INFORMATION TO USERS

This dissertation was produced from a m icro film co p y of th e original docum ent.
W hile th e m ost advanced technological means to photograph and reproduce this
d ocum ent have been used, th e q u ality is heavily dependent upon the q u a lity of
the original subm itted.
T he

fo llo w in g explanation o f techniques is provided to

help yo u

understand

markings or patterns which m ay appear on this reproduction.
1.

T h e sign o r " ta rg e t" fo r pages apparently lacking from the docum ent
photographed

is "Missing Page(s)". If it was possible to o btain the

missing page(s) o r section, they are spliced in to the film along w ith
adjacent pages. T h is may have necessitated cu tting thru an image and
d uplicating adjacent pages to insure you com plete co ntin u ity.
2.

W hen an image o n the film
m ark, it
copy

is o bliterated w ith a large round black

is an in d icatio n th at th e photographer suspected th a t the

may

have moved during

exposure and thus cause a blurred

image. Y o u will fin d a good image of th e page in the adjacent fram e.
3.

W hen a map, drawing or chart, etc., was part o f the m aterial being
p h o to g ra p h e d

th e

photographer

"section in g " the m aterial.

fo llo w ed

a

d efin ite

m ethod

in

It is custom ary to begin photoing at the

upper le ft hand corner o f a large sheet and to continue photoing from
le ft

to

right

sectioning

in

equal sections with

a small

overlap.

If necessary,

is continued again — beginning b elo w th e first ro w and

continuing on u n til com plete.
4.

T h e m ajo rity of users indicate th a t the textual content is of greatest
value,

however,

made fro m
dissertation.

a som ewhat higher q u ality

"photographs"
Silver

prints

if essential
of

reproduction could

be

to the understanding o f the

"photographs"

may

be

ordered

at

additional charge by w ritin g th e Order D epartm ent, giving the catalog
num ber, title , a u th o r and specific pages you wish reproduced.

University Microfilms
3 0 0 N orth Z e e b Road
A n n A rbor, M ic h ig a n 4 8 1 0 6
A X e ro x E d u catio n C o m p a n y

73-5400

HOLLOWAY, William Harold, 1934AN EXPLORATORY STUDY OF SELECTED ASPECTS OF
THE PUBLIC SCHOOL SYSTEM IN MICHIGAN
EMPLOYING SYSTEM SIMULATION.
Michigan State University, Ph.D., 1972
Education, administration

University Microfilms, A XEROX Company , Ann Arbor, Michigan

AN EXPLORATORY STUDY OF SELECTED ASPECTS
OF THE PUBLIC SCHOOL SYSTEM IN MICHIGAN
EMPLOYING SYSTEM SIMULATION

By

William Harold Holloway

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Administration and Higher Education

1972

PLEASE NOTE:

Some pages may have
in d istinct

print.

F i l me d as r e c e i v e d .

U n i v e r s i t y M i c r o f i l m s , A Xe rox E d u c a t i o n Company

ABSTRACT

AN EXPLORATORY STUDY OF SELECTED ASPECTS
OF THE PUBLIC SCHOOL SYSTEM IN MICHIGAN
EMPLOYING SYSTEM SIMULATION
By
William Harold Holloway

This study was both developmental and analytical.
A computer simulation model was developed to represent
two components of the public school system in Michigan.
The two components were:

the student population sector

and the teacher population sector.

The basic assumption

was that the number of public school students for any
given year represent a primary drive of the system.
Therefore,

a dynamic supply-demand function should exist

that would permit prediction of the number of professional
staff needed to provide services to the public school
students in Michigan in any given year.

Specifically,

the

question was asked whether such a simulation model be
developed;

and, given that development was possible would

the model be efficacious?

That is, could the simulation

vehicle generate predicted levels of needed professional
staff which would be more accurate than predictions which

William Harold Holloway

could be obtained by conventional forecasting techniques,
such as the method of moving averages
exponential smoothing

(two year)

and

(a = .8).

Data related to student and teacher populations
(SPOP and TPOP respectively)

were aggregated at the state

level and also collected for factors and parameters within
each component which contributed to variance of the two
status variables SPOP

(t) and TPOP

(t).

System identi­

fication was completed by formulation of operating charac­
teristics for each component and specification of the
hypothesized supply-demand relationship detailing component
interaction.

The mathematical model was translated into a

computer program employing Fortran IV and written for the
Michigan State University, CDC-6500 system.

This completed

the development phase of a linear, dynamic, discrete,

and

deterministic simulation model.
The analytical phase of the study required con­
sideration of model verification, model validation, and
completion of planned experiments.

Thiel's U statistic

was employed to guide model verification as an estimate of
the congruence of simulator generated time series with the
corresponding real world time series for the primary
endogenous variable TPOP

(t).

Model validation required a presentation of the
structural elements of the model in relation to correspond­
ing elements of the real world system of interest.
Questions from a list which had been formulated prior to

William Harold Holloway

model identification were subsequently answered.
addition,

In

a rationale was provided which attempted to

explain why the model had been conceptualized in the
present form.
Two experiments were conducted after model verifi­
cation and validation was completed.

Both experiments

compared the accuracy of forecasts achieved by simulation,
moving averages,

and exponential smoothing.

The first

experiment concerned forecasts required for short-range
(year to year)

planning and the second experiment concerned

forecasts for long-range

(ten year)

ment employed a fixed effects,

planning.

analysis of variance model.

The independent variable was treatments
casting)

Each experi­

(method of fore­

and the dependent measure was the difference

between attained predictions and actual values of TPOP
A ten year period of time

(N = 10, 1959-1968)

was designated

as the period for comparison.

All statistical tests

employed an alpha

.05.

(a) level of

(t).

In the first experiment the attained value of the
mean square ratio for types of forecasting methods
was not significant at the

(2.79)

.05 level and the null hypothesis

of equal accuracy in forecasting was retained.

In the

second experiment the attained value of the mean square
ratio 9.85 for types of forecasting methods was significant
at the .05 level.

Follow-up tests were conducted using

post hoc procedures.

Of the three pair-wise comparisons,

two were found to be significant.

That is, both simulation

William Harold Holloway

and exponential smoothing forecasts were found to be
significantly more accurate than moving averages.

There

was no significant difference between simulation forecasts
and predictions achieved by exponential smoothing.
both experiments,

In

it was observed that the mean difference

for simulation forecasts was more accurate than the mean
difference forecast by either of the aforementioned
methods.
It was concluded that a linear, discrete,

dynamic,

and deterministic simulation model could be developed;

and,

the model would generate time series data which were
congruent with time series data for corresponding variables
of the real world system of interest.

Where short-range

planning forecasts are desired any one of the three methods
will provide equally accurate predictions.
forecasts are desired,

When long-range

predictions obtained by simulation

or exponential smoothing methods will be significantly
more accurate than moving average predictions.

Implications

and suggested areas for future research were discussed.

DEDICATION

To those who can only wait with infinite patience
and understanding:

my wife and children.

May they find

some measure of satisfaction in the knowledge that this
goal could not have been realized without their support.

ACKNOWLEDGMENTS

The writer wishes to express his appreciation for
the able and ready assistance that was extended to him in
so many unrecorded, yet not unnoticed ways, by the faculty
and staff of the College of Education.
In particular,

the advice and consideration

received from Professor Frederick R. Ignatovich, Chairman,
and committee members, Professor James Costar,
Robert C. Craig,

Professor

and Professor Samuel A. Moore, II, was most

sincerely appreciated.

TABLE OF CONTENTS

Page

LIST OF TABLES

vii

LIST OF FIGURES

viii

Chapter
I.

II.

INTRODUCTION ..................................

1

Statement of the Problem
.................
Need for the S t u d y ........................

4
5

Need for Simulation Research
. . . .
Need for P l a n n i n g ........................

6
8

Purpose of the S t u d y........................
Definition of T e r m s ........................
Limitations of the S t u d y .................

11
13
15

A s s u m p t i o n s ...............................

15

REVIEW OF RELATED LITERATURE .................

17

The Organization as System .................

18

General Systems Theory
.................
Basic Concepts and Associated
D e f i n i t i o n s ...........................
Organizational Systems
.................

18

Aspects of Computer Simulation

. . . .

Historical A s p e c t s ........................
Value and Objective A s p e c t s ..............
Procedural Aspects of Simulation . . .
Aspects of Simulation Models
. . . .
Analysis of Simulation Studies.
. . .

22
27
31
31
33
35
47
52

Chapter

Page
Verification ...............................
V ali d a t i o n ..................................
Experimentation ...........................
Organizational Planning

....................

The Nature of Planning ....................
F o r e c a s t i n g ...............................

III.

IV.

V.

54
56
57
61
61
63

S u m m a r y .....................................

67

TECHNIQUES AND P R O C E D U R E S ....................

69

Formulation of the P r o b l e m .................
Collection and Processing of Data.
. . .
Formulation of the M o d e l ....................

69
72
74

Model C h a r a c t e r i s t i c s ....................
Component Elements ........................

74
76

Estimation of Parameters ....................
Model E v a l u a t i o n ...........................
Formulation of the Computer Program . . .
Model V a l i d a t i o n ...........................
Design of Simulation Experiments . . . .
S u m m a r y .....................................

76
77
79
80
81
85

REPORT OF F I N D I N G S ...........................

86

Model V a l i d a t i o n ...........................

86

Model D e v e l o p m e n t ........................
Variable Definitions and Operating
Characteristics
........................
Model I d e n t i f i c a t i o n ....................
Model Validation Questions

87
89
91
94

Model Verification ...........................
Model Experimentation........................

99
107

Experiment O n e ...........................
Experiment T w o ...........................
Summary.....................................

108
110
113

SUMMARY AND CONCLUSIONS........................

