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6/07 p:/ClRC/Date0ue.indd-p.1

A COMPARISON OF USER PERFORMANCE ON
SPECTRAL COLOR AND GRAYSCALE
CONTINUOUS-TONE MAPS
By

Michael D. Hyslop

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

MASTER OF ARTS

Department of Geography

2007

ABSTRACT

A COMPARISON OF USER PERFORMANCE ON
SPECTRAL COLOR AND GRAYSCALE
CONTINUOUS-TONE MAPS
By

Michael D. Hyslop

Continuous surfaces such as elevation, precipitation, and temperature are often mapped
using isarithms. These representations may be difficult for map readers to understand.
Continuous-tone maps are an alternate way of depicting continuous surfaces. Three real
surfaces were used to generate continuous-tone maps using spectral color and grayscale
color schemes. To assess the effectiveness of these maps, fifty nine subjects were tested.
Questions were designed to evaluate how the color scheme affected perception of the
surface, and to compare performance on specific map reading tasks. Subjects were shown
a grayscale and a spectral color representation of each of the three surfaces. Questions
involved the location of surface extremes, elevation estimation, profile identification,
landscape position, and interpretation of surface form. Subjects performed significantly

better on the spectral color maps than on the grayscale maps.

T o my family, for their support and encouragement

iii

ACKNOWLEDGEMENTS

My thanks to the Department of Geography and the Center for Remote Sensing (now
Remote Sensing & Geographic Information Science Research and Outreach Services) for
financial assistance as a Teaching and Research Assistant while I was at MSU.

My thanks also to Dr. Richard Groop and Dr. Judy Olson for their guidance
throughout the course of my research. It would not have been completed without their
help, suggestions, and answers to my many questions and problems. Dr. David Lusch
served as third reader and provided invaluable comments and final edits to this
manuscript.

In addition, I must acknowledge my colleagues at Michigan Technological
University. Their persistence in encouraging the completion of this thesis is appreciated.

Finally, I would like to thank my parents for always supporting learning, especially
my father for suggesting I “take a few Geography classes”; and special gratitude to Mary,
Ian, Sean, Wes and Seth for putting up with my many late nights and weekends over the

past year.

iv

TABLE OF CONTENTS

LIST OF TABLES ...................................................................................................... vi
LIST OF FIGURES ................................................................................................... vii
Chapter I An Introduction To Quantitative Surface Maps ................................... 1
Chapter 11 Statement of Problem ......................................................................... 10
Chapter III The Map Test ...................................................................................... 13
Chapter IV Results ................................................................................................. 25
Chapter V Summary and Conclusions ................................................................. 52
References ........................................................................................... 55
Appendices
Appendix 1 — Consent Form .................................................. 59
Appendix 2 — Test Booklet Part I ........................................... 60
Appendix 3 — Test Booklet Part 11 Version A ........................ 68
Appendix 4 - Test Booklet Part II Version B ........................ 75

LIST OF TABLES

Table
l. The Twelve Test Illustrations .......................................................................... 15
2. Order of Triads in Test Booklet Section I ....................................................... 18
3. Order of maps in test booklet Section II a ....................................................... 22
4. Order of maps in test booklet Section II b ....................................................... 22
5. Summary of responses, Test Section I ............................................................. 25
6. Kruskal-Wallis H test for differences between test groups ............................. 28
7. Linear mixed effects analysis to test for learning, aggregate ........................... 3O
8. Linear mixed effects analysis to test for learning, separate ............................. 31
9. Average scores for map types and the twelve maps, Section II ....................... 33
10. Chi-square analysis of test booklet Section I ................................................... 36
l 1. Chi-square tests of differences, color and grayscale maps .............................. 4O
12. Wilcoxon signed rank test comparing color and grayscale maps .................... 4]
13. Chi-square test of differences, color vs. gray maps, by question .................... 43
14. Chi-square test comparing profile magnitude selections ................................ 44

vi

LIST OF FIGURES

Figure
1.

2.

10.

ll.

12.

l3.

14.

15.

16.

l7.

l8.

Stepped and smooth statistical surfaces ............................................................. 3
USGS isarithm map ........................................................................................... 4
Shaded relief map combined with elevation tint ............................................... 5
Perspective block diagram ................................................................................. 6
Isoline and continuous-tone grayscale maps of elevation ................................. 6
Groop and Smith hexagon snowfall map ........................................................... 7
Johnson dot-matrix map .................................................................................... 8
Lavin quasi-random dot map ............................................................................. 8
Visual sensitivity and spatial frequency curves ............................................... 10
Growing Degree Days for Lower Michigan, 1993 ........................................... l3
Elevations for a portion of Keweenaw County, Michigan ............................... 14
SEMCOG rainfall, 1993 ................................................................................... 14
Orientation and scheme of test illustrations ..................................................... 16
Sample grayscale and color map triads from test Section I ............................. 19
Sample maps from test Section II .................................................................... 20
Test questions from Section II ......................................................................... 21
Average map score differentiating color and grayscale maps ......................... 32
Maps B3 and B5 .............................................................................................. 47

vii

Chapter I
An Introduction to Quantitative Surface Maps

Most maps are two-dimensional representations showing objects relative to a set
of x and y coordinates. A typical example would be a standard highway map showing the
locations of roads, railroads, cities, lakes, etc. Other examples include maps illustrating
land use, forest cover type, soil series, or election results by state or county. Standard
symbols may be used to show these features, and they tend to be conceptually
straightforward.

In the last 50 years, there has been growth in the production of quantitative maps.
Quantitative maps are more complex than simple reference maps or maps showing what
is where rather than how much of something is there. Quantitative maps Show the
location of features measured on ordinal, interval, or ratio scales. Ordinal data provides
the map user with information about rank or hierarchy, for example, populated places
classified as a city, town or village. Interval and ratio data are continuous and provide
more detailed and precise information. They employ a scale of measurement, often
revealed in the map legend. Interval data have no natural zero and ratios are meaningless;
temperature in degrees Fahrenheit is interval data (2 degrees is not twice as warm as 1
degree). Ratio data have a natural zero point and ratios make sense; rainfall in number of
inches per year is ratio data (twenty inches per year is twice as much as ten inches per
year). Ordinal, interval, and ratio data as a group are referred to as quantitative data, and
may be contrasted with qualitative, or nominal data (Slocum, 1999). Qualitative data
show categories that have no quantitative relationship to one another, such as the cities,

roads, and lakes on the road map. Quantitative maps, and the surfaces they represent,

require innovation and map reading skills beyond the mere visual recognition of standard
symbols. The number of methods developed for mapping quantitative surfaces
(discussed below) support this idea.

A common feature shown on a quantitative map is elevation of the earth’s surface
above or below a datum. Elevation is not the only phenomenon that may be thought of as
a “volume” to be mapped, however. Any feature that changes quantitatively as it varies
across space may be represented by a statistical surface (J enks, 1963). Depending on how
data are enumerated, or on the type of feature being mapped, there may be discontinuities
in the data. These gaps may be caused by abrupt changes at the boundaries of the
mapping units, or by voids where the mapped feature does not exist. Surfaces such as
these are known as stepped statistical surfaces (Figure 1, top maps). An example of a
stepped surface is population mapped at the county level. Smooth statistical surfaces
consist of data that vary continuously, not discretely, over geographic Space (Figure 1,
lower maps). Some examples of smooth statistical surfaces include elevation above sea
level, air pressure, ocean temperature, and precipitation. To map statistical surfaces, it is

necessary to Show both position and change in magnitude.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1. Stepped and smooth statistical surfaces, fiom Groop and Smith, 1982.
Reprinted with permission from The American Cartographer 9, October 1982, 123-131.
Cartographers have developed a number of ways to map smooth statistical
surfaces. Perhaps the oldest and most often used method of portrayal is the isarithmic, or

isoline, map (Figure 2). Though appropriate for many purposes, isarithmic maps can be
difficult to read because they are two-dimensional representations of three-dimensional
data (J enks, 1963). Studies have shown that map users may perform well on some tasks
when using isarithmic maps, such as estimating the value at a location, but may have
difficulty understanding the overall surface (Phillips et al, 1975; Griffin and Look, 1979;

Phillips, 1979). The lines are not continuous symbols across the field of the map, so

readers must interpolate values between them (Lavin, 1986). Because of these
difficulties, cartographers have sought alternate methods for depicting smooth statistical

surfaces.

 

Figure 2. USGS topographic quadrangles include isarithms (“contours” in this case
because they represent land elevation). Contours are brown on these maps.

Hill shading is one alternative method for showing continuous surfaces. With hill
shading, various tints Show the aspect of the statistical surface, with northwest-facing
slopes illuminated and southeast-facing slopes in shadow. This combination of
illumination and shadow gives a 3-d efi'ect to the surface being mapped. It is difficult to
produce quality hill shadings manually, so automated (computer) methods have been .
developed. Early automated methods could not match the quality of shadings produced
manually (Y oeli, 1967; Brassel, 1979), but more recent improvements in computing
power and software have made shaded relief maps not only faster and easier to produce,
but also of extremely high quality (Thelin and Pike 1992, Lewis 1992). Hill shading gives

a general impression of the form of the statistical surface, but as it shows aspect and not

the values of the distribution, it is not useful for estimating values on the surface. Hill

shading is sometimes combined with tints that represent value (Figure 3).

 

Figure 3. Shaded relief (hill shade) map combined with elevation tints,
Baraga County, MI.

