
analysis which determined the most effective discriminant function was Analysis
4. Therefore, an examination of variables from this analyses will provide the
comparison base. Table 5.11 identifies all ten variables that were initially
involved in determining the most effective discriminant function for Analysis 4

in both effective data sets.

125

Table 5.11
Before Period Raised Effective All and Rear End vs
Before Period Raised Non-Effective All and Rear End,

 

 

 

 

 

 

 

 

 

 

 

 

Rear End Accidents
All Rear
Variables Effective Non- Effective N on-
(Mean) Effective (Mean) Effective
(Mean) (Mean)

DRYWAYE 1.95 1.43 2.1 1.43
PERC_IN_ 74.5 77.1 78.2 77.1
SKEWNESS 1.08 1.02 .35 1.02
FIXOB_W 23.9 12.4 18.3 12.4
ADT 14138 27287 12921 27287
LANEAG_E 36.5 61.4 36.9 61.4
LANEAG_W 28.1 62.2 32.7 62.2
SKEW .19 .17 .24 .17
KURTOSIS 3.7 3.9 3.1 3.9
HAZ_ACT2 2.90 2.50 3.65 2.50

 

 

 

 

 

 

5.3.7 Coded Variables

The distinguishing difference between the effective data sets and the non-

 

effective data sets is the bi-directionality of the laneage for effective zones, as
opposed to one way facilities for non-effective zones. The laneage data type
distribution comparison continues to confirm that speed zoning is less likely to

be effective on one way multi—lane facilities.

126

5.3.8 Direct Variables

Again referring to Table 5.10, ADT is identified as one of the direct variables
playing a role in defining the best discriminant function for the effective rear data
set. The correlation was strongest overall among the direct variables. The
primary difference between the values obtained in comparing the effective and
non-effective data sets is the large difference in mean ADT values. Median and
mode values also reflect this large difference, contributing to the selection of

ADT as a significant discriminating variable.

SKEWNESS in the effective data sets controlling for rear end accident type
exhibits a pattern similar to when no accident type was selected. Effective rear
zones exhibit a negative skewness index. The value is slightly more negatively

skewed than the effective rear with no control for accident type.

KURTOSIS for both effective all and effective rear is found to be different
between the effective data sets. Effective all value is much closer to the non-
effective value and both values are leptokurtic. However for effective rear, the

value is close to the normal value of 3.0 and is considered mesokurtic.

In summary, for rear end accidents, moderate volumes, a negatively skewed
speed distribution, and a mesokurtic kurtosis are representative of speed zones

that are likely to be effective.

Before Period Raised Effective All--Rear End Accident Select

127

Table 5.12

Comparison of Coefficient Sign and the Magnitude
of the Effective and Non-Effective Means

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Structure Standardized Effective Non- Larger Mean- Sign of
VARIABLE Coefficient Coefficient Mean Effective Effective vs Structure and
Mean Non-Effective Standardized
Coefficient
LANEAG_W .52 2.77 28.1 62.2 N on-Effective Positive
LANEAG_E .32 -1.33 36.5 61.4 Non-Effective Mixed
PERC_IN_ .20 .19 74.5 77.1 N on-Effective Positive
FD(OB_W -.1O -.22 23.9 12.4 Effective Negative
DRYWAYE -.O8 .56 1.95 1.43 Effective Mixed
SKEW -.04 .76 .19 .17 Effective Mixed
HAZ_ACT2 -.04 -.22 2.90 2.50 Effective Negative

 

 

 

 

 

 

 

 

128

Table 5.13
Before Period Raised Effective Rear-—Rear End Accident
Comparison of Coefficient Sign and the Magnitude
of the Effective and Non-Effective Means

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Structure Standardized Effective Non- Larger Mean- Sign of
VARIABLE Coefficient Coefficient Mean Effective Effective vs Structure and
Mean Non-Effective Standardized
Coefficient
ADT .35 2.58 12921 27287 Non-Effective Positive
LANEAG_W .31 1.23 32.7 62.2 Non-Effective Positive
LANEAG_E .22 -2.94 36.9 61.4 Non-Effective Mixed
SKEWNESS .22 1.62 .35 1.02 Non-Effective Positive
KURTOSIS .14 .30 3.1 3.99 Non-Effective Positive
DRYWAYE -.07 .31 2.1 1.43 Effective Mixed
SKEW -.05 .49 .24 .17 Effective Mixed
HAZ_ACT2 -.05 -.24 3.65 2.50 Effective Negative
FIXOB_W —.01 -.56 18.3 12.4 Effective Negative

 

Similar to the effective all and effective rear data sets with no accident type

selected, the sign of the structure coefficients and comparison of means of

variables yields the same finding. If the structure coefficient is signed positive,

the mean value of the non-effective variable is larger than the mean of the

effective variable, the opposite being true when the structure coefficient is signed

negative.