115

Purpose of the S t u d y ........................
Techniques and Procedures
.................

115
116

v

Chapter

Page
Analysis of Findings ........................
C o n c l u s i o n s ..................................
Implications of the S t u d y .................
Suggestions for Future Research.
. . .

R E F E R E N C E S ............................................

118
121
123
125
129

APPENDICES
Appendix
A.

The MSU University M o d e l .....................

137

B.

Michigan Public School System Simulation
Model Schematic ...............................

138

C.

Michigan Birth Rates 1940-1971

139

D.

EDUSIM— Computer Program

141

E.

Certificate Distribution for 1968 . .

.
.

.

142

LIST OF TABLES

Table
1.

Page
Relationships Between Actual Teacher
Populations and Actual and Simulated
Teacher, Student Populations .................

99

2.

Actual and Simulated Response for TPOP(t)

.

.

100

3.

U Statistic and Parameter Values for
Separate Simulation Estimates of TPOP(t)

.

.

102

4.

Simulated and Actual Teacher Population
Parameters (1959-68)........................

104

5.

Fixed Effects ANOVA for Teacher Population
Predictions by Separate Forecasting
M e t h o d s ....................................... 109

6.

Cell Summary for Experiment O n e ................ 109

7.

Fixed Effects ANOVA for Teacher Population
Predictions by Separate Forecasting
M e t h o d s ....................................... Ill

8.

Cell Summary for Experiment T w o ................ 112

9.

Post-Hoc Comparisons for Experiment Two .

.

.

C-l.

Michigan Birth Rates

(1940-1971)

C-2.

Age-Specific Death Rate Per 1,000 Individuals

E-l.

Certificate Distribution for Reported 1968
Professional Staff in Michigan
..............

112
139

.

140

142

r~

LIST OF FIGURES

Figure
1.

2.

Page
Comparison of Actual and Simulator
Predicted Teacher Populations (1959-1968)

.

.

105

Comparison of Actual and Simulator
Predicted Teacher Populations (1959-1968)

.

.

106

viii

CHAPTER I

INTRODUCTION

The investigator's experience in education both as
teacher and administrator has evidenced an enduring inter­
est in applied quantitative methodology and an increasing
interest in the potential value of the computer to the
practice of administration.
During this period of time it has been observed
that educational systems have continued to grow in their
complexity.

School staffs have been expanded to include

heretofore unknown personnel.

Roles have been redefined

to reflect changes in patterns of responsibility and
increasing specialization.

New communications systems

have been implemented to accommodate the information needs
of independently and interdependently functioning sub­
systems.

Increasing attention has been focused on intra­

system linkage and interaction as well as on the relation­
ship of the district with ancillary and supra-systems.
The expansion of traditional boundaries has resulted in
a loss of autonomy and district independence giving way
to greater inter-system dependence.

1

!

2

The growing complexity of the educational enterprise
has predicated change in the character of administration.
Entirely new concepts of control have evolved such as
PERT

(Program Evaluation and Review T e chnique), PPBS

(Planning, Programming,

and Budgeting Syst e m ) , and CMI

(Computer Managed Instruction).

Administrators are

increasingly turning to the computer for storage,

retrieval,

and analysis of information about the status and direction
of the system giving way to concepts of MIS
Information System)

and MBO

(Management

(Management By O b j e c tives).

Such changes have frequently resulted in adoption of
planning and evaluation programs and an accompanying need
for enlightened understanding of the total enterprise.
Comprehensive theory and utilization of advanced technology
appear to have considerable promise in this regard.
The work of Koenig, et a l . (1968), Van Dusen
(1969), and DeLeeuw and Gramlich

(1968)

represents recent

efforts to explore analytical tools which hold promise for
a wholistic approach to the exploration of behavior in
systems.

The inherent value of such techniques to

researchers resides in the extended capability to encompass
a multitude of system variables.
notes,

McNamara

(1971, p. 4 34)

the primary limitation of such approaches is the

necessity for a considerable body of information about the
system.

However,

Holland and Gillespie

previously advocated,

L

" . . .

(1963, p. 23) had

rather than wait for adequate

3

data before doing a simulation,

it would be useful to

make a simulation study before going too far with sta­
tistical research so that the latter could be focused more
sharply on the data that matter most."
At present,

there is a need for further exploration

of educational systems as wholistic entities.
many cases
Michigan)

(for example,

Further,

in

the state public school system in

an adequate base for wholistic analysis already

exists since information is regularly and uniformly
collected from all school districts in the state.

The

availability of the data facilitates the problem of
considering the system with a wholistic perspective.
However, the extensiveness of the data base produces
another associated problem.

How can the multitude of data

that emanates from the system be organized,
analyzed,

assimilated,

and synthesized to produce not just data but

information which

focuses on the functional integration of

parts— in short, preservation of the wholistic perspective?
The writer elected to pursue simulation research
because of long standing interests and past experiences in
education which suggested that a wholistic approach to
organizational analysis is more powerful than a particu­
laristic approach.

A problem which seems ripe for

wholistic analysis is the relationship between student
population levels
supply).

(demand)

and professional staff

(the

Recent experience indicates that professionals

have been trained with little regard for the demand posed
by the market.

There is an obvious need to balance the

supply and demand.

However, even more crucial is the need

to understand the dynamics of supply and demand relation­
ships .
Past investigations
cation Association,

(Costa,

1970; Michigan Edu­

1971) have been particularistic and

have explored various strategies for predicting supplydemand relationships including the method of moving
averages and exponential smoothing.

However,

it is

believed the particularistic studies which tend to ignore
the dynamics of component interaction and conventional
forecasting strategies many of which are no more than
mechanistic algorithms fail to achieve the predictive
potential that may be possible through the wholistic
approach of system simulation.

Statement of the Problem
The basic problem to be studied was methodological
and heuristic in nature.

That is, could a simulation

model be developed and if so, would the model be effi­
cacious?

The investigator attempted to develop a simu­

lation of the public elementary and secondary school
system in the State of Michigan.

Attention was focused

on student population and professional staff levels as two
major components of that system.

Given that such a model

could be achieved, the dynamics of the system would be

explored to determine the predictive potential of the
model.

The predictions of needed professional staff

generated by the simulator were then to be compared
against predictions achievable by conventional forecasting
techniques,

such as the method of moving averages and

exponential smoothing.
Couched in these terms the problem encompassed two
major sub-problems:
1.

Development:

Can a valid simulation model be

developed which would represent the dynamics of
two major components of the public elementary and
secondary schools in the State of Michigan?
2.

Exploration:

Can the simulation model provide more

accurate predictions for planning purposes than
conventional forecasting techniques?

Need for the Study
The nature of the problem selected for study
predicated a two-fold discussion of needs.

First,

development of a computer simulation model addresses the
methodological need for simulation research in education.
Second, application of the model addresses the need to
obtain more valid planning information regarding the
dynamics of supply and demand for certificated professional
teachers in the State of Michigan.
needs is presented in that order.

The discussion of

6
Need for Simulation Research
The behavioral sciences unlike the physical
sciences are disadvantaged by the lack of comprehensive
theories,

tools of analysis,

instruments.

and precise measurement

However, the scientific task of theory

development in the behavioral sciences still moves forward
employing the available instruments regardless of their
incomplete state.

It seems reasonable that a proportion

of research effort should be directed toward exploration,
development,

and perfection of research tools that indicate

some measure of promise.
Rosenhead

In this regard, Elton and

(1971, p. 139) write with reference to the

behavioral sciences in general:
An area which needs particular attention is that of
the testing and validation of simulation models.
The
present position (it works if management says it works)
is less than satisfactory, and there is need for more
objective test procedures.
More experience is needed
in the development of modular simulations--where
particular formulations can be unplugged and others
substituted with a minimum of fuss.
Other authors

(Van Dusen,

1969; Mauch,

1962)

address the need for exploration of such tools as linear
programming, queueing theory,

systems analysis,

simulation in the field of education.
p. 419)

McNamara

and
(1971,

comments:

Management science models which express the organi­
zational environment and its dynamics in mathematical
relationships have been applied in the fields of
business management, military operations research,
public welfare and regional planning.
Although the
value of such models has been demonstrated in the

7

areas listed above, educational administrators and
planning specialists appear to be making little use of
these scientific approaches.
The analysis of systems from a "wholistic" orien­
tation is contrary to current research methodology which
advocates limited arrays of independent and dependent
variables.
suggests:

In this regard, Bertalanffy

(1968, p.

31)

"It is necessary to study not only parts and

processes in isolation, but also to solve the decisive
problems found in the organization and order unifying
them, resulting from dynamic interaction of parts, and
making the behavior of parts different when studied in
isolation or within the whole."

Wholistic studies require

techniques capable of encompassing and manipulating a
multitude of variables.

At present,

such techniques are

not an integral part of the array of educational research
tools.

Smith

(1968, pp.

326-26)

that using all the variables,
10

70

concluded from his study

" . . .

would have required

outcomes to provide a model encompassing all possible

events.

Th ;s figure approaches the estimated number of

atoms in the known universe 10

76

..."

Research approaches dealing with organizations are
frequently limited or prohibited by the necessity to
respect the organization's right to continue uninterrupted,
such as, the problem of experimental control.

Simulation,

as a tool of analysis is an alternative which permits
organizational research without interruption.

At the

8

same time, the need for experimental control is resolved.
Mauch

(1962, p. 159) touches upon this advantage of

simulation studies as further justification for the
employment and exploration of simulation as an important
alternative.

Need for Planning
The need for planning in educational systems may
be interpreted as the need to devise or identify new or
revised procedures through which explicit systemic goals
may be accomplished

(Webster,

7th ed.).

Planning is

further related to policy in the sense that policy is a
legitimized procedure or course of action.