Perspective block diagrams, also known as “fishnet” diagrams, perspective traces,
or transects, Show elevation by placing lines across the statistical surface (Figure 4).
Tedious to produce by hand, perspective diagrams can be produced quickly using
computers. They do have their limitations, however. Regions of high variability—and
thus high relief—can Obscure lower areas behind higher zones, requiring rotation about
the vertical and horizontal axes to minimize masking. On some block diagrams, obscured
areas cannot be eliminated due to the complexity of the distribution. There is no “rule of

thumb” for producing the ideal representation, which will vary from surface to surface.

 

Figure 4. Perspective block diagram, Baraga County, MI.

The Continuous-T one Method

Another way of portraying smooth statistical surfaces is the continuous-tone map.
On continuous-tone maps, gray tones or colors (hues) vary smoothly to illustrate changes
in value from high to low. Unlike an isarithmic map, they Show value everywhere (Figure

5).

 

 

 

 

 

Figure 5. Isoline and continuous-tone grayscale maps of elevation, Baraga County, MI.

Groop and Smith (1982) developed a method that used graduated hexagons for
creating virtually continuous-tone maps where hexagon size was plotted proportional to
data value. Over a field such as a county, apparent darkness then represented the value
(Figure 6). The procedures for this technique were more suited to maps plotted with a pen
plotter than current output technologies, and the method used extensive and (then)

expensive computer time. The plots had to be photographically reduced to page size.

 

Figure 6. Groop and Smith hexagon snowfall map. Reprinted with permission fiom The
American Cartographer 9, October 1982, 123-131.

Johnson (1984) introduced a procedure that employed a dot matrix printer, driven
by a BASIC program, to create continuous shadings (Figure 7). Testing proved the dot
matrix maps as effective as isoline maps at conveying information, but test subjects did

not like their coarse appearance.

 

Figure 7. Johnson dot-matrix map.

Lavin (1986) developed a technique that used dot-density shading to produce
continuous tones. Dots were plotted quasi-randomly in a gridded data matrix to assure
non-overlap (Figure 8). Output was produced on a TektronixTM plotter. Lavin concluded
that dot density maps are one alternative method of smooth surface portrayal that can be

used to supplement, but not replace, isoline maps.

 

 

Figure 8. Lavin quasi-random dot map. Reprinted with permission fi'om The American
Cartographer 13, April 1986, 140-150.

Kumler (1988) created a hybrid method for producing color continuous-tone
maps, which used both digital and photographic techniques. He developed a series of
BASIC programs that displayed gridded data on a high-resolution color computer
monitor in shades of red, green, and blue. He then photographed the monitor, one color at
a time, and the color-separated negatives were process-printed to produce test maps.
These procedures were chosen to suit the technologies of the time. Kumler’s subject
testing indicated improved map reading performance on the color continuous-tone maps
when compared to standard isoline maps for the questions he asked, which included
locating and marking surface lows and highs, estimating the relative elevation of a pair Of
points, estimating the elevation at a point, and interpreting the slope of a line between

map points.

Chapter II
Statement of Problem

On continuous-tone maps, color scheme choice and surface complexity can affect
the characteristics of the distributions that map readers perceive. Questions arise about
the efficacy of the maps and just what information people are able or likely to gain from
them. For example, Rogowitz and Treinish (l 994) report that broad surface variations
(low spatial frequency data) are more easily visualized when mapped using colors, but
local surface variations (high spatial frequency, or fine details) are more evident when
mapped using gray tones (Figure 9). Stated differently, the details (high spatial frequency

components)

A
v

  
 

Luminance

—m:m—-<
~<n—-<—-n—-m:mm

 

Spatial Frequency

Figure 9. Visual sensitivity and spatial fi‘equency curves, after Rogowitz and Treinish,
1995.

in statistical surfaces tend to stand out when a monochromatic color scheme is used (only
luminance varies), whereas broad features (low spatial frequency components) in
statistical surfaces stand out more readily when a polychromatic scheme is used (hue

varies). These observations appear in visualization literature, but have not been noted in

the cartographic journals even though cartographic practice suggests that mapmakers
have an intuitive grasp of that principle: black lines are used to put in fine details such as
small symbols or fine lines, and hue variations are used for heavy lines and over areas.

In addition to issues of visual processing, advances in computing power have
made it possible to produce hi gh-quality, continuous-tone maps relatively simply and
quickly, raising the question of whether previous findings apply to more modern images.
With powerful image processing and graphics software for microcomputers we can
produce maps that are not only of higher quality but accessible to a broader audience, and
producible by a wider range of map makers. These same technological advances also
enable research on problems that require visual stimuli that was not feasible in the past.

Several previous studies have indicated that continuous-tone maps may be
effective for representing smooth statistical surfaces. These studies used several different
(then) contemporary output devices, including dot matrix printers and pen plotters.
Problems noted in these studies, such as coarseness of output or production complexities,
indicate a need for further research into the efficacy of continuous-tone maps, particularly
those produced on newer hardware and with current software.

The study presented in the remainder of this paper was designed to test the
efficacy of these maps in portraying the statistical surface by comparing the responses of
test subjects when gray tone and hue-based continuous-tone maps were presented.

Detailed hypotheses will be given as stimuli are presented in the next chapter, but
the general hypotheses were:

0 map readers will more easily perceive broad trends when hue-based color

schemes are used

11

0 map readers will more easily perceive local details when gray tones are

used

0 questions about surface values will be more accurately answered when

hue-based schemes are used.

Images in this thesis are presented in color.

12

Chapter 111

The Map Test

Three real data sets were used to produce maps for test booklets: growing degree
days for the Lower Peninsula of Michigan in 1993 [surface G]; elevation values from a
portion of Keweenaw County, Michigan [surface E]; and rainfall data collected by the
Southeast Michigan Council of Govemments (SEMCOG) in 1993 [surface R] (Figures
10, 11, 12). These three surfaces have very different spatial characteristics. Surface (G) is
complex, surface (E) presents intermediate spatial complexity, and surface (R) is

relatively simple.

 

 

 

 

 

 

Figure 10. Growing Degree Days for Michigan, 1993. (Surface G).

 

V

 

 

 

 

Figure 1 1. Elevation for a portion of Keweenaw County, Michigan. (Surface E).

 

 

 

 

Figure 12. SEMCOG rainfall, 1993. (Surface R).

The raw data in each set were collected at irregularly spaced locations. SURFER
version 4 (Golden Software, Inc., Golden, Colorado - http://www.goldensoftware.com[)
.was used to interpolate a regular lattice of points, to create a trend surface and to
calculate residuals from the trend surface for each of the three data sets. A 4th order
polynomial was used for these trend surfaces after some trial-and-error experimentation.
The fourth-order surface was deemed, through a visual check, to capture a reasonable

amount of the variation in the actual surface.

Binary grids were output from SURFERTM and imported into Spyglass
TransformTM (Spyglass, Inc, Champaign, IL - the Spyglass visualization suite is now
being sold under the name Noesys by IT'T Visual Information Solutions, Boulder,
Colorado - http://www.ittvis.com/), a data visualization package that was used to generate
the final continuous-tone maps. In Transformm, four different color lookup tables were
applied to each of the three surfaces: a 256-step white-to-black gray-tone scheme; a 256-
step black-tO-white gray-tone scheme; a 256 spectral color “rainbow” red-tO-blue
scheme; and a 256 spectral color “rainbow” blue-to-red scheme. The twelve resulting
maps (three data sets by four lookup tables) were exported as Tagged Image File Format
(TIFF) images. They are listed in Table l and are illustrated in thumbnail form in Figure
13. The images were created and exported at two different sizes: small (approximately 2
by 3 inches) for Section I of the test and large (about 3 by 4 inches) for Section II.
Additionally, Adobe PhotoShOp 4TM (Adobe Systems, Inc., San Jose, CA -
http://www.adobe.com/) was used to increase the resolution of the TIFF images from 72

to 300 dots-per-inch (dpi) to improve their appearance when printed.

Table l. The Twelve Test Illustrations.

Map code Surface Color scheme Triad Section 11 Position
I G black-white 5 B1
11 G white-black 1 1 A4
III G red-blue 3 B6
IV G blue-red 9 Al
V E black-white 10 A2
VI E white-black 4 B5
VII E red-blue 8 B3
VIII E blue-red 1 A6
IX R black-white 2 B2
X R white-black 12 A3
XI R red-blue 7 A5
XII R blue-red 6 B4

15

Figure 13. Orientation and color scheme of test illustrations. G, E, and R indicate the
distributions, Grong degree days, Elevation, and Rainfall. The codes A1, B1, etc.
indicate their positions in Section H of the test; Al means test version A, page 1. Larger
versions of the maps are in Appendices 3 and 4.

 

 

 

Original Orientation 90° Rotation
Spectral Grayscale Spectral Grayscale
A1 A4 B6 B l
G
E
R

 

 

NIH Image, a free image-processing package available from the National

Institutes of Health at http://rsb.info.nihgov/nih-image/, was used to generate surface

 

profiles between selected points on the images. These profiles were exported as raster
image files and brought into FreehandTM 7 (Macromedia, Inc., San Francisco, CA -
Adobe Systems, Inc. acquired Macromedia in December 2005), converted to vector
format, and manipulated by flipping and stretching the correct profile to create a set of six
profile choices for each of the surfaces. These profiles can be described as 1) correct with
low slope, 2) correct with high slope (stretched on the y axis between 17 5 and 600%
relative to the low slope profile), 3) medium slope (stretched on the y axis between 125
and 300% relative to the low slope) then flipped across the x axis, 4) profile I flipped
across the y axis (reverse slope), 5) profile 2 flipped across the y axis, and 6) profile 3
flipped across the y axis. The manipulated profiles were saved as] TIFF images at 300 dpi
for later incorporation into the test booklets.