 

129
Interpretation of the effective versus non-effective variables in Table 5.12

indicates two lane and four lane bi-directional facilities, increasing frequency of
various fixed objects, and higher frequency of driveways are indicators of

effective zones.

The interpretation of Table 5.13 suggests that lower values of ADT, two lane and
four lane bi-directional facilities, a negatively skewed speed distribution, and

higher frequency of driveways are indicators of effective speed zones.

5.3.9 Summary Effective All and Rear End: Rear End Accident Types

The coded variables and direct variables identified with effective zones indicates
that bi-directional two and four lane facilities, a higher frequency of driveways,
and a negatively skewed speed distribution determine whether the speed zoning
action will be effective. A lower range of ADT volume is also found to be

important for the effective rear data set.

5.3.10 Summary--Before Period Raised

Based on the correlation of coded and direct variables to the most effective
discriminant function obtained, and the comparison of the mean values of these
variables, it was determined that effective speed zones can be characterized as
containing bi—directional two lane and four lane streets, ADT volumes in the
range of 6,000 to 9,000, and a speed distribution which is negatively skewed.
These characteristics were found to be present generally across both effective

data sets and with analysis for all and rear end accident types.

130
5.4 Analysis of After Period Speed Raised Zoning Action

As indicated in Chapter 2, Methodology, speed data were not available in the
after period and therefore could not be used in the discriminant analysis.
Consistent with the approach outlined in the methodology, the after period data
will be utilized to compare the change in variable levels between effective and
non-effective groups between the before and after period. The complete data set
is used to determine the mean values for each variable, as opposed to the means
generated from the cases utilized in discriminant analysis. This provides a much
broader spectrum of cases for effective and non-effective data sets, and would
give a complete representation of the data since no cases would be dropped as in

discriminant analysis for missing variables.

5.4.1 Comparison of the Change in Mean Values Between Time Periods for
Location Sensitive Variables-Effective All (All Accidents)

Table(s) 5.14 and 5.15 below compares the mean values of the six parameters that
vary by location within a given zone. These are: DRYWAYE, DRYWAYW,
FD(OB_E, FIXOB_W, SIGNAL_E, and SIGNAL_W. Table 5.14 contains the
values for the effective and non-effective data set(s) for all accidents, while Table
5.15 contains the mean values for the effective and non-effective data set(s) with

rear end accidents.

A t-test was performed on the effective data between the after period mean
values and the before period mean values. The null hypothesis is that the means
of the variables for the before and after data sets are the same, indicating that no

statistically significant change at the .95 confidence level has occurred in the

131

value of the variable within the .10 mile segment (weighted) where accidents

occurred. A change in this case is the result of a shift in the location of accidents

from the before period to after period, leading to a different mean value in the

after period.

Table 5.14
Comparison of the After Period Means with Before Period Means

of Location Sensitive Variables in Discriminant Analysis,
Effective All Data Set--All Accidents

 

 

 

 

 

 

 

 

 

 

EFFECTIVE NON-EFFECTIVE
Variable BP AP t-test @ 0!- BP AP t-test @ 0L
: .95 = .95
DRYWAYE 2.1 2.3 ACCEPT 1.6 1.0 REJECT
DRYWAYW 3.5 3.3 ACCEPT 2.7 2.1 REJECT
FD(OB_E 21.6 20.2 ACCEPT 13.2 12.5 ACCEPT
FIXOB_W 22.0 19.0 REJECT 17.3 19.2 REJECT
SIGNAL_E 2.6 4.2 REJECT 3.1 3.5 REJECT
SIGNAL_W 1.7 2.8 REJECT 11.5 14.0 REJECT

 

 

 

 

 

 

 

 

The results of the t-test for driveway frequency across effective and non-effective

data sets indicate that approximately the same number of driveways in both time

periods were at locations where accidents occurred in the effective zones,

however, the number of driveways were significantly less in the after period for

non-effective zones. This finding is consistent with earlier findings that non-

effective zones have fewer driveway related accidents.

 

132
For both effective and non-effective data sets the Signalization variables reject the

null hypothesis. In both data sets there is an increase in accidents in the after
period. The larger increase in accidents for the effective data set may be
attributed to drivers adjusting to the new speed limits, while in the non-effective
data set, the speed limit increase caused minimal driver adjustments since they

were already driving faster than the existing speed limit.