The logic

suggests that planning ought to precede procedure speci­
fication and formal policy action,

though this may not

always be the case in practice.
Heald and Moore

(1968, p. 122) clearly indicate

that leadership is one of three major responsibilities
which define the role of the school administrator.
(NSSE y r b k . , 1964, p.

122)

Lipham

takes the position that

leadership is the initiation of a new structure or pro­
cedure for accomplishing or changing systemic goals or
objectives.

Clearly then, the school administrator is

responsible for leadership acts,

leadership entails the

initiation of new or modification of existing procedures
and at least a portion of such activity may be broadly
interpreted as planning.

Thus,

the extent to which there

9

is need for revised or new procedures there is need for
planning.

It is contended that examination of the need

for planning may be accomplished indirectly through
examination of the need for new or revised procedures.
The problem at hand concerns the nature of dynamic
relationships between and within two of the four essential
components

(teachers and students)

of public school

systems as identified by Heald and Moore

(1968, p. 10).

To what extent is there evidence of the need for new or
revised procedure in relation to the components of inter­
est?
In a paper reviewing teacher supply and demand
in the State of Michigan,
cation

the State Department of Edu­

(1971, p. 1) notes that:

For more than a quarter of a century, Michigan and the
nation have had a shortage of teachers for the ele­
mentary and secondary schools.
The dimensions of the
problem have varied but never has the problem been of
less than major proportions.
By inference,

it may be reasoned that a primary

objective of the teaching profession and of teacher
training institutions under such circumstances was to
reduce or eliminate the supply disparity

(under-production).

It may additionally be inferred that at least one alterna­
tive to such an objective may have required some change in
procedure and policy in order to accomplish the objective
since the system as defined was not keeping pace with
demand.

The same reference

(MSDE,

1971, p. 1) continues:

10

"Within the past two years

(1969 and 1970)

the shortage

has been alleviated; June,

1970 graduates receiving

teachers certificates frequently found difficulty in
obtaining positions."
Irrespective of what factors were influential in
this change, dynamic equilibrium of the system was
momentarily restored as supply reached the level of demand.
However,

the duration of the resultant state of equilibrium

was brief as other social forces

(increasing salaries,

etc.) converged to attenuate the precarious balance.
Various studies

(MSDE, 1971; NEA,

1970; USOE,

1970)

provide current estimates for Michigan that indicate the
overproduction of teachers for 1971-72 may reach as high as
16,000.

Long range estimates, on the other hand indicate

overproduction will gradually increase to 19,000 by 1979-80.
The mandate for some type of change in procedure is clear as
are some of the alternatives such as control system
design.

Johnson,

et a l . (1967, p. 86) write:

the objective of control system design,

" . . .

therefore,

is to

determine the relevant characteristics which, when conrolled, maintain the function of the system within allowable
variations."
Given the assumption that variation of the system
within tolerable thresholds is desirable,
alternatives can be formulated.

several control

Evidence might indicate

a reduction in pupil-teacher ratio as a solution to the

11

imbalance.

In essence,

a reallocation of resources.

Or,

financial and other factors may dictate that the production
flow be adjusted to produce certificated professionals
according to some pre-determined replacement need and
thereafter to maintain the status quo.

This action would

constitute a re-ordering of policy and procedure which
would initiate repercussions in ancillary components.
In summary,

it seems clear there is a need for the

development and testing of vehicles which enable explanation
and exploration of system dynamics.

Given that such a

model can be developed and validated there is further need
for the testing of alternative policy strategies as one
approach to the generation of planning information which
is in part derived from the evaluation of alternative
strategies.

Purpose of the Study
It was the purpose of this study to examine the
relationships between student population levels and demand
for professional staff in the public school system in
Michigan.

It was expected that boundaries of the sub­

systems would be established,

important system variables

would be identified, a determination of exogenous and
endogenous variables could be accomplished,

and the

functional relationships between such variables could be
established prior to the development of a computer
simulation program.

It was believed that further

12

refinement of the functioning system would provide a basis
for the generation of predictions which would add credence
to the analytical potential of simulation in general, and
this model in particular.
Given that the model could be developed,

a test was

designed to compare simulated prediction results against
those achievable by other forecasting techniques,

such as,

the method of moving averages and exponential smoothing.
The purposes of the test would be to acquire additional
credibility for the model and its performance in relation
to short and long range planning needs.
successfully passed,

If the test were

it would then be possible to examine

the effects of various policy alternatives related to the
current oversupply of teachers at enhanced levels of
confidence.

Such ongoing experimentation would facilitate

production of planning information necessary to edu­
cational administrators as they contemplate new or revised
procedures and policies for the system.
Directly related to the stated purpose of this
study are the following objectives:
1.

Development of a simulation model.

2.

Development of a functional computer program
which embodies the simulation model.

3.

Validation of the model.

13
4.

Verification of the model.

5.

The completion of two related experiments with the
simulation vehicle.

Definition of Terms
The following terms are relevant to this study and
are defined as follows:
C o m p o n e n t .— An identifiable sub-system of the
system of interest.

In this study two components or

sectors are considered;

they are the student population

sector and the professional staff sector.

Deterministic.— Response patterns of simulator
generated data which are fixed as opposed to varying.

D i s c r e t e .— Models which incorporate time as a
series of distinct units as opposed to a continuous time
series.

All simulation models can be considered discrete

since continuous time sequences cannot be operationalized
only approximated by making the incremental unit of time
extremely small.

D y n a m i c .--A system in which the response is
dependent upon past values of the input is said to be
dynamic and to have memory.
tant parameter in the system.

Thus, time becomes an impor­

L

14
M o d e l .— A mathematical description of the system
of interest.
and Ratoosh,

In this sense a "symbolic" model

(Churchman

1959, p. 158) where symbols designate

properties of the system of interest.

Parameter.— A parameter is a variable whose value
may be assigned by the investigator to reflect various
conditions in the system.

A parameter is not necessarily

constant.

Professional S t a f f .— Any individual who is permitted
by virtue of accepted credentials to conduct instruction
in the public elementary and secondary schools of Michigan.

S imulation.— A representation of some aspect of
reality.

Computer simulation implies the representation

will be translated to a computer program medium.

Student.— Any person, who by virtue of age,

is

admissable to the public elementary and secondary schools
of Michigan.

System.— A collection of identifiable,

interacting

parts deliberately constructed to achieve specific goals.
In this study the system of interest is the public schools
in Michigan.

Forecasting Techniques.— Methods or strategies for
obtaining future values of variables of interest.

.

In

15
this study, only the method of moving averages
and exponential smoothing

(two year)

(a = .8) will be considered.

Limitations of the Study
In view of the amount of time and resources
required for most simulation studies,

it seemed advisable

to reduce the scope of this effort to manageable pro­
portions.

Therefore, only two components of the public

school system in Michigan have been included.

Conclusions

derived from the study should not be generalized beyond
the limits of these sectors nor to school systems other
than Michigan.
The test of the predictive ability of the model
could not consider all possible forecasting techniques.
Therefore,

the techniques selected were chosen on the

basis of ease of employment,

general utility and recog­

nition by others in the field.
methods

The modifications of these

(for the purposes of the second experiment) were

constructed on the basis of the expected course of action
by those attempting to employ moving averages or ex­
potential smoothing given the situation calling for long
range planning information,

that is, ten year periods.

Assumptions
The assumption was made that student population
levels in any given year and within prescribed age limits
described a major impetus for system response.

It is

16
believed that sufficient legislative mandate, prior
studies, and empirical evidence exist to support such an
assumption.

At the same time, however,

it is recognized

that a computer simulation model constructed on the basis
of a different postulate could have resulted in a differ­
ent perspective of the system and entirely different
conclusions.
Finally,

it was necessary to assume the system of

interest to be block recursive.

That is,

it was assumed

that interaction among other components of the system of
interest,

such as administrators and Boards of Education

could be considered negligible.
The review of the literature which follows deals
with important areas of simulation research.

First,

general systems theory and the current state of theory
development insofar as the organization is conceptualized
as a system.

Second,

the much lesser developed field of

computer technology and in particular computer simulation.
The third area concerns rational planning and the need for
improved methods of prediction.

CHAPTER II

REVIEW OF RELATED LITERATURE

The review of literature undergirding this study
concerned three topical areas.

First,

consideration of

the organization as system reviews important concepts and
the current state of theory development in this field.

It

is believed that an awareness of organizations as systems
is important as a prerequisite to the rationale for
mathematical analysis and system simulation.

Second,

the

review encompasses technological aspects of computer
simulation concluding with a review of the controversial
issue of statistical analysis.

Third, the review deals

with planning as an integral part of the role of management.
Planning has previously been defined as the development of
new or modified procedures for goal achievement.

In this

sense, planning is predicated upon the acquisition of
information concerning dynamic aspects of the system and
the ability of managers to predict future behavior.

17

18
The Organization as System
Numerous authors

(Bertalanffy, 1960; Griffiths,

1959; Johnson, et a l ., 1967;

and Parsons,

1951)

have

explored the utility of systems thinking as a conceptual
framework for organizational theory.

Each in his own

right has contributed substantially to the further
elaboration of such a theory, yet the work represents only
a beginning.

In view of the absence of a comprehensive

theory from which to depart,

the best strategy would be

to employ a systems approach to the task at hand, taking
full advantage of accepted concepts from General System
Theory

(GST) and drawing appropriate parallels to a theory

of organization where these exist.

Johnson,

et a l . (1967,

p. 69) state:
Thus modern organization theory, as it has evolved,
inevitably merges into concepts of general systems
theories.
Scientific investigation and research
findings using general systems theory as a frame of
reference can provide important understanding of the
most complex of manmade systems--his large scale social
organizations.
This section of the review deals with the organi­
zation as system.