Adobe FrameMakerTM (Adobe Systems, Inc., San Jose, CA -
http://www.adobe.com/) was chosen to assemble the individual maps into test booklets
because it could utilize the higher resolution of the images produced. Three files were
created, one for Section I of the test, and one each for the two versions of Section II
(described below). The booklets were printed on an HP Color LaserJetTM (Hewlett-

Packard Co., Palo Alto, CA - http://www.hp.com/) printer on 24-lb laser paper with a

 

brightness rating of 94. The booklets were numbered by hand on the back
(inconspicuously) to aid in compiling results. A consent form was distributed at the time

of testing; a copy appears in Appendix 1.

l7

Section I of the test booklet was comprised of a series of map triads, with the true
surface at the top of each triad and the trend and residual surfaces below. Each of the
three surfaces (land elevation, growing degree days, and rainfall) was included in Section
I four times, twice as a gray-shaded map (black-to-white and white-to black) and twice as
a spectral color map (blue-to-red and red-to-blue), for a total of twelve triads. Because the
surfaces were rotated and the maps were in a random order (all the same random order),
it was unlikely that subjects recognized the repeated depictions. Also, the order of the
trend and residual surfaces was randomly switched on the test pages (all subjects received
the same order for a given triad).

In Section I of the test, the subject was instructed to circle the map at the bottom
(trend surface or residuals) that looked most like the (actual) surface above. Thesurfaces
and color schemes for Section I are listed in Table 2, and sample color and grayscale map

triads are shown in Figure 14. A complete set of map triads may be found in Appendix 2.

Table 2. Order of Triads in Test Booklet Section I

Position Map code Surface Color Scheme Orientation
1 VIII E blue-red original
2 IX R black-white original
3 111 G red-blue original
4 VI E white-black rotated
5 I G black-white rotated
6 XII R blue-red rotated
7 X1 ~ R red-blue original
8 VI E red-blue rotated
9 IV G blue-red rotated
10 V E black-white original
1 1 11 G white-black original
12 X R white-black rotated

18

   

 

Figure 14. Sample grayscale and color map triads of Surface R from Section 1. Original
surface is at tOp, residuals are at outside positions, trend surfaces inside on
these examples. Note that the orientation is not the same for the two uiads but
the map data are identical.

   

.
, .

.dl

 

Section II of the test consisted of six maps, three grayscale and three color
renditions. Each map had the same eight associated questions, which were designed to
gauge the subject’s perception of the surface: slope, roughness, high and low points, and
elevation. The surfaces used in Section II were larger versions of the surfaces used in
Section I of the test. The maps in Section 11 included the addition of a scale bar below the
map, as well as labeled map points used in a number of the questions. Example grayscale
and color maps from Section II are shown in Figure 15, and a complete set of maps fi‘om

Section 11 may be found in Figure 13, or in Appendices 3 and 4 at larger size.

 

 

Figure 15. Sample maps—Surfaces R and E—fiom Section II. Larger versions are
available in Appendices 3 and 4.

Section [I contained two versions of each of the three surfaces—E, R and G—
shown once with a spectral color scheme and once with a grayscale scheme. The surfaces
were presented in a random order to help minimize the chance that the duplication would
be noticed, and the numbers on the scale bar for three of the six maps were changed to
‘ different values to help reduce recognition. In Section H the subject answered questions
by drawing on the map, circling the correct answer, or filling in blanks. The questions

used in Section II are illustrated in Figure 16.

20

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map
3) Imagine a line. from point A to point B. This slope along most of this line is generally

a) uphill b) downhill cuter (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression

c) on a slope between a ridge or hilltop and a valley or depressimr ( circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around '1‘ is
a) firmer b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the prolile below that most closely matches its slope
a) b) c) d)

/‘ "\ _/ \c’_/0\i

8) Which quadrant is most irregular? (circle one)

 

 

 

 

 

III IV

 

Figure 16. Example test questions from Section II.

Section I of the test was identical for all subjects. However, there were two
versions of Section 11 used in the test. The two versions (“A” and “B”) were used to keep
the test a reasonable length. The same twelve maps used in Section I wereincluded in
Section II, with half in each version. Approximately 50% of subjects had a version “A”
booklet (n=29) and 50% a version “B” booklet (n=30). A complete version of Section I
of the test booklet is included in Appendix 2, and versions “A” and “B” of Section II of
the test booklet are included in Appendices 3 and 4, respectively. A listing of the surfaces
and color schemes used in Section 11, test versions “A” and “B”, may be found in Tables

3and 4.

21

Table 3. Order of Maps in Test Section 11 Version A

Position Map code Surface Color Scheme
Al IV G blue-red

A2 V E black-white
A3 X R white-black
A4 11 G white-black
A5 . XI R red-blue

A6 VIII E blue-red

Table 4. Order of Maps in Test Section 11 Version B

Position Map code Surface Color Scheme
B1 I G black-white
B2 IX R black-white
B3 VII E red-blue

B4 XII R blue-red

BS VI E white-black
B6 111 G red-blue

22

The specific working hypotheses concerning subject performance on spectral

color and grayscale continuous-tone representations of smooth statistical surfaces are:

H2

H3

H5

H6

On map triads, a majority of subjects will choose the residuals map as
appearing more like the actual surface when the three maps are in gray

IOI'ICS .

On map triads, a majority of subjects will choose the trend map as

appearing more like the actual surface when the three maps are in spectral

color.

Subjects will select the profile of correct shape with least vertical

exaggeration as correct on grayscale maps.

Subjects will select the profile of correct shape with higher vertical

exaggeration as correct on spectral color maps.

Subjects will estimate elevation more accurately on spectral color maps.

Subjects will locate surface extremes more accurately on spectral color

maps.

23

Administration of the test

Students in one undergraduate and one graduate Forestry class at Michigan
Technological University were invited to take the test on a voluntary basis. Subjects were
allowed approximately 25 minutes to complete it. Both undergraduate and graduate
students were included to help ensure a broad range of map reading backgrounds.
Additionally, a number of other volunteers took the test. These additional volunteers did
not take the test as a group, but were supervised while doing so, with the same time limit
as the class subjects.

A short verbal introduction was given in addition to the information on the
consent form and sample questions. No names were included on the test booklets to
ensure anonymity. In all, fifty-nine subjects took the test. The subject population in the
two classes included twelve graduate students and twenty-five undergraduates; the
twenty-two additional volunteers were drawn fiom students, faculty and staff at Michigan

Technological University.

24

Chapter IV
Results and Analysis

Before presenting any analysis, it is useful to look at raw results. For Part I of the
test, subjects were asked to circle one of two maps (the “choice maps”) that looked most
like the one above it (Figure 14). The two choice maps were the trend and the residual
surfaces generated from the surface above. Recall that the order of the choice maps—
trend on left, residual on right, or residual on left, trend on right—was changed randomly
throughout the section. Answers to Section I of the test booklets were recorded for each

respondent. The results are summarized in Table 5 below.

Table 5. Summary of responses, Test Section I.

Boxed cells indicate the one map triad where the majority of respondents chose opposite

 

what was predicted
Triad # l 2 3 4 5 6 7 8 ‘ 9 10 ll 12
Map VIII IX 111 VI I XII XI VI IV V II X
Surface E R G E G R R E G E G R
Scheme b-r k-w r-b w-k k-w b-r r-b r-b b-r k-w w-k w—k
Trend/
Residual UR R/L R/L UR R/L UR R/L R/L UR R/L UR UR
Trend
selected 47 13 52 4 l 8 26 30 38 58 3 4 6
Residuals
selected 12 46 6 54 41 32 29 21 l 56 54 53
Responses 59 59 58 58 59 58 59 59 59 59 58 59
% trend 79.7 22.0 89.7 6.9 30.5 44.8 50.8 64.4 98.3 5.1 6.9 10.2
% resld 20.3 78.0 10.3 93.1 69.5 55.2 49.2 35.6 1.7 94.9 93.1 89.8

 

 

 

25

In Part II of the test, the answers to questions one and two—which asked subjects
to mark the high and low positions on the map—were marked correct if the subject
placed their letter within one-quarter inch of the true low or high points on the map.
Responses to question three, which dealt with the slope of a line between two points,
were compared with a profile generated fiom the surface and scored accordingly. A block
diagram and contour map were used to determine the correct answer to question four,
which asked subjects to consider the landscape position of a point. Question five asked
subjects to estimate the elevation at a point and was marked correct if the responses were
within one-quarter of the interval used on the map legend. This is the same criterion used
by Kumler (1988) for his test instrument. To determine the correct answer to question six,
which asked readers to estimate the relative surface roughness around two points on the
map, a block diagram and contour map were used to assess the landscape position and
elevation changes (ups and downs) around the two points. On question seven, subjects
were to choose the profile that best fit their interpretation of the slope between two points
on the map. There were two possible correct answers—one with greater vertical
exaggeration than the other—that were counted as right, but a comparison was made
between the spectral color and grayscale maps as to which level of exaggeration was
most often chosen. The final question, eight, asked respondents to identify the roughest
quarter of the map. Before scoring subject responses, a grid was used to count the number
of changes in slope direction within each quadrant of the three surfaces. The quadrant

having the most changes from up to down and vice versa was deemed “roughest”.