Table 5.15
Comparison of the After Period Means with Before Period Means

of Location Sensitive Variables in Discriminant Analysis
Effective All Data Set--Rear End Accidents

 

 

 

 

 

 

 

 

 

 

 

EFFECTIVE NON-EFFECTIVE
Variable BP AP t-test @ 0: BP AP t-test @ CL
= .95 = .95

DRYWAYE 1.9 2.2 ACCEPT .. 1.4 0.6 REJECT
DRYWAYW 3.6 3.6 ACCEPT 1.9 1.6 ACCEPT
FIXOB_E 22.6 23.9 ACCEPT 12.4 11.5 ACCEPT
FIXOB_W 23.8 22.4 ACCEPT 17.4 20.9 REJECT
SIGNAL_E 3.4 4.3 ACCEPT 2.9 2.9 ACCEPT
SIGNAL_W 2.0 2.1 ACCEPT 12.9 16.8 REJECT

 

 

 

 

 

Table 5.15 confirm that speed zoning is least effective in reducing rear end
accidents where there is a pre-existing high accident frequency at or near

signalized intersections.

133
5.4.2 Summary-Change in Mean Values Between Time Periods for Location

Sensitive Variables—Effective All (All Accidents)

A comparison of the findings between the effective data sets and non-effective
data sets mean values across time periods finds that the conclusions from the
before period regarding characteristics of effective speed zoning are validated
using the after period data sets. Where rejection of mean values in the effective

data set occurred, the differences were minimal.

5.4.3 Summary--Analysis of After Period Speed Raised Zoning Action

The findings indicate that the before period location or environmental conditions
predicting effectiveness of speed zoning are found to be consistent with the
location and conditions in the after period. This indicates that: (1) there has not
been a statistically significant shift in accident locations within the speed zone,
and (2) the consistency in the results suggests that the methodology undertaken

here to characterize effective and non-effective zones is valid.

 

CHAPTER 6
Analysis of Speed Limit Lowered Zoning Actions
6.1 Before Period Speed Limit Lowered Zoning Action
There are seven zones out of a total of thirteen that were found to be effective in

reducing accident rates after their speed limits were lowered. The type of zone

and the amount which the speed limit was lowered is presented in Table 6.1

 

 

 

 

 

 

 

 

 

 

below.
Table 6.1
Listing of Speed Limit Raised Effective Zones
Districts Zone Zone Type
District 8* 33—001-84TA UL—5, 40 TO 35
District 8 33-001-84TB TL-5, 50 TO 45
District 8* 33-001-84TC UL-10, 45 TO 35
District 8* 81-003-85T UL-5, 45 TO 40
District 8* 81-023-84 UL-10, 45 TO 35
District 8* 33-028-88T UL-10, 35 TO 25
District 9* 82-049-85TA TL-5, 45 TO 40

 

 

 

 

A subset of these seven zones were also effective in reducing rear end accidents.
Those identified with an asterisk (*) comprised this set. This set of zones

effective in reducing rear end accidents are not analyzed separately for speed

134

135

lowered zoning actions because their results in discriminant analysis indicated

no difference with the effective all data set restricted to rear end accidents.

6.2 Variable Selection

Similar to the analysis performed on the before period speed limit raised zones, a
variable selection process was conducted which led to an initial set of variables
utilized in a stepwise discriminant analysis. The stepwise variable selection
process was performed to identify variables which contributed the majority of
the minimization of Wilks' lambda. As before, variables which contributed
approximately 80% to 85% of the minimization of Wilks' lambda were identified
and used in the analyses. Also, accident type was investigated in conjunction
with variable selection to determine if certain variables were related to accident

type in discriminating between effective and non-effective zones.

For the before period lowered effective analysis, the effective all data set is
analyzed for all and rear end accidents. Table 6.2 displays the results of the

variable selection process from the stepwise discriminant analysis.

136
Table 6.2
Before Period Lowered Variable Identification

 

 

 

 

 

 

BP LOWERED EFF ALL BP LOWERED EFF ALL
ACCIDENT TYPE: ALL ACCIDENTS ACCIDENT TYPE: REAR END
DATA SET: ALL DATA SET: ALL

DRYWAYE ADT

EIGHT5_P DRYWAYE

ROAD_ TYP SIGNAL_E

SKEWNESS SIGNAL_ W

SIGNAL_ W SKEWNESS

BP LOWERED EFF REAR BP LOWERED EFF REAR
ACCIDENT TYPE: ALL ACCIDENTS ACCIDENT TYPE: REAR END
DATA SET: REAR DATA SET: REAR

DRYWA YE DRYWA YE

SIGNAL_ W PERC_IN_

PERC_IN_ SIGNAL_ W

SKEW SKEW

SKEWNESS SKEWNESS

 

 

 

 

6.3 Discriminant Analysis--Before Period Effective All: All and Rear End

Accidents

Accident types of interest consisting of all and rear end were identified for each
discriminant run with each combination of variables. The variable groupings

generally consisted of the following typology:

0 Analysis 1: All Direct Variables common to before period and after
period,

0 Analysis 2: All Direct Variables common to before period and after
period and in either the before period or after period,