Three sub-topics will be considered:

general systems theory,

concepts and definitions in GST,

and finally the organizational system.

General Systems Theory
While definitions of the term system have been
advanced by many authors in the field, there appears to
be emerging agreement upon at least two levels of

19
definition.

The more general,

(1968, p. 38) as,

" . . .

advocated by Bertalanffy

sets of elements standing in

interaction . . .," speaks to every possible system.
Other authors support the more particularistic viewpoint
such as that advanced by Heald and Moore

(1968, p. v i i i ) ,

" . . . a system is a series of essential components whose
functions are coordinated for the purpose of achieving the
goals of the organismic whole."

The term organization

varies as a function of the particular theory, but may be
approached in terms of system.
(1968)

and Etzioni

Thus, Cooper and McGillem

(1964) provide the basis for the

following definition which will be used throughout the
study.

An organization is a planned system of interacting

components deliberately constituted and reconstituted to
achieve desired goals.
It should be stressed that the above definition of
organization requires that social organizations be con­
sidered only one category or subset of all possible
systems.

Boulding

(1967, pp.

10-13) has proposed an

ordering of systems according to their general character­
istics or lack of them.

Specific levels in the ordering

scheme are as follows:
1.
2.
3.
4.

5.

Static structure systems— atoms, the planets.
Dynamic systems— the level of clockworks.
Cybernetic systems— the level of feedback.
Life-maintenance systems— the level of open systems,
distinguished by life as opposed to not life, the
cell.
Genetic-societal systems— the level of division of
labor, blueprinted growth, typified by the plant.

20
6.

7.

8.
9.

The animal system— a level characterized by
increased mobility, teleological behavior, and
self-awareness.
The human system— a level which possesses all of
the characteristics of the previous six and in
addition, self-awareness, and self-consciousness,
i.e., man not only knows but he knows that he
knows.
Social systems— the level of organization.
Transcendental systems— the level of systems of
systems.
The ordering scheme proposed by Boulding

(1967)

has been devised so that each ensuing system is a more
advanced and complex level incorporating the character­
istics of all foregoing levels.

Bertalanffy

(1968, p. 32)

thus concludes that organizations as systems may be
expected to display such characteristics as distinct
physiologies, metastasis,

homeostasis,

and self-maintenance.

The author further suggests:
It seems legitimate to ask for a theory, not of
systems of a more or less special kind, but of uni­
versal principles applying to systems in general.
In
this way, we postulate a new discipline called General
Systems T h e o r y . Its subject matter is the formulation
and derivation of those principles which are valid for
systems in general.
General systems theory is concerned with developing
a systematic, theoretical framework for describing general
relationships of the empirical world.

A broad spectrum

of potential achievements for such a framework is evident.
Existing simularities in the theoretical construction of
various disciplines can be pointed out.

Models can be

developed which are applicable to many systems, whether
physical, biological, behavioral or social.

An ultimate

21
but distinct goal will be a framework,
theory

transcendental

(a system of systems of systems) which will tie

all disciplines together in a meaningful relationship.
In the words of Boulding

(1967, p. 6),

" . . . this is

the quest of GST."
Johnson, et a l . (1967, pp.

9-10)

summarizes the

state-of-the-art in theory development using Boulding's
ordering scheme as a frame of reference:
Dynamic clockwork systems, where prediction is a
strong element, are evident in the classical natural
sciences such as physics and astronomy; yet even here
there are important gaps.
Adequate theoretical models
are not apparent at higher levels.
However, in recent
years closed-loop cybernetics, or "thermostadt" systems
have received increasing attention.
At the same time,
work is progressing on open loop systems with selfmaintaining structures and reproduction facilities.
Beyond the fourth level we hardly have a beginning of
theory, and yet system description via computer models
may foster progress even at these levels in the complex
of general systems theory.
Bertalanffy

(1968, p. 196)

criticises the efforts

of "Functionalist theories" as represented by the work of
Parsons, Merton,

and others.

The main critique of functionalism particularly in
Parson's version, is that it overemphasizes mainte­
nance, equilibrium, adjustment, homeostasis, stable
institutional structures, and so on, with the result
that history, process, sociocultural change, innerdirected development, etc., are underplayed and, at
most, appear as "deviants" with a negative value
connotation.
The theory therefore appears to be one
of conservatism and conformism, defending the "system"
(or the megamachine of present society, to use
Mumford's term) as is, conceptually neglecting and
hence obstructing social change.
Obviously, general
system theory in the form here presented is free of
this objection as it incorporates equally maintenance
and change, preservation of system and internal

22
conflict; it may therefore be apt to serve as logical
skeleton for improved sociological theory.

Basic Concepts and
Associated Definitions
A number of basic concepts have become recognized
by authorities in the field.

The basic concepts are

defined by varying authors and presented as follows:

1.

Boundary:

Bertalanffy

(1968, p. 215) proposes:

Any system as an entity which can be investigated in
its own right must have boundaries, either spatial or
dynamic.
Strictly speaking, spatial boundaries exist
only in naive observation, and all boundaries are
ultimately dynamic.
One cannot exactly draw the
boundaries of an atom (with valences sticking out, as
it were, to attract other a t o m s ) , of a stone (an
aggregate of molecules and atoms which mostly consist
of empty space, with particles in planetary distances),
or of an organism (continually exchanging matter with
the environment).
The boundary concept suggests that some determi­
nation may be made to distinguish that which is considered
an inherent part of the system of interest
zation)
respect,

and that which is not

(the organi­

(the environment).

In this

it is not unlike the concept of "set" though

eminently more difficult to determine particularly where
the reference is to dynamic systems.
pp.

21-32)

Pheiffer

(1968,

in discussing the procedures of a systems

approach concludes that identification of the boundaries
of a problem is a prerequisite to problem definition.
The concept of boundary leads quite naturally to
the related concepts of open and closed systems.

23
2.

Open and Closed S y s t e m s :

boundaries,

As all systems have

the open-closed continuum concept provides a

relative description of boundary permeability.
(1951)

Parsons

speaks of the term "boundary exchange" in describing

the exchange between two systems or between a system and its
environment.

Johnson,

et a l . (1967, p. 11) contributes the

following in the same regard:
An important aspect of general system theory is the
distinction between closed and open systems.
An
example of an open system is a living organism which
is not a conglomeration of separate elements but a
definite system, possessing organization and wholeness.
An organism is an open system which maintains a con­
stant state while the matter and energy which enter it
keep changing (so-called "dynamic equilibrium").
In reality, the completely open or completely
closed system does not exist, since the one would preclude
the existance of any boundary and the other would admit to
an impermeable boundary.

Thus, systems are often described

as relatively open or relatively closed which relates to
the degree of freedom associated with boundary exchange.
3.

Equilibrium:

An important concept in GST is that

of equilibrium which relates to balance in the system.
Static equilibrium,

for example,

is the balance point

reached in chemical reactions where two or more substances
react and arrive at a final, predictable state.
equilibrium,
Bertalanffy

however,

Dynamic

is not so easily formulated.

(1968, p. 132) writes,

24
We are not in a position to define such equilibrium
state in complicated organic processes, but we can
easily see that such a conception is, in principle,
inadequate.
For, apart from certain individual
processes, living systems are not closed systems in
true equilibrium but open systems in a steady state.

4.

Feedback:

Carzo and Yanouzas

(1967, pp.

364-65)

define feedback as information received describing existing
conditions.

In this respect,

with the environment,

the feedback may originate

so-called external

with the performance of the system.

feedback, dealing

Feedback may also be

internal relating to the performance of internal components
or elements.

5.

E q u i f inality:

Important to the theory of open

systems is the concept of equifinality about which
Bertalanffy

(1968, p. 132)

says,

An aspect very characteristic of the dynamic order in
organismic processes can be termed as equifinality.
Processes occurring in machine-like structures follow
a fixed pathway.
Therefore, the final state will be
changed if the initial conditions or the course of
processes is altered.
In contrast, the same final
state, the same "goal," may be reached from different
initial conditions and in different pathways in
organismic processes.
Humans,

in a biological sense, achieve similar stages of

development given widely differing inputs of diet
and environments

(social).

Another example,

(physical)

is that of

school districts which achieve similar goals given widely
differing teaching staffs,
facilities,

financial resources, physical

and student populations.

25
6.

Stress:

The concept of stress in open systems

embodies aspects of force, drive, need,

disparity and in

the Parsonian model is specifically identified as "tension
management."

Stress is conceived as an imbalance between

two entities such as supply and demand or between two
individuals in power relations.

In modern organizational

theory the concept of stress is increasingly becoming
accepted as a state that is not necessarily detrimental
to the system.

That is, perhaps a certain amount of

stress is necessary to the functioning of the system.

This

is in contrast to the former ideology that any evidence of
stress or strain in relations was indicative of dysfunction
in the system.
7.

Input-Output;

In closed systems, there is an

absence of boundary exchange.

In open systems,

exchange between ancillary systems,

there is

such as, system to

system or between the system and the supra-system
ment) .

(environ­

Boundary exchange may be beneficial or detrimental

to the system and its state of equilibrium.

That is, in a

biological sense an organism may "input" a toxic substance
or a nutritious one.

Similarly, output in an organi­

zational sense may take the form of well trained p r o ­
fessionals or it may take the form of heavy volumes of
unwanted fumes such as automotive or industrial exhaust.

26
8.

Process:

In open systems, process relates inputs

to outputs and tends toward progressive segregation,

that

is, increasing autonomy of parts and development of new
structure.

In closed systems, process tends toward sys­

temic entropy,

that is, tendency toward disorder.

Or g a n i ­

zations as open systems continually devise and implement
new structure while chemical substances in a relatively
closed system tend toward a heterogenous state.
The concept of "process"

in the public school

systems is crucial to this study as is the concept of
"stress" upon which the study is founded.