26

Scores for individual maps were tallied, with eight being the highest score
possible on a given map (if six questions were answered correctly, the subject would
score a six for that particular map). Scores on individual maps ranged from a low of one
to a high of eight. A composite score was calculated for each subject by counting the

number of correct answers out of 48 possible (six maps, each with eight questions).

Preliminary analysis of groups, test Section II

After compiling scores for each subject, preliminary analysis was performed on
the results fi'om the three groups—the graduate class, undergraduate class, and
volunteers—to see if they were from the same population. As there were two test
booklets used, the results for versions “A” and “B” were first analyzed separately to see if
there were any significant differences in subject performance between the two booklet
versions. No differences were expected, but if they exist, they could confound the testing
of the major hypotheses.

A Kruskal-Wallis Rank Sum test was used to determine if subjects in the three
test groups were drawn from the same population. This is a nonparametric test that does
not rely on normally distributed data and the groups need not have the same number of
members. The Kruskal-Wallis test is used in cases where there are three or more groups
of data. It is called a “rank sum test” because the scores in all groups are ranked from
highest to lowest, the ranks are summed by group, and a mean rank by group is
calculated, along with the total sum and overall mean of ranks for all subjects. These
factors are used to calculate the H statistic, which can be used to estimate the probability

of differences measured in the group scores occurring by chance. The R statistical

27

 

software version 2.41 (http://www.r-project.org/) was used for analysis. The average
score, number of participants by group, H statistic and significance are listed in Table 6.
The H value for both versions of the test, “A” and “B”, was well above the
rejection value for significance at the or = 0.05 level. The differences in scores can be
attributed to variation in sampling: the results for the two booklets are not significantly

different.

Table 6. Kruskal-Wallis H test for differences between test groups (G: graduate students;
U: undergraduate students; 0: other volunteers)

Ho: Samples are from populations with identical distributions

((1 = 0.05)

. Group
Test G U 0 H statistic Probability Decision
version
A 63.33 68.91 66.66 1.715 0.424 accept Ho
(n=29) (n=5) (n=1 3) (n=1 1)
B 68.45 68.75 69.51 0.379 0.827 accept Ho
(n=30) (n=7) (n=12) (n=1 1)
Map order effects

The order of maps in each of the two versions of Section II of the test was varied,
the surfaces were rotated, and the numbers on the legends were altered to minimize the
likelihood that subjects would recognize maps and improve as they worked through the
test. Even so, it was possible that subjects could better their results as they took the test
because of more experience with the maps and familiarity with the questions, or that they

might recognize later surfaces as similar to, or the same as, maps they saw earlier, and

28

perform better. To ascertain if such learning bias did take place, the score for each map
was tested for dependence on its position in the booklet. If subjects improved their scores
as they went along, it is an indication that learning took place, a finding that could
confound the testing of the major hypotheses.

A'repeated measures analysis was used to detemrine statistically if learning
occurred. Repeated measures is a form of linear regression, where score (the performance
on an individual map by each subject), is correlated with time (the position of each map
in the booklet), to see if significant improvement occurred. A linear mixed effects (lme)
model in R version 2.4 was applied to the aggregated raw scores for each subject using
the statement lme (score~map, random=~1 I subj , data=learn) . This
statement translates to “apply an lrne analysis to the data set “learn”, look at score as a
function of map position in the booklet (which equates to time), and treat each subject as
a random effect”. This approach is suggested in Kutner et al. (2005).

The slope of the resulting regression line was very low—0.01 , and the p-value, at
0.78, is well above the rejection value for a significance level of 0.05. These results
indicate that significant learning did not occur by subjects taking the test, i.e., scores did
not improve sufficiently to bias further analysis. Table 7 presents the summary output of

the linear mixed effects analysis.

29

Table 7. Linear mixed effects analysis to test for performance improvement, aggregate
scores, Part II of test

Ho: Performance did not improve with time

(or = 0.05)
Fixed effects: score ~ map
Value Std. Error DF t-value Probability
(Intercept) 5.4135 0.14963 294 36.179 0.0000
map 0.010169 0.03714 294 0.2738 0.7844

Decision: Accept Ho

To determine if learning occurred by the subjects who had either booklet version
“A” or “B”, the results from Section II of the test were looked at separately. A linear
mixed effects analysis was performed on the scores stratified by test booklet (“A” and
“B”) and by subject group (g, u, and o) to see if learning occurred within these groupings.
As expected, neither of these analyses, summarized in Table 8, revealed any significant

learning effects.

30

Table 8. Linear mixed effects analysis to test for performance improvement, separate
scores, Part II of test

Ho: Performance did not improve with time

(or = 0.05)

Fixed effects: score ~ map for booklet version A

Value Std.Error DF t-value p—value
map 0.0945 0.05467 144 1 .7298 0.0858
Fixed effects: score ~ map for booklet version B

Value Std. Error DF t-value p-value
map -0.0714 0.0496 149 -1.4374 0.1527
Fixed effects: score ~ map for group g

Value Std. Error DF t-value p-value
map 0.0143 0.07621 59 0.1874 0.8519
Fixed effects: score ~ map for group It

Value Std. Error DF t-value p-value
map 0.0068 0.05775 124 0.1 187 0.9057
Fixed effects: score ~ map for group 0

Value Std. Error DF t-value p-value
map 0.0117 0.0628 109 0.1859 0.8528

A Linear Mixed Effects analysis was not appropriate to assess the results stratified
by color scheme, as no subject had only spectral color or only grayscale maps in their
booklet. Instead, the scores were plotted to show map position in the booklet, average
score, and color scheme. No obvious pattern was evident in the graphs. The performance

on each map for booklets “A”, “B”, and the combined results, is shown in Figure 17.

31

V

 

(D

lllllllllllllllllllIlllllll|ll [14L]

 

N (A) A 01

Average score by map (8 possible)

 

O

 

 

 

 

Booklet A Booklet B Combined

Map 1-6
fl Color map
. Grayscale map

a Color in one booklet, grayscale in the other

Figure 17. Subject performance on maps fi'om Section II. Scores are out of 8 possible.
Map position increases from left to right (map 1 is leftmost bar, map 6 rightmost)

The Kruskal-Wallis analysis indicted that there was no significant difference in the
three test subject samples. The repeated measures analysis of all scores from Section 11
showed that map position did not affect how subjects performed on a given map: i.e.,
significant learning did not occur during the test. Therefore, the results fi‘om Section H
were combined for further analysis. Average subject scores from Section II for the
twelve test illustrations; the four color schemes (black-to-white, white-to-black, red-to-
blue, and blue-to-red); and the two color scheme classes (spectral color and grayscale) are

listed in Table 9.

32

Table 9. Average Scores for Map Types and the Twelve Maps, Section II of test

Map code Surface Color scheme Sample size Avg Score
I G k-w 30 72.1
11 G w-k 29 60.3
III G r—b 30 71.7
IV G b-r 29 70.7
V E k-w 29 569
VI E w-k 30 58.3
VII E r-b 30 68.3
VIII E b-r 29 75.4
Ix R k-w 30 70.0
x R w-k 29 72.4
XI R r-b 29 66.8
XII R b-r 30 74.2
IV IX G E R k-w 89 66.4
11 VI X G E R w-k 88 63-6
III VII XI G E R r-b 89 690
IV VIII x11 G E R b-r 88 73-4
I II V VI IX X G E R Grayscale 177 65.0
111 IV VII VIII
XI XII G E R Spectral Color 177 71.2

Subject performance, Test Section I

The main purpose of this research was to test the efficacy of continuous-tone
spectral color and grayscale maps in displaying smooth statistical surfaces. The first part
of the test was designed to determine if subjects saw a low spatial frequency surface—a
fourth-order trend surface—as more like the original surface when it was presented using

a spectral color scheme, and a high spatial fi'equency surface—residuals from the trend

33

surface—as more like the original surface when it was depicted in grays. The first two

research hypotheses, H1 and H2, are a restatement of the above:

H1 On map triads, a majority of subjects will choose the residuals map as
appearing more like the actual surface when the three maps are in gray

tones

H2 On map triads, a majority of subjects will choose the trend map as
appearing more like the actual surface when the three maps are in spectral

color

A Chi—square analysis, a non-parametric test of statistical significance for
differences in performance on bivariate, or paired, data, was performed on the results
from Section I of the test. For triad l in Section I of the test, there were 59 subject
responses recorded. If there was no difference in response to the question, i.e., subjects
did not choose one map preferentially over the other, one would expect that half of the
subjects (29.5) would choose the trend map as most like the original surface and half
would choose the residual map. The Chi-square analysis tests for significant differences
between the expected and observed responses to the question, using the following

formula:

1 2 =2 (Observed-Expected)2 / Expected

34

For triad 1, forty seven subjects chose the trend surface and twelve chose the

residual surface. Thus, the chi-square value would be calculated as follows:

Observed Expected Obs-Exp. (Obs-Exp.)2 (O-E)2/E
47 29.5 17.5 306.25 10.38
12 29.5 -17.5 306.25 10.38
x2 =(47-29.5)2/29.5 + (12-29.5)2/29.5

12 = 10.38 + 10.38

12 = 20.76

For a pair of observations, the degrees of freedom is one, and the chi-square
required for significance at the a = 0.05 level is 3.841. A chi-square value of 20.76 is
statistically significant beyond the 0.001 level (i.e., the odds of a chance occmrence of
these results are less than one in one thousand). The results of the chi-square analysis for
the aggregated spectral color and grayscale map scores, as well as for the twelve

individual maps in Section I, are presented in Table 10.