137
0 Analysis 3: All Direct and Coded Variables common to before period
and after period and,
0 Analysis 4: All Direct and Coded Variables common to before period
and after period and in either the before period or after period

As an example, the variable list for the before period effective all is as follows:

Analysis 1: PERC_IN_, SKEWNESS

Analysis 2: EIGHT5_P, PERC_IN_, SKEWNESS, and SKEW

Analysis 3: DRYWAYE, PERC_IN_J SKEWNESS, ROAD_TYP, and SIGNAL_W

Analysis 4: DRYWAYE, EIGHT5_P, PERC_IN_, SKEW, SKEWNESS,
ROAD_TYP, and SIGNAL_W

Discriminant analysis operations between the effective zones and non—effective
zones were repeated through each of the variable sets and discriminant functions

obtained for each analysis along with associated statistics.

6.3.1 Measures of Effectiveness—-Before Period Lowered Effective All Analysis:
All Accidents

A comparison of the measures of effectiveness was undertaken to determine how
the variable groupings performed in discriminating between the effective and

non-effective zones. The results are presented in Table 6.3.

138
Table 6.3
Before Period Effective All Comparison of
Measures of Effectiveness: All Accidents

Lambda Classification Classification

 

Based on the eigenvalue, Wilks' lambda, and correct group classification for the
cases used in the analysis to derive the discriminant function, the variables used
to form Analysis 4 were slightly more effective on the before period effective all
data set with no specific accident type analyzed.

Table 6.4 which follows, contains the correlation coefficients as previously
defined for the discriminant function in Analysis 4.

139

Table 6.4
Before Period Lowered Effective All Structure Coefficients and
Standardized Coefficients

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effective All
Variable Structure Standardized
Coefficients Coefficients

SIGNAL_W .48 .54
SKEWNESS .46 .63
DRYWAYE -.45 -.34
EIGHT5_P .26 .56
SKEW -.19 -.19
PERC_IN_ -.17 -.21
ROAD_TYP -.1O —.84

 

 

 

Table 6.5
Mean Values of the Variables in the Before Period Lowered Effective All
vs Before Period Lowered Non-Effective-—All Accidents

Variab
I NAL_W

DRYWA E
El P

PERC_IN_
R

 

140

6.3.2 Coded Variables

SIGNAL_W has a relatively large positive structure coefficient indicating that it
acts in concert with the discriminant function to discriminate between the
effective and non-effective groups. The sign of the standardized coefficient is

also positive.

Large values on SIGNAL_W would increase the function value. The desire is to
have the largest distance or space possible between the two data sets. The mean
values indicate that the frequency distribution of coded values is such that the
mean is larger for non-effective zones. Review of the specific codes and their
percentages within each data set reveals that effective zones have approximately
70% of their accident locations where there was no Signalization in the

westbound direction, compared to 37% for non-effective zones.

This fact, along with the positive sign of the standardized coefficient, indicates
that larger values on the variable will lead to large function values. The absence
of a strong correlation with any other variables except SIGNAL_E tends to
support the belief that the coefficient is accurate and not compromised. This
lends strong support to the conclusion that zones with fewer accidents at

signalized locations will more likely benefit from speed zoning

DRYWAYE has a negative sign on both the structure coefficient and
standardized coefficient. For the structure coefficient this indicates a negative
correlation with the discriminant function. The size of the structure coefficient is

not large, and in general, correlation values of this magnitude would be

141
considered weak. The sign indicates that the variable acts against or inverse to

the discriminant function attempting to achieve the largest space between the
effective and non-effective data sets. The presence of a large number of

driveways would tend to decrease the size of the discriminant function value.

The standardized coefficient is not correlated with other variables, leading to the
conclusion that this coefficient is not sharing its' contribution on the discriminant
function with other variables to a meaningful degree. Although there are no
large correlations, DRYWAYE has its' largest correlation with LANEAG_E and
LANEAG_W at -.43 for both. Since this correlation is not positive and large it
does not appear that the magnitude and sign would be affected for DRYWAYE .
The size of the standardized coefficient places it second among those with a
negative sign, and fifth among all such coefficients regardless of sign. This

denotes its’ overall weak role in determining the discriminant function value.

For DRYWAYE analysis of the distribution for effective all indicates 82% of
accidents in effective zones occurred where driveways were present. In
comparison, for non-effective zones, this percentage for all driveway frequencies
was 25%. The remaining 75% were locations where no driveways were present.
Driveway frequency for this data set is associated with decreasing the
discriminant function value. In this case, the high frequency values are
associated with effective zones. However, since the correlation of the structure
coefficient is described as weak and the standardized coefficient absolute
magnitude is small, the descriptive impact of the coefficients is minimized.
Instead, the means and distributions of the effective and non-effective data sets
are clear in their description of the characterization of effective vs non-effective

speed zones.