Within the

public school system there are numerous interactions
within and between the components of the system for which
process ought to provide some explanation.

For example,

students enter the system and constitute a demand for
service.

Provisions of appropriate service requires

allocation of the resources of the system.

Primary

resources generally take the form of physical facilities,
professional and non-professional staff,
and supplies.

and materials

Since the allocation of systemic resources

is not instantaneous,

advance information

the expected level of demand

(stress)

(predictions)

of

is periodically

sought as are estimates of the expected level of resources
(supply).
Stress occurs in different forms
served, power imbalances,

(goals to be

clients to be served).

Further,

27
it is possible to visualize distinct sub-processes of the
overall educational process

(resource acquisition and

distribution, non-professional staff service, program
evalua t i o n ) .

This study assumes that the number of

students to be served is a primary demand on th e system
for professional staff services.

The process to be

identified and modeled concerns the interactions that
occur within and between the student population and pro­
fessional staff components as the supply-demand function
moves toward a state of equilibrium.
Other concepts such as sensitivity,

stability, and

progressive segregation are discussed in the literature
(see for example, Johnson,

et a l ., 1967, pp.

72-73) but

complete closure is not necessary for the purposes of this
study.
The foregoing part of the review identified basic
concepts and stated rather commonly accepted interpre­
tations of these concepts.

The present level of theory

development as regards GST is only now in its infancy.
That is, the work at present is concerned with concept
identification and construct development.

Organizational Systems
Current research in organization theory recognizes
at least three models, the rational,
and the analytical

the natural systems,

(Johnson, et al . , 1967, p.

44).

28
1.
p.

Rational M o d e l ;

Phiffner and Sherwood

(1960,

30) define the rational model for organization as:

" . . . the pattern of ways in which large numbers of
people, too many to have intimate face-to-face contact
with all others, and engaged in a complexity of tasks,
relate themselves to each other in the concious,

systematic

establishment and accomplishment of mutually agreed
purposes."

2.

Natural Systems M o d e l :

Much of the current

literature utilizes the natural systems model as a basis
for analysis.

March and Simon

(1958, p. 4) define organi­

zation as follows:
Organizations are assemblages of interacting human
beings and they are the largest assemblages in our
society that have anything resembling a central
coordinative system . . . the high specificity of
structure and coordination within organizations— as
contrasted with the diffuse and variable relations
among individuals— marks off the individual organi­
zation as a sociological unit comparable in signifi­
cance to the individual organism in biology.

3.

The Analytic M o d e l :

The analytic system model for

organization theory is described by Andrew

(1965, p. 198):

The general analytic model presents an organization as
an adaptive system (goal directed) with a set of
interdependent variables, adjusting to each other upon
stimulation of one or more of them from system
parameters.
The plastic nature of adaptive systems
is characterized essentially as the ability of those
systems to arrive at goals under a variety of differ­
ent conditions.
The concept of an adaptive system,
thus defined, permits explanations of the nature of
both persistence and change in an organization and
further of the nature of interrelationships between
subparts of the total organization.

29

Thus, there are at least three recognized orien­
tations to organizations as systems.

The rational model

could well lead to a process representation which would
depict system process as the relationship of input to
output and where output was the result of rationally
determined systemic goals.

Such a representation could

easily differ from a model developed from a natural system
or analytical orientation.
modeling.

However,

More remains to be said about

the remainder of the discussion is

presented in the ensuing section which deals with simu­
lation.
Carzo and Yanouzas

(1967, p. 236)

integrate

concepts and definitions to present a functional picture
of the organization as system.
In essence, society (the environment) is a suprasystem and has a mutually dependent relation to the
formal organization (the system). As a basis for
design, we treat the formal organization as a system
of interconnected components performing processes on
flows of matter, energy, and information.
In this
context, the formal organization transforms matter,
energy, and information into different states or
output values.
These values are the end product of
the flows; they comprise the objectives or desired
performance of the system, and through design decision
makers are placed in a position to regulate these
flows.
By regulating these flows, they are supposed
to produce the values agreed upon by participants,
that is, meet the organizational objectives.
The authors clearly posit the concept of regu­
lation or control as being necessary if organizations are
to serve systemic goals and hence society.
(1967, p.

16)

Johnson, et a l .

suggests that in fact the functions of

management are fourfold:

30
Although the management process has been described in
numerous ways, four basic functions have received
general acceptance— planning, controlling, organizing,
and communicating.
They can be defined in terms of
systems concepts as follows:
1.
Planning— selecting the organizational objectives
and the policies, programs, procedures, and methods of
achieving them.
2.
Organizing— to coordinate people and resources into
a system so that the activities they perform lead to
the accomplishment of system goals.
3.
Controlling— assuring that the various subsystems
are performing in conformance to the plans.
The
measurement and correction of activity of the sub­
systems to assure the accomplishment of the overall
plan.
4.
Communication— transfer of information among
decision centers in the various subsystems throughout
the organization and the interchange of information
with the environmental forces.
The planning function has particular significance
in this study and is treated separately as part three of
this review.
In summary,

GST is a viable,

theoretical framework

for consideration of the organization as system.

The

state of theory development in GST has progressed to the
identification of an increasing number of concepts and
definitions from which relationships are evolving.
Griffiths

(1959, p. 70) concludes,

"Theory builders are

struggling with problems of concept development,
form,

lack of testable hypotheses,

theory

and lack of precision."

While this may no longer be true of some theories
cation of the Getzels-Guba model,

for instance)

(appli­

it remains

true of the development of GST in the field of educational
administration.

31
Aspects of Computer Simulation
In the sense that simulation is interpreted as
representation,

the act of simulating could be attributed

a history as old as man himself.

Simulation as repre­

sentation of certain aspects of reality may abbreviate the
historical sequence to some degree, but is still open to
considerable interpretation.

Computer simulation, however,

is a manageable subset of all simulations which is both
tractable and more relevant to this review.

Historical Aspects
Two bibliographies were identified
Werner,

1969;

and Dutton and Starbuck,

an important basis
(1969)

for review.

(Werner and

1971) which provide

The Werner and Werner

publication reviewed simulations other than computer,

such as, role playing or "people simulations" categorized by
type.

Dutton and Starbuck

(1971)

examined only computer

simulation works classified by an ordering scheme related
to both nature and substance of the study.
Dutton and Starbuck

(1971, p. 9) for example,

reviewed some 12,000 articles and concluded that 1,921
of these were relevant to the topic of computer simu­
lation, had been published prior to 1969, and estimated
that these represented about three-fourths of all available
published works on computer simulation.
The majority of computer simulation studies are
not related to the field of educational administration

32
nor,

for that matter,

to education; however, there is

evidence of early works and a growing incidence of
increasing attention to educationally oriented simulation
studies.

Cruickshank

(1969, p.

191)

cites the work of the

University Council on Educational Administrators

(UCEA)

in

development of the "Whitman Elementary School" simulation
in the late 1950's as an early effort.
recent vintage is reviewed by Hallworth

Work of more
(1969, p. 62) who

refers to the Gullahorn simulation of social interaction
(1964) and the work by Cogswell and Loughary

(1967) who

attempted to simulate a school counselor.
Attempts to define simulation have been made by
numerous authors

(Guetzkow,

Naylor, et a l ., 1967;

1963; Elton, et a l ., 1971;

and Schechter,

1971) among others.

The latter three tend to include references to the o per­
ating model,
they suggest,

for example,
" . . .

(Elton, et a l ., 1971, p. 118)

a method of making deductions from a

mathematical model of a system."

However,

for outright

simplicity and efficacity the definition suggested by
Guetzkow

(1963, p. 25)

is both parsimonious and functional.

That is,

" . . . simulation is an operating representation

of central features of reality."

Inclusion of the term

"operating" performs a gestalt function which distinguishes
simulation from inanimate forms of representation and
permits schemes of classification which focus on the manner
of operation as opposed to the nature of model construction.

33
Thus, computer simulation speaks to the manner in which
the model is operationalized.

Further delineation may

then be achieved by considering subsets related to the
nature of the model.

Where concern is focused on computer

simulation of mathematical models, Cooper and McGillem
(1967, pp.

11-14)

provide an important schema accompanied

by appropriate explanation.

Value and Objective Aspects
The importance of simulation research in general,
may be inferred from a review of the associated values
which have been previously identified.
(1968, pp.

Naylor, et a l .

8-9) provides an inclusive list of such values

which have been collapsed to provide the following:
1.
2.

3.
4.

5.
6.

Simulation makes it possible to experiment with
complex, internal interactions (Multi-variate v a l u e ) .
Allowance for changes in the model makes it possible
to study informational, organizational, and
environmental changes (Decision-making v a l u e ) .
Simulation develops a greater awareness of the
system and the means of improving it (Design v a l u e ) .
Simulation provides a pedagogical device for
teaching basic skills in theoretical analysis,
statistical analysis, and decision-making
(Training va l u e ) .
Simulation yields insight into which variables of
a system are important (Analytic val u e ) .
Simulation can serve as a "preservice test" to try
out new policies and decision rules as it permits
study of dynamic systems in real time, compressed
time, or expanded time (Planning v a l u e ) .
A number of authors

Cunningham,

(Beck and Monroe,

1966; Cruickshank,

1967; and Rice,

1964)

lation in training.

1969;

1969; Entwisle and Huggins,

review the specific values of simu­
Wynn

(1964, pp.