35

Table 10: Chi-square analysis of Test Booklet Section I
Ho: Performance differences are evenly distributed ‘

(on = 0.05)
Map x2 DF Scheme Probability Decision
All color 63.92 1 color 1.295e-15 Reject Ho
All gray 1 86.1 8 l gray <2.2e-16 Reject Ho
1 20.76 1 color 5.199e-06 Reject Ho
2 18.46 1 gray 1.73e-05 Reject Ho
3 36.48 1 color 1.54e—09 Reject Ho
4 43.10 1 gray 5.19e-11 Reject Ho
5 8.97 1 gray .002750 Reject Ho
6 0.62 1 color 0.4308 Accept Ho
7 0.02 1 color 0.896 Accept Ho
8 4.89 1 color 0.027 Reject Ho
9 55.07 1 color 1.164e-13 Reject Ho
10 47.61 1 gray 5.2e-12 Reject Ho
11 43.10 1 gray 5.192e-11 Reject Ho
12 37.44 1 gray 9.42e—10 Reject Ho

For the scores aggregated by color scheme (spectral color and grayscale), subjects
much more often chose the residuals map as appearing more like the original map when
portrayed in grayscale, i.e., they preferentially chose the high spatial fiequency surface.
Of three hundred and fifty two responses, only forty eight chose the trend surface (14%
of respondents), while three hundred and four chose the residual surface (86% of
respondents), which yielded a chi—square value of 186. Subjects also overwhelmingly
chose the trend maps as more like the original surface when shown with a spectral color

scheme, i.e., they preferentially chose the low spatial frequency surface. The tendency

36

was not as strong with the color surfaces, however, as two hundred and fifty one
respondents chose the trend surface (71%) vs. 101 respondents who chose the residual
map (29%). This produced a chi-square value of 63.92. Both research hypotheses one and
two were accepted.

When analyzed separately (no corrections for multiple tests), ten of the twelve
triads had chi-square values significant enough to reject the null hypothesis: respondents
did preferentially choose one representation over the other. However, maps six and seven
had chi-square values of 0.62 and 0.02, respectively, which were well below the value of
3.84 required to reject the null hypothesis. Triads six and seven were both spectral color
surfaces, and triad six was the only one of the twelve triads where a (small) majority of
subjects chose the surface opposite of what was predicted — thirty two subjects chose the
residual map as appearing more like the original surface, and twenty six chose the trend
surface. On map seven, an even slimmer majority—thirty—chose the trend surface as
most like the original, while twenty nine chose the residual surface. Triads six and seven
were the two color versions of the rainfall surface (R), and the trend maps included in the
test accidentally had their color order reversed with respect to the original map to which
they were being compared; the colors ran from red to blue and blue to red instead of the
opposite order for these two trend maps. This inadvertent color sequence reversal reveals
an interesting point: even though the opposite color sequence was used on the trend map,
the residual map (with correct color order) was not chosen over the trend map. Rather,
the choice seemed to have become a random one, with close to equal numbers choosing
the trend and residual surfaces. Given the problem with these two maps, it makes the

results even more overwhelmingly in favor of the research hypothesis.

37

Subject Performance, Test Section II

Section II of the test was designed to assess how well subjects could interpret the
three surfaces when shown in spectral colors vs. graytones, and to compare differences in
their performance when answering questions about spectral color and grayscale maps. A
chi-square analysis was performed on the aggregated scores for all spectral color and
grayscale maps in Section II. The'results of this analysis are presented in Table 11.

When scores from Section II of the test were analyzed as a whole, a significant
chi-square value, 12.25, was the result. Overall, subjects performed significantly better
on the spectral color maps than on the grayscale maps. However, when looking
separately at the six pairs of maps from the two versions of the test (“A” and “B”), only
three pairs, A1/A4, A6/A2, and B3/BS, had chi-square values large enough to reject the
null hypothesis. In each case, performance was significantly better on the spectral color
map. In the other pairing from test version “A”, and for two pairings from version “B”,
there was no significant difference in subject performance on the color surfaces vs. the
grayscale representations. Maps A1 and A6 used spectral schemes that ran from blue to
red; B3 used a red-to-blue spectral scheme. The paired maps, A4, A2, and B5, used
white-to-black, black-to-white, and black-to-white grayscale schemes, respectively, so
the color tables of the pairs are not consistent. However, this result may indicate that the
blue-to-red color scheme is the most effective of those color schemes used. This
observation (is supported by the information in Table 9, which lists the average map score
by scheme. Subjects performed best on maps shown with the blue-to-red color scheme,
with an average score of 73.4% correct. This is four percent higher than the next closest

color scheme, and six to ten percent better than the two grayscale schemes.

38

In the three non-significant pairings, performance was slightly better on the
grayscale maps in two instances (AS/A3 and B1/B6) and slightly better on the spectral
color maps in the third (B4/BZ). The chi-square values for Al/A4, A6/A2, and B3/B5,
were high enough, at 16.2, 12.5, and 7.54, to produce the overall significant chi-square
value of 12.25, and override the non-significant chi-square values of the other three

pairings.

39

Table 11: Chi Square Tests of differences between spectral color and grayscale maps

Ho: Performance differences are evenly distributed
(a = 0.05) '

The dijflzrence between pairs and total in the table below is where performance was the same,
e.g., for all maps, there were fifty-nine pairings (one for each subject). Eight subjects performed
equally well on the color and grayscale maps. Thirty-eight scored higher on the color maps and

thirteen on the grayscale, yielding a total of fifty-one.

All maps, color vs. grayscale

Higher

Scheme Maps Pairs scores x2 Probability Decision

Color A1 A5 A6 59 38 12.2549 0.000464 Reject Ho

B3 B4 B6
Grayscale A2 A3 A4 13
B1 B2 B5
Total 51
Booklet “A”
Higher

Scheme Maps Surface Pairs scores 1 2 Probability Decision

Color A1 G 29 19 16.2 5.7 0e-05 Reject Ho
Grayscale A4 1

Total 20

Color A6 13 29 22 12.4615 0.0004154 Reject Ho
Grayscale A2 4

Total 26

Color A5 R 29 10 0.6667 0.4142 Accept H0
Grayscale A3 14

Total 24

Booklet “B”
Higher

Scheme Maps Surface Pairs scores x2 Probability Decision

Color B6 G 30 9 0.2 0.6547 Accept Ho
Grayscale B1 11

Total 20

Color B3 E 30 20 7.5385 0.00604 Reject Ho
Grayscale B5 6

Total 26

Color B4 R 30 12 0.8 0.371 1 Accept Ho
Grayscale B2 8

Total 20

40

To obtain a second measure of performance differences shown by subjects
between the spectral color and grayscale maps in Section II of the test, a Wilcoxon
Signed Rank Test was performed on the aggregated results of all maps from booklet
versions “A” and “B”. The Wilcoxon Signed Rank Test is used for two-sample data
involving matched pairs, repeated measures, or “before” and “after” measures when the
populations are not normally distributed. In this case, the “pairs” are the differing
performance of each subject on the color maps vs. the grayscale maps. The absolute
difference of each pair is determined, |Xa -Xb|, then observations where performance is
tied are dropped (IXa — Xbl = 0). The remaining absolute differences are ranked from
smallest to largest, and ranked values are given signs: "+" when Xa-Xb > 0 and "-" when
Xa-Xb < 0. The signed ranks are then summed and used to calculate W. R version 2.41
was used for this calculation, and the resulting W statistic was 1066, with a p-value of
0.00014. This result, like the chi-square test, indicates there were significant performance
differences between the color maps vs. the grayscale maps: subject performance was
significantly better on the spectral color maps. The result of the Wilcoxon Signed Rank

Test is listed in Table 12.

Table 12: Wilcoxon Signed Rank Test comparing color and grayscale map performance

Ho: Performance differences are evenly distributed

(a = 0.05)
W value Probablility Decision
1066 0.0001382 Reject Ho

41

Testing the Other Research Hypotheses, Test Section II

Section II of the test was designed to assess how well subjects could interpret the

three surfaces when shown in spectral colors vs. gray tones. Research hypotheses three

through six addressed specific map reading tasks from Section II of the test:

H4

H5

H6

Subjects will select the profile of correct shape with least vertical

exaggeration as correct on grayscale maps.

Subjects will select the profile of correct shape with higher vertical

exaggeration as correct on spectral color maps.

Subjects will estimate elevation more accurately on spectral color maps.

Subjects will locate surface extremes more accurately on spectral color

maps.

A chi-square analysis was performed on the results from Section II of the test on a

question-by-question basis to compare the performance differences between spectral color

and grayscale maps. The results of this analysis are listed in Table 13.