142

6.3.3 Direct Variables

The structure coefficient for SKEWNESS indicates a weak positive correlation
with the discriminant function. The positive sign indicates that increasing values

for skewness will serve to increase the discriminant function value.

The standardized coefficient is also positive. However, the variable was found to
be moderately negatively correlated (-.53) with ADT. This relationship is
interpreted to mean that SKEWNESS does not share the same information as
ADT. The moderate degree of correlation is also interpreted to mean that the
likelihood of the magnitude and sign of the standardized coefficient being very
different is unlikely. Values found in the distribution of each data set for
SKEWNESS and factored by the standardized coefficient for SKEWNESS are

expected to contribute to maximizing the function value.

Review of the distribution of values for skewness for the effective all data set
indicate that 77% of accident locations occurred where the speed was negatively
skewed. For non-effective zones, this percentage was 45%. The negatively
skewed speed distribution indicates that drivers were selecting speeds which
were spread less throughout the speed distribution and were generally clumped
together at or near the 85th percentile speed. The opposite behavior would lead
to a positively skewed distribution, meaning a greater variation in driver speeds
throughout the speed profile and from various findings a recognition that this is
a more unsafe driving condition because of the speed variation in the traffic
stream. The finding in relation to speed zoning effectiveness is that locations

which have a speed profile in the before period which tends to be negatively

 

143

skewed are found to be a precursor of effective speed zones. This fact may

indicate that this variable may be used to predict the effectiveness of speed

zoning prior to the speed limit change.

An interesting finding involves the signs of the structure coefficients and

standardized coefficients and whether the means of the effective zones were less

than or greater than the means of the non—effective zones. Table 6.6 separates the

variables and related coefficients first by sign of the coefficients and then ordered

by structure coefficient size.

Table 6.6

Before Period Lowered Effective All--All Accidents
Comparison of Coefficient Sign and the Magnitude of
the Effective vs Non-Effective Means

 

 

 

 

 

 

 

 

 

VARLABLE Structure Standardized Effective Non- Larger Mean- Sign of
Coefficient Coefficient Mean Effective Effective vs Structure and
Mean Non-Effective Standardized
Coefficient
SI GNAL_W .48 .54 7.4 23.3 Non-Effective Positive
SKEWNESS .46 .63 .47 1.03 N on-Effective Positive
EIGHT5_P .26 .56 42.9 46.3 Non-Effective Positive
DRYWAYE -.45 -.34 3.4 .72 Effective Negative
SKEW -.19 -.19 .06 .03 Effective Negative
PERC_IN_ -.17 -.21 76.9 72.9 Effective Negative
ROAD_TYP -.10 -.84 2.06 2.00 Effective Negative

 

 

 

 

 

 

 

 

144
6.3.4 Summary--Before Period Effective All:

A review of those variables with significant structure coefficients and a
comparison of their means and distributions indicate that for the effective all
data set, speed zoning effectiveness was characterized by zones with fewer
accidents at signalized intersections, a negatively skewed speed distribution, and
a high driveway density as compared to non-effective zones where speed limits

had been lowered.

6.3.5 Before Period Effective All Analysis--Rear End Accident Select

In comparing the measures of effectiveness and mean values for variables used
in the most effective analysis, the selection of rear end accidents as the accident
type was conducted for both the effective all data set and the non-effective data
set. Therefore, the results are specific to rear end accidents in both effective and

non-effective data sets.

145

Table 6.7
Before Period Effective All Comparison of
Measures of Effectiveness: Rear End Accident Type Selected

 
   
  

   
  
 
   

  
  

Accident Type:
REAR ENDS

e
All

    

1.18

   
  
  

Eigen

  
  

  

Classification Classification
G 1 G 2

Lambda

    

   

  
  
    
 
 
 

  
      
    
  

       
    
    
 

     
     
    
 

     
    
   
   

.72
.69
.40
.38

79.
83.9%
95
95

96.
96.
83.6%

.39

.46
1.51
1.66

For effective all zones where rear end accident types are selected and analyzed as
a group, the measures of effectiveness (MOE) identify the variables used in

Analysis 4 as the most effective. The specific variables used in this analysis are:

Analysis 4: DRYWAYE, EIGHT5_P, PERC_IN_, SKEW, SKEWNESS,
ROAD_TYP, and SIGNAL_W

Table 6.8 which follows, contains the correlation coefficients of variables for the
discriminant function in Analysis 4. Similar to effective all with all accident
types, variables that formed Analysis 4 are displayed with their structure

coefficients and standardized coefficients.