171-73) however,

34
provides a summary of what other authors have found
regarding specific values of simulation in training.
First, the evident face validity of the situation
stimulates interest and motivation in learning and
encourages the subject to behave as he might in reality.
Second, the written record of performance results in
the accumulation of normative data and permits
clinical examination and comparison of "on-the-job"
behavior in identical situations.
Third, simulation
permits the learner to profit from mistakes that
might be disastrous on the job.
Fourth, the instructor
in the simulated situation can provide the subject
with concepts, research evidence, models, or other
information which he can't always send in during the
actual game.
Fifth, simulation provides an oppor­
tunity to see the whole picture, to view each problem
in broad context.
Sixth, simulation permits a degree
of introspection rarely provided on the real job.
Rabow

(1969, p.

41)

speaks to the multi-variate

capability of system simulation.
It seems that the greatest difficulties in under­
standing social phenomena are due to both the large
amount and variety of factors and occurrences which
contribute to social phenomena.
Accordingly, both
conceptual means and tools must be devised to deal
with such a mass of data.
The author advocates that simulation is one such tool that
now is in need of further exploration since for the
present the potential of computer simulation as a tool of
analysis has been sufficiently demonstrated.
Of particular concern to this study however,

are

values associated with rational planning and decision
making.

Johnson, et al

(1967, pp. 183-84)

identify at

least two such values.
First of all, since those persons involved in making
decisions in the operation as a whole must verbalize
their decision-making process to the researcher, they
cannot avoid becoming better acquainted with their

35
own operation.
The explicitness with which the
activities and decisions must be set forth for a
simulation model forces those involved to define their
own functions clearly.
Often this activity in itself
can result in benefits . . .
The author continues to fully elaborate the
second value as follows:
The model of the total system, including accumulation
of raw materials, production, and distribution, can be
used to evaluate changes in given policies.
A policy
change can be made in any one segment of the total
process, and the impact of this change can be evaluated
by the simulated operating results.
This tool gives
management an opportunity to test and evaluate
proposals without running the risk of actually
installing new approaches and absorbing the necessary
costs associated with system changes.
The values of simulation which directly correlate
with the purposes of this study are those of analysis,
multi-variate capability, planning, and decision-making.
Obviously, once the model is developed and validated,
associated values will be realized.
reviews a final important value.

Guetzkow

(1963, p. 75)

"It is through simulation

that we may examine possible relationships among any or
all variables that we are able to put into the simulation;
that is, we can use simulation as a theory-building
device."

Procedural Aspects of
Simulation
The review and discussion of the procedural
aspects of simulation may be organized around three broad
topics.

First, under what circumstances is it feasible

to use simulation?

Second, what problems may be

36
anticipated when simulation is employed?

Third, what are

the key aspects of simulation procedure?

Simulation feasibility.— Choice of simulation as
the tool of analysis relates in part to the expected values
that may be anticipated.

Thus, the previous section

provides at least some criteria for choice.
when multi-variate capability is desired,
available tools of analysis is limited.

For example,

the choice of
If an investi­

gation of dynamic relationships is desirable for planning
or decision-making the choice of alternatives narrows to
simulation or application of other mathematical tools,
i.e., queueing theory, or dynamic programming.
et a l . (1971, pp.

Elton,

120-21) discusses the nature of final

determination.
In brief, simulation is a means of making deductions
from a mathematical model or hypothesis.
As such, it
is an alternative to mathematical analysis.
When the
mathematics is tractable, analysis is normally the
most efficient means of making deductions from the
model to compare with observations from the real
world.
However, the mathematics is often intractable,
particularly when the model involves a large number of
interacting variables, many of them probabilistic, and
when the model is dynamic— that is, the state of the
modeled system at any time depends on its states at
earlier points in time.
This study encompassed an attempt to deal with the
dynamic nature of a complex system in development of the
simulator.

Thus,

simulation as the tool of analysis

appeared to be a valid choice.
p.

314)

Johnson, et a l . (1967,

speaks to another aspect which is frequently

37
employed as a criterion of choice.

The issue is that of

system complexity.
Management science in general, and simulation in
particular, can be useful in implementing the systems
concept.
Model building forces decision-makers to
structure the operation under analysis as an integrated
system tied together by a series of equations.
The
use of computers in symbolic system simulation allows
treatment of large-scale, complex systems.
Thus the
analyst can develop a model of a group of subsystems,
their interrelationships, and the total system.
Such
an approach provides a framework for more detailed
analytical examination of various segments of the
system.
In all cases,

the choice of a particular alternative

always involves certain trade-offs.

The advantages gained

from the selection of one particular method are accompanied
by disadvantages not associated with the choice of the
other.

Associated p r o b l e m s .— Selection of simulation as
the tool of analysis is not without its share of associated
problems which ought to be given consideration as a
function of choice or certainly prior to embarking upon
development.

1.

Resource Requirements:

Several authorities speak

to the issue of resource requirements.
(1971, p. 138)

states,

" . . .

Elton, et a l .

it would be unrealistic at

this time to expect a reasonably comprehensive model to
reach a stage at which its output would have predictive
power in under two to three years, with an involvement
over that period of a two-to-three strong team."

Hopkins

38
(1971, pp.

475-76)

is critical of the cost of development

and operation of large complicated simulation models.

In

concluding, he strongly suggests the use of simpler models
These findings suggest that the simulation should be
reduced to manageable proportions.

That is, one or two

components of the system should be selected for analysis
as opposed to the entire system.

2.

Limiting A ssumptio ns:

The conduct of research

generally requires certain important assumptions related
to the nature of reality.

Election of computer simulation

particularly where the focus of interest must be reduced
to encompass some subset of the system,
assumption which is discussed by Blalock

requires an
(1969, p. 73).

A little thought should convince one that whenever a
theorist decides to delimit the number of variables
that he will consider— and of course this will always
be necessary— he is basically assuming that the world
is block recursive.
More correctly, he is assuming
that a block recursive model can give a reasonably
accurate representation of reality.
First, he must
assume that variables in higher-numbered blocks can
safely be ignored.
Thus he cannot allow for the
possibility of feedback from every other variable.
In effect, his blocks must be hierarchically arranged.
But he must also take some variables as exogenous, or
as "givens" which his theory cannot explain.
As we
have seen, he must assume negligible feedback to those
exogenous variables.
The need for the assumption is implicit in all
research though it is seldom explicitly stated.

However,

in simulation analysis the researcher is repeatedly
confronted with the need to deal with this problem in the
formulation of mathematical relationships.

39

3.

Mathematical Formulation:

System identification

by symbolic representation involves the issue of mechanistic
versus theoretical representation.
p. 172)

Bertalanffy

(1968,

advocates an appropriate choice and provides an

accompanying rationale:
Here is a first illusion we must destroy.
It is a
mathematical rule of thumb that almost every curve can
be approximated if three or more free parameters are
permitted— i.e., if an equation contains three or more
so-called constants that cannot be verified otherwise.
This is true quite irrespective of the particular form
of the equation chosen; the simplest equation to be
applied is a power series,
y = aQ + a^x + a 2x

2

+ . . .

developed to, say, the cubic term.
Such calculation
is a mere mathematical exercise.
Closer approximations
can always be obtained by permitting further terms.
The consequence is that curve-fitting may be an
indoor sport and useful for purposes of interpolation
and extrapolation.
However, approximation of empirical
data is not a verification of particular mathematical
expressions used.
We can speak of verification and of
equations representing a theory only if (1) the
parameters occurring can be confirmed by independent
experiment; and if (2) predictions of yet unobserved
facts can be derived from the theory.
An example drawn from physical theory demonstrates
the point.

The principal relationship S = l/2gt

theoretically based on the force of gravity
acting over a period of time

2

is

(the parameter)

(the principle variable)

predict the speed of a falling body.

to

In contrast, the

relationship which describes the second law of thermody­
namics

(— energy always deteriorates to a less accessible

form— ) is mechanistic.

The relationship predicts quite

accurately but the parameters cannot be confirmed by
independent experiment.

40

4.

V ariation in Observational A g r e e m e n t :

(1968, pp.

222-23)

Bertalanffy

points out another simulation problem

in his discussion of a principle attributed to Benjamin
Whorf which has become known as the "Whorfian Hypothesis."
We are thus introduced to a new principle of
relativity which holds that all observers are not led
by the same physical evidence to the same picture of
the universe, unless their linguistic backgrounds are
similar. . . . We cut up and organize the spread and
flow of events as we do largely because, through our
mother tongue, we are parties of an agreement to do so,
not because nature itself is segmented in exactly that
way for all to see.
Simulation models representing the same phenomena
devised by different individuals are particularly vulner­
able to this problem.

The specific components identified

as well as the elements within components and the boundaries
established may well be a function of individual experi­
ence not reality.

All models are suspect in this respect

and in need of validation.

5.

Statistical A n a l y s i s ;

Statistical analysis of

simulation research has given rise to a host of problems
and has resulted in a growing body of literature dealing
with this topic.

Since this topic will be reviewed

separately in a subsequent sub-section no further dis­
cussion of this review,
In summary,

is given here.

the problems identified are major

concerns for the would-be-researcher who attempts analysis
of complex entities employing symbolic simulation.

No

attempt has been made to provide exhaustive coverage of

41

all possible problems.

Simulation as a tool of analysis

is yet in its infancy and such an objective as in-depth
coverage would constitute a study in itself.

Simulation procedure.— Naylor, et a l . (1968,
pp.

23-24) present a detailed schema of the procedures

employed in a simulation study accompanied by a flow-chart
displaying iterative sequences.

The nine steps following

have been extracted from that strategy.
1.

Formulation of the problem.

2.

Collecting and processing of real world data.

3.

Formulation of the mathematical model.

4.

Estimation of parameters of operating character­
istics .

5.

Evaluation of the model.

6.

Formulation of a computer program.

7.

Model validation.

8.

Design of simulation experiments.

9.

Analysis of simulation data.
The last three steps of the series are related to

analysis and will be considered in a subsequent section
dealing with that particular topic.

The first six will

be treated in sequential order beginning with the first.

1.