42

Table l 3: Chi-Square Test Comparing Spectral Color and Grayscale Map Performance

Ho: No difference in performance with color vs. grayscale maps

(a = 0.05)
Aggregate Scores
Number Number
correct correct ‘

Question Color Gray X 2 Probability Decision
1 171 170 0.0029 0.9568 Accept Ho
2 165 160 0.0769 0.7815 Accept Ho
3 117 132 0.9036 0.3418 Accept Ho
4 110 77 5.8235 0.0158 Reject Ho
5 99 80 2.0168 0.1556 Accept Ho
6 131 142 0.4432 0.5056 Accept Ho
7 130 95 5.4444 0.0196 Reject Ho
8 72 75 0.0612 0.8046 Accept Ho

Significant chi-square values are in bold

A brief assessment of the results of this chi-square analysis would suggest that
subjects performed equally well on the spectral color and grayscale maps on six of the
eight associated questions. Only questions four and seven produced chi-square values that
were significant. These two questions (four and seven) dealt with the landscape position
of a point and the form of a slope between two points. Subjects performed significantly
better on the spectral color surfaces on questions four and seven.

To assess research hypotheses three and four, which suggested that higher
magnitude profiles would be chosen on spectral color maps and lower magnitude profiles
on grayscale maps, the compiled answers to question seven were scrutinized. There were
130 correct answers selected on color maps: 59 of these were the profile of lesser
magnitude, and 71 were higher magnitude. On the grayscale maps, 95 correct answers

were recorded: 50 were the lesser-magnitude profile and 45 the higher magnitude. At first

43

glance, these results support the research hypotheses, as a majority of subjects preferred
the higher-magnitude profile on color surfaces and the lesser-magnitude profiles on
grayscale surfaces. To test these observations for significance, the correct answers——
which included both the low and high magnitude profiles—were subjected to chi-square
analysis. Both the color and grayscale profile results did not have chi-square values large
enough to be significant. Research hypotheses three and four were rejected and the null
hypotheses of no difference was accepted. The results of the chi-square analysis

comparing actual and high-magnitude profile selection are presented in Table 14.

Table 14: Chi-Square Test Comparing Profile Magnitude Selections,
' Spectral Color and Grayscale Maps

Ho: Performance differences are evenly distributed

(or = 0.05)
Number Number
correct correct
Scheme Actual Higher x 2 Probability Decision
type Magnitude
Color 59 71 . 1.1077 0.2926 Accept Ho
Grayscale 50 45 0.2632 0.6080 Accept Ho

Research hypothesis five predicted that subjects would be able to estimate
elevation at a point more accurately on spectral color maps. Though performance was
better on the color maps when compared with the grayscale maps, with 99 and 80 correct
responses respectively, the difference in performance was not statistically significant. The
resulting chi-square value was 2.01 , below the necessary significance threshold of 3.84.
Research hypothesis five was, therefore, rejected and the null hypothesis of no difference

was accepted.

44

Research hypothesis six proposed that test subjects would be better able to locate
surface extremes—the high and low points—on spectral color maps than on grayscale
maps. Test questions one and two dealt with marking the surface extremes on each map.
With 171 (color) and 170 (gray) correct answers for question one, and 165 and 160
correct answers for question two, performance was again (marginally) better on the color
maps when compared with the gray surfaces. The resulting chi-square values—0.0029
and 0.0769 for questions one and two—were far from significant enough to accept the

hypothesis. Research hypothesis six was also rejected and the null hypothesis accepted.

Summary of Results

The test instrument discussed above was designed with two goals in mind. The
first was to see if gray tones better represent high spatial fi'equency data, and spectral
colors (hue) better represent low spatial frequency data. The second was to compare map
reading performance on spectral color vs. grayscale representations of the same statistical
surfaces.

The first part of the test was designed to help assess how subjects saw spatial
fi'equency. Research hypotheses one and two predicted that a majority of subjects would
choose a residual map as most like an original surface when shown in grays, and a trend
surface as most like the original surface when mapped in spectral colors. A chi-square
analysis of the results fi'om Section I showed significant differences in the selections
made by test subjects. As a result, both research hypotheses one and two were accepted.

In Section II of the test, subjects were asked to answer a series of eight questions

on each of six maps — three surfaces shown in two color schemes: once in grayscale and

45

once in spectral color. Differences in performance on these map reading tasks were
tested for significance, to assess whether the color scheme type—spectral color or
grayscale—affected performance. Subjects scored higher overall on the color surfaces
when compared with the grayscale surfaces—about six percent better on average. A chi-
square analysis of the subject performance showed that subjects performed significantly
better on the spectral color maps than on the grayscale maps. When performance on
selected indiVidual questions were subjected to the chi-square test, however, research
hypotheses three through six, which dealt with profile selection, elevation estimation, and
location of surface extrema, were rejected, as significant differences between the

grayscale and spectral color surfaces were not evident in the subject response data.

Discussion

Some oversights in test design and production occurred while carrying out this
research. In addition to the inverted color schemes used in triads six and seven, one other
error was present in the test booklets. In Section II of test “B”, map five was rotated to
help reduce the chance that it would be recognized as the same surface as map three, but
the corresponding map points were not moved accordingly. Answers were adjusted so
they were correct relative to the points as actually shown, but the comparability of the
two maps was not as well controlled as in the other pairs. Maps B3 and B5 are shown in

Figure 18.

46

    

Figure 18. Maps B3 (left) and B5 (right, map points unrotated).

This omission reduced the effectiveness of directly comparing B5 with its paired
map, B3. Like three of the other six map pairs, however, there was no significant
difference in subject performance on map pair B3/B5, so the oversight may not have
effected a significant change in answers.

Conversations with some of the subjects after testing revealed an interest in the
study and questions about how the maps might be used. One subject mentioned that he
felt the maps were easy to use, but found the color maps easier than the grayscale, which
were “too dark”. This may be only a preference due to the appearance of the bright
spectral color scheme used, but it also suggests that the overall darkness of the grayscale
maps may have been part of the reason for inferior performance with them. On the other
hand, the values ran virtually the full gamut fiom white to black and any changes to
lighten the maps would have meant less differentiation in the lighter end of the scale.
The increased visual differentiation afforded by the spectral scheme is much more likely
responsible for the better performance.

It is interesting that all the research hypotheses involving specific questions were

rejected (i.e., the null hypotheses were accepted). Since the one involving question 7

47

(selection of profile) did not deal with correct vs. incorrect answers, but whether subjects
answering correctly selected the less exaggerated or more exaggerated profile, its
rejection is not contrary to the overall hypothesis of better performance with color maps.
The others, however, involving Questions 1, 2, 3, 5, and 6, each showed no difference in
performance with the two maps. The significant overall difference, then, was attributable
to other questions, and Table 13 indicates these are 4 and 7.

Perhaps a different criterion for assessing questions 1 and 2 would have yielded
different results, e.g., a smaller radius in which answers were marked correct. However, it
is likely that marking the “blackest” or “whitest” regions on a grayscale map is no more
difficult than marking the “reddest” or “bluest” locations on a spectral color map, and the
non-sigrrificant results are, therefore, not surprising. It may be that the non-linear nature
of the spectral color schemes used in the test affected the results for question 3, as
performance was marginally, but not significantly, better on the grayscale maps.

Question 5 dealt with estimating elevation at a point on the map, which had better,
but not significantly so, results on the spectral color maps. Again, a different criterion,
such as a smaller margin for correct answers, might have given a different outcome.
Questions 6 and 8 were both about roughness of the surfaces, and non-significant
differences were found again. Performance was slightly better on the grayscale maps, so
“roughness” may be a characteristic better communicated by the luminance changes of a
grayscale presentation.

Questions 4 and 7 were the two with significant chi-square values, and these
questions addressed landscape position and slope profile selection. It may be that the non-

linear appearance of the spectral color scheme aided in assessing the location of point A

48

on question 4, e.g., the rapid change between red and green (through yellow) or betWeen
blue and green (through cyan) gave better clues to the form of the landscape than the
steady progression of grays in the grayscale maps. Perhaps the same clues in the color
table assisted the subjects in selecting profiles for question 7.

What does all this mean for mapmaking? It seems clear that spectral color allows
better performance on at least some of the questions, but not on all. It is particularly
interesting that it was form of the distribution on which subjects performed better with
the spectral scheme because it has been the non-sequential nature of spectral colors that
has long made cartographers reluctant to use them for representing quantitative data.

One potential area for additional research would be to test monochromatic color
schemes against grayscale, and even more important, a spectral scheme with a
progression of value (say, light yellow through medium-value greens through dark blues
and even darker reds), since progressive schemes resulted in good performance in
Mersey's (1990) study and Brewer (1997) recommends them for diverging data. Would
we, for example, see the shift of Visual emphasis from broad patterns to local features if
we compared a light-to-dark spectral scheme to the li ght-to-dark grayscale? And for the
questions posed in Section II of the test, would we continue to see superior performance
(perhaps even more superior performance) with a light-to-dark spectral scheme? For the
questions they asked, Brewer et al. (1997) had good results with a diverging spectral
scheme (yellow for the middle category, with light oranges to highly saturated red in one
direction and light greens to highly saturated blue in the other), and even better results for
more conventional bi-color diverging schemes. The spectral scheme used in this thesis

research does not have continuous-appearing values and is not arranged as a diverging

49

scheme. This means certain hues—such as yellows and cyans that occupy a narrow
portion of the color spectrum compared to greens or blues—can give the impression of
greater importance (because of greater contrast) than is warranted to the areas mapped in
those colors. This phenomenon can be especially pronounced on some data distributions,
where the combination of data values, surface form and color scheme can cause
representations that are not true to the surface due to visual artifacts.