146
Table 6.8
Before Period Lowered Effective All Structure Coefficients and
Standardized Coefficients: Rear End Accidents

 

 

 

 

 

 

 

 

 

 

 

 

Effective Rear
Variable Structure Standardized]
Coefficients Coefficients

DRYWAYE -.54 -.43
SIGNAL_W .54 .71
SKEWNESS .39 .43
EIGHT5_P .28 .56
PERC_IN_ -.22 NT
SKEW -.17 -.17
ROAD_TYP -.07 -.50

 

 

 

 

 

 

147

Table 6.9
Before Period Lowered Effective All vs
Before Period Lowered N on-EffectivenRear End Accidents

DR AYE
SIGNAL_W

EI _P
PERC_IN_

R AD__TYP

 

Table 6.10

Before Period Lowered Effective All--Rear End Accident Selected
Comparison of Coefficient Signs and the Magnitude of
the Effective vs Non-Effective Means

 

 

 

 

 

 

 

 

 

 

 

VARIABLE Structure Standardized Effective Non- Larger Mean- Sign of
Coefficient Coefficient Mean Effective Effective vs Structure and
Mean Non-Effective Standardized
Coefficient
SIGNAL_W .54 .71 7.8 25.8 Non-Effective Positive
SKEWNESS .39 .43 .49 1.02 Non-Effective Positive
EIGHT5_P .28 .56 42.4 45.9 Non-Effective Positive
DRYWAYE —.54 -.43 3.4 .39 Effective Negative
PERC_IN_ -.22 NT 78.3 72.9 Effective Negative
SKEW -.17 -.17 .06 .03 Effective Negative
ROAD_TYP -.07 -.50 2.00 2.00 Tie Negative

 

 

 

 

 

 

148

6.3.6 Coded Variables

DRYWAYE has a relatively large negative structure coefficient, indicating that it
is not acting in concert with the discriminant function. The negative correlation
indicates that in this case driveway frequency has an inverse relationship with
the discriminant function. The standardized coefficient is also negative, however
its' magnitude relative to all other standardized coefficients is not very large and
therefore the impact on the function value is minimal relative to the other
coefficients. In general, the impact of the negative sign would tend to decrease
the discriminant function value, thereby diminishing the separation between the

data sets.

In the non-effective category 82% of the accident occurrences were where there
were no driveways. In comparison to the effective zones, the category with the
largest percentage is five driveways with 36%. The effective category had 89% of
its‘ accident occurrences where at least one driveway was present. This
cumulative percentage value is comparable to the effective all no accident select
data set which was 82%. For the non-effective data set no accident select, the
accident locations with driveways was 25% compared to the effective all rear end
accident select of 18%. For DRYWAYE, it is concluded that a high frequency of

driveways characterizes effective speed zoning where the speed limit is lowered.

SIGNAL_W is similar to the select all accident data set and has relatively large
positive values for the structure and standardized coefficients. The difference
here is that the standardized coefficient is the largest among these coefficients,

where for select all it was third in magnitude. The magnitude of the coefficient in

 

149
this data set may indicate that Signalization plays a more important role in

identifying zones where rear end accidents are reduced than in identifying those

where all accidents are reduced.

It was found that 68% of accident occurrences took place where there was no
Signalization present in effective zones compared to 27% in the non-effective
zones. The percentages for no Signalization present are very similar between the
effective zone for all and rear end accidents. However, the percentages for no
accident occurrence in the comparison of non-effective zones for all and rear
accidents indicate that rear end accidents occur somewhat more frequently (73%
vs 63%) at signalized intersections. This finding may indicate that speed zones
may exhibit minimal differences in accident involvement near signalized
intersections by all and rear end accident types. In conclusion, for SIGNAL_W,
the lack of accidents at or near signalized intersections is found to characterize

effective speed zoning where the speed limit is to be lowered.

6.3.7 Direct Variables

The structure coefficient for skewness is positive and in overall magnitude is
third behind SIGNAL_W and DRYWAYE . The positive sign on the coefficient
indicates that values for the variable will lead to increasing the overall

discriminant function value.

The comparison between data sets indicate that for effective all rear end accident
select, 80% of the accidents occurred where there was a negatively skewed speed
profile compared to non-effective with 55%. The vast majority (54%) of accident

occurrences in the effective all rear end select data base were associated with a

150
skewness index value of 0.0. The largest skewness index value for effective all

(rear end accidents) was 1.09 with 7.0% of all occurrences. This compares to a

skewness index value of 1.17 at 23.0% for non-effective all.