Formulation of the p r o b l e m :

Naylor, et a l .

(1968, p. 27) suggests:
. . . before we can begin work on any simulation
experiment, two important decisions must be made.
First, we must decide on the objectives of our
research.
Second, we must decide on a set of criteria
for evaluating the degree to which our objectives are
fulfilled by the experiment.
Research objectives in
business and economics, as well as in most social
sciences, usually take the form of (1) questions to
be asked, (2) hypotheses to be tested, and (3) effects
to be estimated.
2.

Collecting and processing real world d a t a :

(1971, p. 122)

Elton

reviewed the problem concerning the level

of aggregation.

It was determined that appreciable in­

creases in bias,

in standard error of estimates and in the

difficulty of detecting mis-specified model formulations
occurred at different levels of aggregation.
At the conclusion of a number of experiments,
Naylor, et a l . (1968, p. 28) concluded that:
a.
b.

c.
d.

e.

3.

Descriptive and quantitative information is a
prerequisite to problem formulation.
Meaningful distillation of data may suggest
hypotheses which can be used in the formulation of
mathematical models describing the behavior of a
given system.
Data may suggest improvements or refinements of
existing mathematical models.
Data reduced to a final form may be used to
estimate parameters of the operating character­
istics relating the system's endogenous, exogenous,
and status variables.
Without data it would be impossible to test the
validity of the simulation model.
Formulation of the mathematical model:

The primary

concern of this step in the schema is that of achieving
better system definition.

A specific example of this is

given by Benchoff

(1969, p. 20) who states:

The functional relationships which describe the inter­
action of the variables and components of the combat
area and its logistics system can be separated into
two distinct groups.
Each group of relationships,
called a sector, provides a means of describing the
behavior of that portion of the system in mathematical
terms.
Naylor, et al

(1968, p. 10) identifies,

defined elements
1.
2.
3.
4.

" . . .

four well-

(of mathematical m o d e l s ) :

Components (sectors)
Variables
Parameters
Functional relationships
System identification is the term employed to

describe the process whereby each of the above listed four
elements is identified and related.
The variables of the system of interest may be
classified as exogenous,

status, or endogenous variables.

They are defined as follows:
a.

Exogenous variables— the independent
input variables,

(factor)

or

assumed to have been predetermined

and given independently of the system being
modeled.

They act upon the system but are not

acted upon by the system.
b.

Status variables— describe the state of the system
or one of its components at some particular time
instant.

44

c.

Endogenous variables— the dependent

(response)

or

output variables of the system, generated by the
interaction of the status variables and the
exogenous variables according to the system's
operating characteristics.
The functional relationships which compose the
final part of system identification are of two kinds:
identities and operating characteristics.

Identities are

either definitions or tautological statements about the
components of the model.
an hypothesis,

An operating characteristic is

usually a mathematical equation,

relating

the system's endogenous and status variables to its
exogenous variables.
Cooper and McGillem,
Sterling and Pollack,

A number of authors

(Blalock,

1967; Naylor, et a l ., 1968;

1969;

and

1968) deal with the topic of

identifying functional relationships.

However,

further

treatment of this area is beyond the scope of this study.
4.

Estimation of parameters from real world d a t a :

Schmidt and Taylor
parameter as,

(1970, pp.

" . . .

479-80)

define a system

a quantity which affects the per­

formance of the system, can be predicted with certainty,
but either cannot or will not be altered by those operating
the system.

It should be noted that a parameter need not

be a constant."

Blalock

(1969, p. 64) notes that in

models containing reciprocal causation and feedback it is
questionable whether it is possible to find mathematical

45

procedures for disentangling the various components of the
system unless the parameters can be estimated.
Elton, et a l . (1971, pp.

122-23)

Finally,

in reporting the results

of a micro-simulation of market economy states:
Starting from the initial version of the model it is
possible to investigate how sensitive its outputs are
to the precision with which the values of particular
model parameters are estimated, or to the replacement
of one particular formulation by another.
These
procedures can offer great savings in research effort
and in the cost of data collection.
To test all the
individual hypotheses which go to make up a simulation
model would involve designing and carrying out numerous
experiments either in a laboratory environment or in
the real world.
To obtain precise estimates of all
the model parameters can necessitate massive data
collection.
At any stage in the model construction it
is important that resources should be employed so as
to reduce the residual variation by as much as
possible.
In this way the model can develop most
speedily to the point where it has value to management
— a major tactical consideration.

5.

Evaluation of the m o d e l :

This step of the pro­

cedure is defined as an iterative loop in the sequential
flow.

In essence, the process of achieving increasingly

more accurate approximations of the system through minor
adjustments of certain of the elements.
p. 15)

Blalock

(1969,

states:

We must start with a finite number of specified
variables.
Obviously, a good deal of thought and
research would be necessary prior to the decision as
to exactly which variables to include in the system.
But once having made this decision, we must confine
ourselves to these explicit variables, though we may
introduce error terms to take care of the effects of
whatever variables we have not considered.
If the
model proves inadequate, then we may wish to introduce
additional variables or modify the model in other
ways, but at least for the time being we must confine
our attention to a specific set of variables.

46
Otherwise, we cannot derive testable conclusions from
the model.
Having thus committed ourselves to this
particular choice of variables, we in effect admit
that had another set been selected, our model might
have looked quite different.
In other words, there
is nothing absolute about any particular model, nor
is it true that if two models make use of different
variables, either one or the other must in some sense
be "wrong."

6.

Formulation of a computer p r o g r a m :

Naylor, et a l .

(1968, pp. 239-309) provide a most comprehensive treatment
of simulation languages including general programming
languages such as Fortran, Cobol,

and special purpose

simulation languages such as Simscript, GASP,
Dynamo.

SIMPAC,

and

For the purposes of this study it is only necessary

to note that language is a concern and that particular
languages offer certain advantages over others.

In

addition it should be noted that previously programmed
routines exist which have been designed to facilitate
certain operations,

such as square root and extrapolation

of time series data.
Consideration of Naylor's procedural design
concludes this portion of the review which has treated
the general procedures and concerns associated with
system simulation.

The following two sections regarding

modeling and analysis are procedural in nature but are of
a magnitude which deserves separate consideration.

47

Aspects of Simulation Models
Boardman

(1969, p. 179)

states,

In general terms, model-making involves abstracting
from reality components and relationships which the
observer wishes to understand.
A model is therefore,
simply a collection of assertions about some reality.
Naylor,

et a l . (1968, p. 9) are somewhat more functional

as they contend,

"A scientific model can be defined as an

abstraction of some real system that can be used for
purposes of prediction and control."

The functionalistic

definition appears to be less parsimonious though the
"system" aspect is useful.

The definition employed

throughout this study interprets a model as a collection
of assertions which constitute an abstraction of some real
world system.
Bertalanffy

(1968, p. 200) contends that,

Conceptual models which, in simplified and therefore
comprehensible form, try to represent certain aspects
of reality, are basic in any attempt at theory;
whether we apply the Newtonian model in mechanics, the
model of corpuscle or wave in atomic physics, use
simplified models to describe the growth of a popu­
lation, or the model of a game to describe political
d e c isions.
Various criticisms of the problems inherent in
modeling have been leveled by different authors
(Bertalanffy,
1968;

1968, Johnson, et a l ., 1967; Naylor, et a l .,

and Schechter,

1971) .

First, the job of constructing

a model of a particular system is analogous to the work of
an artist
Second,

(lack of control;

the "Whorfian Hypothesis").

abstracting and relating elements and components

48

of the real world is an exercise vulnerable to the
principle of parsimony often referred to as "Bonini's
Paradox."

That is, a simple model is parsimonious but may

likewise represent too great a departure from the real
world system of interest.

The opposite extreme is a model

which accurately depicts the real world system but is too
complex to understand and utilize.

Hopkins

(1971) argues

for the employment of simple models while Bertalanffy
(1968, pp.

100-01) notes:

Enthusiasm for the new mathematical and logical tools
available has led to feverish "model building" as a
purpose in itself and often without regard to empirical
fact.
However, conceptual experimentation at random
has no greater chances of success that at-random
experimentation in the laboratory.
One would do well
to remember the old Kantian maxim that experience
without theory is blind but theory without experience
is a mere intellectual play.
Consideration of problems in modeling and associated
criticisms are useful as they give pause to the would-be
modeler.

The ultimate test of a model is the explanations

and predictions it is able to provide.
conclusive.

No model is

Models are at best only approximations

requiring subsequent testing and correction.

In close

interaction between experiment and conceptualization,
not confined to either,

but

lies the further development of a

field.
Church and Ratoosh
of models.

(1959, p. 158) offer a typology

49

1.

The iconic— a model which visually or pictorially
represents reality (a photograph), perfect one-toone correspondence.
The analogue— a model which uses one set of proper­
ties to represent a similar set of properties in
another system, i.e., the analogy of water flowing
through pipes as a way of explaining the flow in
electrical circuits.
The symbolic— a model which employs symbols to
designate elements and relations in a system,
i.e., an equation or identity.

2.

3.

Simulation models vary among all three types
though there tend to be fewer iconic models if in fact
there are any that could be classified as iconic.

Mathe­

matical models are usually symbolic.

the

For example,

many queueing models and the Herbart and Richardson
Blalock,

(from:

1969) models which will be discussed shortly.

A

considerable number of simulation models being developed
today and in the recent past are of the analogue type.
Naylor, et a l . (1968, pp.

30-32) have identified

six prime considerations of mathematical representation
which relate to symbolic models:
1.
2.
3.
4.
5.

6.

How many variables to include in the model.
General complexity of variables and relations.
Amount of computer time required to achieve some
specific experimental objective.
Requisite computer programming time.
Validity of the model in terms of its represen­
tation of reality and ultimately the accuracy of
prediction.
Compatibility with the type of intended experi­
mentation.
It may be useful as an integral part of this

review to consider a limited number of symbolic models in
both a macroscopic sense and a microscopic sense.