Another area for further research is the perception of broad patterns on spectral
maps and local variation on grayscale ones. The fourth-order surfaces showed strong
differences in choices between trend and residual maps depending on whether the maps
were in color or grayscale. But was it just because of the trial and error selection of the
fourth-order that was based on our visual inspection? Is there something inherent in that
level of trend surface? Rogowitz et a1 (1995) do not use trend surfaces to determine the
appropriate color scheme to use for a given data set. Instead, their software uses what is,
in effect, a low-pass filter to derive new data from the original. It then subtracts the
original data values fi'om the filtered. The standard deviation of difference values is
computed, then divided by the original data values. The resulting “normalized standard
deviation” is used to assess the complexity of the surface. An image with a normalized
standard deviation (N SD) of less than 0.1 is deemed “low frequency” and can use a
spectral color map, whereas an image with a NSD of greater than 0.1 is flagged as “high
frequency” and only monochromatic color maps are available.

Is the Rogowitz method the best way to choose a color map? Not necessarily: they

state that the method was chosen for its speed and simplicity, and it maylnot stand up to

50

rigorous scrutiny. It might not be the best for a data set that has both high and low
frequency areas.
This thesis research has added to favorable results with spectral color maps. It

has also provided food for thought.

51

Chapter V
Summary and Conclusions

Mapping quantitative surfaces has been somewhat problematic for cartographers.
A number of techniques have been developed to portray statistical surfaces, with varying
degrees of success. Research has shown that many map readers have difficulty in
perceiving quantitative surfaces when depicted with isolines, and numerous alternate
techniques have drawbacks as well, both with reader perception and production by map
makers. The purpose of this research was twofold: to develop a new technique for
producing continuous-tone maps using both free and commercial software, and to test the
effectiveness of these maps at representing quantitative surfaces by testing map readers.

Moore’s Law, observed in 1965 by Gordon Moore of Intel, the CPU
manufacturer, roughly states that computing power doubles every two years. This
phenomenon has had several effects: computers that were once too large or too expensive
for the average user have become ubiquitous over the last twenty years, and tasks that
were once relegated to mainfi'ames or minicomputers can now be easily accomplished
with widely available software on desktop computers. Continuous improvement has also
occurred in output devices, and currently, hi gh-resolution color laser printers can be
purchased for under $500. The map production technique outlined in this study was
performed on desktop computers with software available commercially and for free, and
the test illustrations were produced on a Hewlett-Packard color laser printer that is
relatively stande equipment in modern computer labs and offices.

The test instrument was designed to assess two things: first, whether high-spatial

frequency data is best represented with grayscale color schemes and lower spatial

52

frequency data with spectral colors, and second, to compare subject map reading
performance on spectral color and grayscale depictions of the same three quantitative
surfaces. Three real surfaces fiom Michigan were used: elevation, rainfall, and growing
degree days.

To answer the color scheme vs. spatial frequency question, readers were shown a
small version of each surface, along with two additional representations: a fourth-order
polynomial trend surface derived from the original, and the residuals from the trend
surface. These map triads were shown once in each of the four color schemes, for a total
of twelve triads. A significant number of subjects chose the trend map as most like the
original surface when shown in spectral colors, and the residuals map when shown in
grays. These results indicate that a significant number of subjects perceive high spatial
frequency features when surfaces are shown in grayscale, and they perceive broad trends
when surfaces are shown in spectral colors.

To compare map reading performance on spectral color and grayscale maps,
readers answered questions about high and low spots on each map, the landscape position
of points, the slope between map points, and surface roughness. Subjects saw each of the
three surfaces twice, once in colors and once in grays. The maps were rotated to help
reduce possible recognition of duplication, but map points were, with one inadvertent
exception, in the same locations so direct comparisons from map to map could be made.
Overall, the subjects performed significantly better on the color maps than on the
grayscale representations. The highest average score was on maps shown in the blue-to-

red spectral color scheme, and the worst performance was observed on the white-to-black

53

grayscale maps. Only two of the eight individual questions, however, showed
significantly higher performance on the color maps.

Mapping quantitative surfaces as outlined above is practicable. No unusual
hardware or expensive software is necessary to produce the maps, and high-quality
output may be obtained on an inexpensive color laser printer with ordinary paper.

Continuous-tone maps are planimetric, and, unlike isopleth maps, present the map
reader with a continuous-appearing symbology for interpretation. They represent the
quantitative surface as faithfully as other maps produced from the same data. Previous
studies have shown them to be more effective at conveying information about the
mapped surface than isoline maps. The results from the fifty-nine subjects tested during
the course of this research showed that spectral color, continuous-tone maps are easier for
subjects to interpret than continuous-tone, grayscale maps. However, caution should be
used when applying a spectral color scheme to a surface with potentially important
components that are high in spatial frequency, as they could be masked. In these
circumstances, regional components may look more important than is warranted, due to

the non-linear nature of the spectral color scheme.

54

References

Brassel, Kurt E. and Jack J. Utano. January 1979. “Design Strategies for Continuous-
Tone Area Mapping” American Cartographer 6: 39-50.

Brassel, Kurt. January 1974. “A Model for Automatic Hill Shading” The American
Cartographer 1:1: 15-27.

Brewer, Cynthia A., 1997. “Spectral Schemes: Controversial Color Use on Maps,”
Cartography and Geographic Information Systems, 24(4): 203-220.

Brewer, Cynthia A., Alan M. MacEachren, Linda W. Pickle, and Douglas Herrmann.
1997, “Mapping Mortality: Evaluating Color Schemes for Choropleth Maps,”
Annals of the Association of American Geographers, 87(3): 411-438.

Griffin, TLC. and BF. Lock. December 1979. “The Perceptual Problem in Contour
Interpretation.” The Cartographic Journal 16: 61-71.

Groop, Richard E. and Paul Smith. October 1982. “A Dot-Matrix Method of Portraying
Continuous Statistical Surfaces.” The American Cartographer 9: 123-131.

Jenks, George F. March 1963. “Generalization in Statistical Mapping” Annals of the
Association of American Geographers 53: 15-26.

Johnson, William F. 1984. “A Dot-Matrix Method for Representing Smooth Statistical
Surfaces.” Unpublished Master's thesis, Michigan State University.

Kumler, Mark. 1988. “Mapping Smooth Surfaces with Continuous Tone Maps.”
Unpublished Master's Thesis, Michigan State University.

Kumler, Mark P. and Richard E. Groop. October 1990. “Continuous-Tone Mapping of
Smooth Surfaces.” Cartography and Geographic Information Systems 17: 279-
290.

Kutner, Michael H. et al. 2005. “Applied Linear Statistical Models” 5th Ed. Duxbury
Press. ISBN 0-07-238688-6

Lavin, Stephen. April 1986. “Mapping Continuous Geographical Distributions Using Dot
Density Shading.” The American Cartographer 13: 140-150.

Lavin, Stephen, Jay Hobgood and Paul Kramer. May 1986. “Dot-Density Shading: A
Technique for Mapping Continuous Climatic Data.” Journal of Climate and
Applied Meteorology 25: 679-690.

Lewis, Peirce. 1992. "Introducing a Cartographic Masterpiece: A Review of the US.
Geological Survey's Digital Terrain Map of the United States, by Gail Thelin and

55

all.

 

 

Richard Pike," Annals of the Association of American Geographers, Vol. 82, No.
2 (June), 289-299.

Mersey, Janet E. 1990. Colour and Thematic Map Design: The Role of Colour Scheme
and Map Complexity in Choropleth Map Communication. Monograph 41,
Cartographica 27 (3).

Phillips, Richard J ., Alan DeLucia and Nicholas Skelton. 1975. “Some Objective Tests of
the Legibility of Relief Maps.” The Cartographic Journal 12: 39-46.

Phillips, Richard J. “An Experiment With Contour Lines.” December 1979. The
Cartographic Journal 16: 72-76.

Pike, Richard J. and Gail P. Thelin. 1992. "Visualizing the United State in Computer
Chiarascuro," Annals of the Association of American Geographers, Vol. 82, No. 2
(June), 300-302.

Rogowitz, Bernice E. and Lloyd A. Treinish. 1994. “Using Perceptual Rules in
Interactive Visualization.” SPIE Proceedings Vol. 21 79 Human Vision, Visual
Processing and Digital Display V: 287-295.

Rogowitz, Bernice E. and Lloyd A. Treinish. 1995. “How NOT to Lie with
Visualization.” Proceedings of the 1996 IBM Visualization Data Explorer
Symposium. http://opendx.npaci.edu/cdsiproceedings96/pravda/truevis.html

Slocum, Terry A. 1999. Thematic Cartography and Visualization. New Jersey: Prentice
Hall.

Smith, Paul. 1980. “Representing the Statistical Surface Using Continuous-Appearing
Grey-Tone Variation.” Unpublished Master's Thesis draft, Michigan State

University.

Yoeli, Pinhas. 1967. “The Mechanisation of Analytical Hill Shading.” The Cartographic
Journal 4: 82-88.

56

all.

 

 

General References

Bergman, Lawrence D., Bernice E. Rogowitz and Lloyd A. Treinish. 1995. “A Rule-
based Tool for Colorrnap Selection.” Proceedings of the IEEE Conference on
Visualization, 1 18-125.