Comparing the two effective data sets, reveals that the percentage of accidents
occurring where negative skewed profiles were obtained are fairly close, 77% for
effective all no accident select and 80% with rear end accident select. The
difference between non-effective values is 10% with non-effective all at 45% and
non-effective rear with 55% for negatively skewed speed profiles. The key
difference appears to be that a larger proportion of rear end accidents occurred
where the speed profile was negatively skewed prior to implementing the speed
zone. The conclusion is an existing negatively skewed speed profile is a

characteristic for effective speed zoning where the speed limit is lowered.
6.3.8 Summary--Before Period Effective All Analysis-Rear End Accidents

The variables found to be effective in discriminating between the effective and
non-effective data sets are essentially the same found for the all accident analysis.
For rear end accidents the structure coefficient sizes were marginally smaller
than the all accident analysis. However, the mean values were consistent with
related findings in the all accident case. Therefore, the characteristics for
effective speed zoning when speed limits are lowered and rear end accidents

analyzed are essentially no different than the all accident case.

151

6.4 Analysis of After Period Speed Lowered Zoning Action

Similar to the analysis conducted in the after period speed raised discussion, the
means of variables which reflect a change in the location of accidents would
indicate if the conditions and locations predicted for effective zones are
confirmed in the after period. The same variables of : DRYWAYE, DRYWAYW,
FIXOB_E, FIXOB_W, SIGNAL_E, and SIGNAL_W will be compared between the
before and after time periods for effective all data sets, as well as non-effective,
for all and rear end accident type. As with speed raised, the complete data set is
used to determine the mean values for each variable, as opposed to the means

generated from the cases utilized in discriminant analysis.

6.4.1 Comparison of the Change in Mean Values Between Time Periods for
Location Sensitive Variables

Again, similar to the after period raised analysis, a comparison of the mean
values between the before and after time periods for effective all and rear data
sets with non-effective data sets is undertaken. Table 6.11 below compares the
mean values of the effective all data set for all accident types with the non-

effective data set, also including all accident types.

152
Table 6.1 1
Comparison of the After Period Means with Before Period Means

of Location Sensitive Variables in Discriminant Analysis,
Effective All Data Set--All Accidents

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EFFECTIVE N ON-EFFECTIVE
Variable BP AP t—test @ 0t BP AP t-test @ 0:
= .95 = .95
DRYWAYE 3.3 3.3 ACCEPT .90 1.1 ACCEPT
DRYWAYW 2.0 2.2 REIECT 1.5 1.9 REIECT
FIXOB_E 12.9 13.8 REIECT 9.6 9.9 ACCEPT
FIXOB_W 14.9 17.1 REJECT 11.9 11.2 ACCEPT
SIGNAL_E 11.5 13.3 REJECT 17.6 13.9 REJECT
SIGN AL_W 6.9 8.9 REJECT 19.9 15.3 REJECT

 

Reviewing the results for driveways indicates that although the null hypothesis
was not accepted in both directions, the actual differences are small. The
important factor is that there is no substantial change in number of driveways in
the effective data set and that the values are not decreasing. In the non-effective
data set the values increased in the after period, indicating a shift toward
locations with more driveways. The results are consistent with earlier findings,
which predicted that the level of driveway frequency in the before period would
be higher than that found in non-effective zones. The results indicate that this is

also true for the after period when compared to the non-effective zones.

The null hypothesis for fixed objects is rejected for the effective data set and
accepted for the non-effective. This finding indicates that the location of

accidents in relation to type and frequency of fixed objects has changed for the

153
effective data set. The increase in the mean value indicates an increase in types

of objects associated with an urban environment. Where for the non-effective
data set, acceptance of the null hypothesis indicates no change between time
periods. The significance of this finding for non-effective zones is that no change
in fixed objects indicates accidents are occurring in approximately the same
locations identified with non-effective zones and rejection of the null hypothesis
is further substantiation of the predicted characteristics for effective speed

zoning.

Signalization results for effective data sets finds the null hypothesis is rejected
primarily because of the increase in values. Where for non-effective the opposite
is true. These results indicate that for effective zones there may be a slight
increase in accidents at or near signalized intersections, where for non-effective
there is a more substantial shift in location away from signalized intersections.
Overall, the finding for effective zones is still valid for signalized intersections,
which is that their mean values are less than for non-effective zones. However,
here it appears that the action of lowering the speed limit in non-effective zones

has an impact on the distribution of accidents away from intersections.

The results of the t-test for the comparison of mean values between time periods
for the effective all and non-effective data sets confirms the findings from the
discriminant analysis regarding the location of accidents in the effective and non-

effective zones.

Table 6.12 presents the results of the t—test for the effective all data set with rear

end accidents and the non-effective data set restricted to rear end accidents.