Brewer, Cynthia A. 1999. “Color Use Guidelines for Mapping and Visualization.”
Chapter 7 from Visualization in Modern Cartography

Castner, Henry W. and Roger Wheate. December 1979. “Re-assessing the Role Played
by Shaded Relief in Topographic Maps.” The Cartographic Journal 16: 77-85.

DiBiase, David and Thomas Paradis. 1994. “Weighted Isolines: An Alternative Method
for Depicting Statistical Surfaces.” Professional Geographer 46(2): 218-228.

Irnhof, Eduard. 1982. Cartographic Relief Presentation. New York: de Gruyter.

Marchak, Frank M. et a1. 1993. “The Psychology of Visualization.” Proceedings of the
IEEE Conference on Visualization: 351-354.

Peterson, Michael P. 1999. “Cognitive issues in Cartographic Visualization.” Chapter 3
from Visualization in Modern Cartography.

Rheigans, Penny. 1992. “Color, Change, and Control for Quantitative Data Display.”
Proceedings of the IEEE Conference on Visualization: 252-259.

Robertson, Philip K. 1990. “A Methodology for Scientific Data Visualization: Choosing
Representations Based on a Natural Scene Paradigm.” Proceedings of the first
IEEE Conference on Visualization: 114-123.

Robinson, Arthur H. 1961. “The Cartographic Representation of the Statistical Surface.”
International Yearbook of Cartography 1: 53-61.

Rogowitz, Bernice E., Daniel T. Ling and Wendy A. Kellogg. 1992. “Task Dependence,
Veridicality, and pre-Attentive Vision: Taking Advantage of Perceptually-Rich
Computer Environments.” SPIE Proceedings Vol. 1666: Human Vision, Visual
Processing and Digital Display 111: 504-513.

Rogowitz, Bernice E. and Lloyd A. Treinish. 1993. “Data Structures and Perceptual
Structures.” SPIE Proceedings Vol. 1913: Human Vision, Visual Processing and
Digital Display IV: 600-612.

Rogowitz, Bernice E. and Lloyd A. Treinish. 1993. “An Architecture for Rule-Based
Visualization.” Proceedings of the IEEE Conference on Visualization: 236-243.

57

Tanaka, Kitiro. 1950. “The Relief Contour Method of Representing Topography on
Maps.” Geographical Review 40: 444-456.

White, Daniel J. 1974. “An Application of Continuous Tone Photography in Cartographic
Design.” Unpublished Master's Thesis, Bowling Green State University.

58

PP!“

Appendix 1
Consent Form

Map Study

You are being asked to participate in a map perception study. The study is being
conducted by Michael Hyslop as part of a master’s program in geography, under the
direction of Drs. Richard Groop and Judy Olson of the Geography Department at
Michigan State University.

You will be asked to answer questions on maps provided in a test booklet.

The length of time for participation is approximately 25 minutes.

There are no foreseeable risks to you if you participate in this study. Your
participation will not affect your grade in any course, and you are free to discontinue
participation at any time without penalty.

You are assured that you will remain anonymous in any reports of the research.
Within these restrictions you may receive a copy of results upon request.

You may receive further information about the study at the end of this session if you
request.

For further information about the research, you may contact:

Michael Hyslop voice: 906-487-2308
MTU School of Forestry fax: 906-487-2915
101 UJ Noblet Forestry and Wood Products Bldg

1400 Townsend Drive

Houghton, MI 4993 1-1295

01'

Dr. Richard Groop or Dr. Judy Olson voice: 517/355-4649
Department of Geography fax: 517/432-1671
Natural Science Building

Michigan State University

East Lansing MI 48824 .

For information about your rights as a subject in a research project, you may contact:

David Wright voice: 355-2180
Univ. Comm. for Research Involving Human Subjects fax: 517/432-1 171
246 Hannah Administration Bldg.

Michigan State University

East Lansing, MI 48824

I understand the above statements and freely consent to participate in this study.

 

Signed

 

Date

59

Appendix 2 - Test Booklet Part I

Test Booklet

PLEASE DO NOT OPEN UNTIL INSTRUCTED.

60

Section I

In this part of the test you will be shown maps in sets of three. Circle one of the two lower maps
- the one that looks the most like the top map.

Example:

Which map, b or c. looks more like map a?

(circle your choice)

 

Go ahead and complete this section of the test

61

 

62

 

63

 

 

 

66

 

67

Appendix 3 — Test Booklet Part H Version A

Section II

In this part of the test you will be shown individual maps and asked a series of questions.
Circle the correct answer, fill in the blank, or draw on the map as asked.

 

Example:
a t
25 50 '75 100 125 150 175
1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

inc (1 line from point A to point B. This slope along most of this line is generally
a) uphil b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop ”or depression
c) on a slope benveen a ridge or hilltop r r . a ley or depression (circle one)
5) Estimate the elevation at point C 2 § 2

6) book at the circle to the right - 3 m . and imagine it centered around points T and U.
The area around T is a) flatter , ;« lar than the area around U (circle one)

V’N

 

8) Which quadrant is most irregular? (circle one)

MI

68

 

 

1600 1800 2000 2200 2400
I) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and C. The area around T is
a) flatter b) more irregular than the area around C (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
8) / b) \ c) d) e) 0
8) Which quadrant is most irregular? (circle one) in \ /
9

MI

 

 

600 700 800 900 1000 1 100 1200
1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)
5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
a) b) C)

d) e) 0
J \r
8) Which quadrant is most irregular? (circle one) n

n-

70

 

 

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map
3) Imagine a line from point A to point B. This slope along most of this line is generally

a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression

c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a)fiatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
8) e) f)

b) c) d
M N“ .N m ~— -~
8) Which quadrant is most irregular? (circle one)
In

M-

71

 

 

 

 

 

3200 3600 4000 4400 4800
1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map
3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)
4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)
5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and C. The area around T is
a) flatter b) more irregular than the area around C (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope

3) b) C) d) e) f)
In

8) Which quadrant is most irregular? (circle one) u

72

 

I) Put an H at the highest point on the map 2) Put an L at the lowest point on the map
3) Imagine a line from pointA to point B. This slope along most of this line is generally

a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression

c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
8) b) c) d) e) f)

8) Which quadrant is most irregular? (circle one)

II

 

 

1200 1300 1400 1500 1600 1700 1800

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from pointA to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
a) b) e) t)

«frxww

8) Which quadrant is most irregular? (circle one)

u-

Appendix 4 — Test Booklet Part H Version B

Section II

In this part of the test you will be shown individual maps and asked a series of questions.
Circle the correct answer, fill in the blank, or draw on the map as asked.

 

Example:
75 100 12 5 150175
1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

ine a line from point A to point B. This slope along most of this line is generally
a) uphil b) downhill c)flat (circle one)

4) Point A IS a) on a ridge or hiIIto b) m a valley or depr sion
c) on a slope between a ridge or hilltop701 I i epression (circle one)

5) Estimate the elevation at point C

6) Look at u =- '- « right of the map and imagine it centered around points T and U. The area around T is
a) flatter h more irregular an the area around U (circle one)

 
   
 
  

. u - int C to point B. Circle the profile below that most closely matches its slope

C) \/\\d )A/ e) \/\0 ~/\/
8) Which quadrant' 15 most irregular? (circle one) I "m -m

7) Imagine a line
a)

75

 

 

3200 3600 4000 4400 4800

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map
3) Imagine a line from point A to point B. This slope along most of this line is generally

a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression

c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and C. The area around T is
a)fiatter b) more irregular than the area around C (circle one)

7) lrnagine a line from point C to point B. Circle the profile below that most closely matches its slope
a) \ b) c) d) e) o
8) Which quadrant is most irregular? (circle one)

II

76

 

 

I) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c)flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
a) b) C) d) e) t)

8) Which quadrant is most irregular? (circle one) I u

MI

77

 

600 700 800 900 1000 1100 1200

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B Circle the profile below that most closely matches its slope
a) ) c

\W-r/d\/\

8) Which quadrant is most irregular? (circle one) in

 

10 12 14 1B

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) PointA is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
a) flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B. Circle the profile below that most closely matches its slope
8) b) C) d) e) f)

‘-\/\ l\/" W V\- -\/\ ~—
8) Which quadrant is most irregular? (circle one) an

El

 

 

1200 1300 1400 1500 1600 1700 1800

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c) flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a valley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and U. The area around T is
o)flatter b) more irregular than the area around U (circle one)

7) Imagine a line from point C to point B Circle the profile below that most closely matches its slope
a) b) c) d) e)

JM/“NLJ

8) Which quadrant is most irregular? (circle one) l“

ml

80

 

 

1600 1800 2000 2200 2400

1) Put an H at the highest point on the map 2) Put an L at the lowest point on the map

3) Imagine a line from point A to point B. This slope along most of this line is generally
a) uphill b) downhill c)flat (circle one)

4) Point A is a) on a ridge or hilltop b) in a volley or depression
c) on a slope between a ridge or hilltop and a valley or depression (circle one)

5) Estimate the elevation at point C

6) Look at the circle to the right of the map and imagine it centered around points T and C. The area around T is
o) flatter b) more irregular than the area around C (circle one)

7) Imagine a line frbom point C to poicnt B. Circle the profile below that most closely matches its slope
3) 0

\W/\/\/

8) Which quadrant is most irregular? (circle one)

u-

   

IIiii‘liifliiilflljljiilWill

.........