154

Table 6.12

Comparison of the After Period Means with Before Period Means

of Location Sensitive Variables in Discriminant Analysis

Effective All Data Set--Rear End Accidents

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EFFECTIVE NON-EFFECTIVE
Variable BP AP t-test @ 0: BP AP t-test @ a
= .95 = .95
DRYWAYE 3.3 3.3 ACCEPT .60 .65 ACCEPT
DRYWAYW 1.9 2.3 REJECT 1.7 2.3 REJECT
FIXOB_E 12.4 12.9 ACCEPT 9.4 10.7 ACCEPT
FIXOB_W 15.7 17.8 REIECT 13.2 12.8 ACCEPT
SIGNAL_E 13.3 13.4 ACCEPT 20.9 17.4 REIECT
SIGNAL_W 7.3 9.8 REIECT 22.6 15.5 REJECT

 

The mean values for driveways and the results of the t-test are not substantially

different than the effective all case. The findings indicate that there is no

substantial change between time periods for either effective all or non-effective

data sets. The important point being that the values indicate that the locations

are essentially the same for both data sets, with values for both consistent with

predictions from discriminant functions.

Fixed objects for the effective data set are found to either not change or increase,

while for the non-effective essentially no change is registered. Importantly, the

consistency in results again conforms earlier findings of the location of accidents

for effective and non-effective data sets relative to roadside friction elements.

 

155
Therefore, the agreement provides additional confirmation that effective data

sets would have a higher mean value relative to non-effective data sets.

The t-test results for Signalization for effective all finds no change or a slight
increase in mean values. Where for non-effective the decrease in mean values is
also found here, leading to rejection of the null hypothesis. Similar to the
effective all and all accident case, the substantial lack of change in locations is
found for rear ends. And, the pattern for non-effective is repeated, with values
indicating a shift in locations away from signalized intersections. The
consistency of the locations for the effective zones is confirmed. The shift in
locations for the non-effective indicates the action of lowering limits has had a
limited effect on shifting accident locations relative to signalized intersections.
The conclusion however is that the predicted locations of accidents in
discriminant analysis relative to signalized intersections for effective zones and

non-effective zones is upheld.

CHAPTER 7

Summary and Conclusions

7.1 Basis and Objectives

An analytical study was performed on twenty-six speed zones to determine
those factors which are associated with the effectiveness of speed zoning in
urban areas. The sites are located in the state of Michigan and the zones were

implemented between 1983 and 1989.

The objectives of this research were to: (a) determine if the speed zoning actions
undertaken by the state were effective in reducing accidents, and, (b) to develop
a model to predict the conditions under which a speed zoning action would be

effective.

7.2 Conduct of the Research

The research project was performed in three phases: (1) an analysis of the
accident history in the subject sites and matched control sites to determine which
zones had been effective in achieving a statistically significant reduction in
accidents, (2) an analytical investigation of speed related, roadside friction, and

roadway related factors to determine which characteristics are associated with

156

157
effective and non-effective speed zones, and (3) an investigation of the

consistency of the characteristics associated with effective and non-effective

speed zones after implementation.

7.3 Summary and Conclusions of Each Phase of Research

A summary of each phase of the research undertaken with conclusions derived at

each phase are presented below.

(1) Effectiveness of Speed Zones: The results in this study indicate that speed
zoning was not effective in the aggregate in reducing accidents at the .05 level of
significance for speed zones where the speed limit was raised, in speed zones

where the speed limit was lowered, and in all speed zones.

These results are consistent with past experience which also show mixed results
from speed zoning. In Michigan as in other locations, simply changing the speed
limit sometimes results in a decrease in accidents and other times results in an

increase or no change in accidents.

(2) Predicted Characteristics of Effective Speed Zoning: The derivation of
mutually exclusive groups (i.e. effective and non-effective speed zones) utilized
in discriminant analysis procedures permitted the identification of variables that

distinguish between the groups.

In the analysis, the most significant variables identified by the discriminant
functions were: skewness index, Signalization, driveway frequency (density), and

85th percentile speed. In general the following was found for effective zones:

 

158

0 The speed distribution is negatively skewed,

0 Relatively few accidents occur at or near signalized intersections,

0 Driveway frequency is higher by a factor of three (compared to non-
effective zones), and

0 85th percentile speeds were lower.

When speed variables were omitted from the analysis the role of Signalization
and driveways were unchanged, and land use and ADT became prominent

variables.

In the sites studied, using these variables to define a discriminant function
model, over 90% of the speed zones were correctly classified as effective or non-

effective.

(3) Temporal Stability of Predicted Characteristics of Effective Speed Zoning:
Analysis of the characteristics and variables in the period of time after
implementation of the zoning action was undertaken. The analysis focused on
those variables which would indicate if there had been a significant change in the
location of accidents in the after period. The variables utilized for this analysis
are: driveway density, fixed object density, and the presence of a signalized

intersection within .10 miles of each accident.

The results of the analysis indicate the accident locations did not shift
significantly. In general, the change in mean values from the before period to
the after period were not statistically significantly different. Where this was not

the case, the difference was not significant in practical terms.

IL

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