Herbart

(c. 1800) devised one of the earliest known mathematical

50

systems which is dynamic and demonstrates the utility of
the exponential relation in growth and decay functions,

T = S (1 - e- t )

where

(T) tau represents the suppressed portion of an idea

in time

(t) and

(S) is the aggregate amount suppressed.

From previous definitions it is possible to determine that
the model is representative of a real world system which
has been depicted as dynamic, discrete, and nonlinear.
In general, discrete systems are represented as
difference equations while continuous systems require the
use of differential equations.

An example of a simple

difference equation is the general linear regression model
for one independent and one dependent variable,

Y i = by .x

(Xi - u > + uy

where

(b) is the regression coefficient,

mean,

(uy)

(X^)

(u) is the grand

i-s the mean of the dependent measures,

and

is a particular value of the independent variable

from which
by contrast

(Y^) is to be predicted.
(Bertalanffy,

represented as,

1968, p.

Continuous systems
56), are generally

which is the general model for a system of
variables.

(n) continuous

A specific example of a continuous,

linear

system is Richardson's model of armament races between two
nations

(Blalock, 1969, p. 127).

= kY - aX + g
dY
| | = IX - bY + h

Richardson's model is a two nation model where

(X) and

(Y)

represent the levels of armaments in the two countries.
(k) and

(1) are defense coefficients which modify the

respective levels of armaments.

(a) and

(b) are feedback

terms which represent fatigue coefficients and

(g) and

(h)

are constants referred to as grievance terms.
While all real world systems are continuous with
respect to time,

it does not follow that representation of

such systems must be continuous thereby utilizing only
simultaneous, differential equations.

For some purposes,

52

particularly where periodic phenomena are of central
interest,

it is sufficient to devise a discrete time

system represented by simultaneous, difference equations.
Such representation may also be dictated by the objectives
of the study.
In summary, Bertalanffy

(1968, p. 28) notes:

Thus, there is an array of system models, more or less
progressed and elaborate.
Certain concepts, models
and principles of general systems theory, such as
hierarchic order, progressive differentiation, feed­
back, systems characteristics defined by set and graph
theory, and others are applicable broadly to material,
psychological and sociocultural systems; others, such
as open system defined by the exchange of matter, are
limited to certain sub-classes.
As practice in applied
systems analysis shows, diverse system models will
have to be applied according to the nature of the case
and operational criteria.

Analysis of Simulation Studies
In the past decade, the ability of researchers to
simulate complex systems has greatly improved.

Along with

the improved ability have come a host of problems evolving
from efforts to analyze the results of simulation experi­
ments.

The associated problems have led to a growing body

of literature and to two schools of thought regarding
analysis.
The first position reviewed by Elton,
(1971, p. 129)

et a l .

is typified by the view which holds that,

" . . . for a complex model which necessarily contains
residual errors its truth or falsity is less relevant than
its degree of usefulness.

This approach would preclude

53

the application of standard statistical tests."

The

second position has been supported by Naylor and Finger
(1967) who were among the first to advocate the use of
statistical test procedures in the validation of simu­
lation studies.

The literature sometimes implies that in

performing simulations the investigator is differently
motivated than in other studies where simulation is not
the mode of model solution.
states,

Schechter

(1971, p. 79)

"In fact, there is not— and should not b e — any

such distinction,

...

it is how we solve the model,

not

why we solve it that distinguishes simulation from other
techniques."
Fishman and Kiviat

(1968, p. 186) discuss aspects

of discrete event simulation analysis.

They contend that

regarding the problems associated with analysis many of
them have not yet been recognized as serious problems.
The authors further provide a useful scheme for decomposing
and classifying analytical problems:
Verification, validation, and problem analysis are
tasks demanding careful statistical analysis.
Verifi­
cation determines whether a model with a particular
mathematical structure and data base actually behaves
as an experimenter assumes it does.
Validation tests
whether a simulation model reasonably approximates a
real system.
Problem analysis seeks to insure the
proper execution of experiments and deals with a host
of matters:
the concise display of solutions,
efficient allocation of computer time, proper design
of tests of comparison, and correct estimates of
sample sizes needed for specified levels of accuracy.
The definitions posed by Fishman and Kiviatt
(1968)

appear to be clear and to lack discernable overlap.

However, the review of related literature revealed that
use of the terms by various authors is less than uniform.
Therefore,

in this study verification

(the quantitative

aspect) will refer to the process which demonstrates to
what extent the model approximates the real world system
of interest, validation

(the qualitative aspect) will refer

to the manner in which the simulation model purports to
represent the real world system of interest,

and experiment

will be used in the same context as that used by the
authors.
Verification
In reporting the verification of a model of the
economy, Holland and Gillespie

(1963, p. 208)

state:

A true historical verification would require the
existence of time series data on all the major
exogenous variables and on all the variables used
to measure the performance of the economy during
periods when it was subjected to a variety of
exogenous events.
Moreover, the time series against
which the performance of the simulation is tested
should be independent of any used in formulating
the model.
It would also be essential that no major
changes in basic parameters of the system had taken
place between the periods, used for verification and
those used for formulation of the model.
Naylor,

et a l . (1968, p.

316)

suggest that hi s ­

torical verification is only one of two possible approaches
to model verification.
second.

Verification by forecasting is a

In this regard the authors state:

It is our position that the ultimate test of a computer
simulation model is the degree of accuracy with which
the model predicts the behavior of the actual system
(which is being simulated) in the future.
Furthermore,

55

we would argue that the possibility that computer
simulation models may be able to predict the future
constitutes the major source of justification for the
use of computer simulation as a tool of analysis.
While the general process of what is to be
accomplished in verifying a model is relatively clear,
methods to be used are not.
square,

That is, various methods

regression analysis, etc.)

the
(Chi

are employed by

different investigators to measure goodness-of-fit, but
there appears to be no clear-cut pattern of what is
acceptable or valid under the circumstances.
Cyert

Cohen and

(1961, p. 121) write:

Although the final details have not yet been adequately
developed, there appears to be at least three ways in
which the validation (verification, by previous
definition) problem for process models can be
approached.
First, distribution-free statistical
methods can be used to test whether the actual and the
generated time series display similar timing and
amplitude characteristics.
Second, simple regressions
of the generated series as functions of the actual
series can be computed, and then we can test whether
the resulting regression equations have intercepts
which are significantly different from zero and slopes
which are significantly different from unity.
Third,
we could perform a factor analysis on the set of
generated time paths and a second factor analysis on
the set of observed time paths, and we can test
whether the two groups of factor loadings are signifi­
cantly different from each other.
The absence of comprehensive theory for statistical
analysis of computer models insofar as verification is
concerned is not however,
analysis.

sufficient reason to avoid

One must accept, however,

that at present each

research effort will be judged independently until the
time when a sufficient body of information is available
to give direction to future efforts.

56

Validation
The problem of validating the model, of demon­
strating the validity of the mathematical representation
of the real world system of interest is considerably
different.

Clarkson

(1962, p. 63)

states:

In the case of (verification of) simulation models the
model as a whole can be subjected to statistical tests
by matching the time series generated by the model
against the actual time series of the variables under
consideration.
In this way a measure of "goodness-offit" can be obtained on its ability to predict the
time series.
The problem of testing the mechanism
employed by the model is not so simple because there
is no clear way of either testing the functional form
of the equations or the estimates of the parameters.
Schechter

(1971, p. 84) adds:

It is not unusual for the investigator to act as the
final arbitrator concerning the reasonableness of his
model, basing his judgment on partially subjective
criteria.
Validation thus remains one of the most
acute and timely problems in simulation . . .
As one approach to this problem several authors
and Starbuck,

1971; Elton, et a l ., 1971)

(Dutton

are recommending

thorough reporting of the variables and relationships as
well as the computer program which represents the simu­
lation model.

McMillen and Gonzalez

(1965, pp.

498-99)

state:
The manner of treating these tactical problems should
be described when reporting simulations, along with
the description of the model and its output.
Criticism
of methodology will continue, and for the present each
simulation will be judged in terms of its credibility
and utility.

57
Experimentation
Analytical experiments with simulation models
continues to be another area of ferment and agitation.
There is controversy between the two schools of thought,
such as, the experimentalists and the non-experimentalists.
Within the experimentalist's group there are those who
favor and defend the use of one procedure over another and
those who employ or accept any procedure on the basis
that such practices cannot be openly debated until they
have been employed.
Van Dusen

(1969) and Benchoff

(1969)

for example,

present no statistical analysis of the simulation models
in their studies.

Bonini

(from:

Dutton and Starbuck,

1971) uses a factorial design and others have employed
factor analysis,

analysis of variance, and multi-variate

analysis techniques.

An important focus of controversy

is the matter of independence in stochastic models
opposed to deterministic models).
(from:

Dutton and Starbuck,

(as

Fishman and Kiviatt

1971, p. 595) contend that

random number generators do not produce independent
numbers but in fact result in unwanted correlation.
Stochastic models introduce random variation into
the simulation and use this variation as part of the
argument for employment of certain techniques.
regard Schechter

(1971, p. 84) writes:

In this

58

Furthermore, when the generated data are stochastic in
nature and behave according to certain assumptions
(mainly, independence, normality, and homogeneity of
var iance), it becomes possible to use two powerful
statistical techniques of data analysis— analysis of
variance and regression methods.
Two immediate problems arise from this approach
to simulation experiments.

First,

if the methods are

applicable to stochastic models are they also correct for
deterministic models?

No answer to this question was

found in the literature.

Further, most if not all

published accounts considered in this review spoke of
simulation analysis in a general way.

That is, clarifi­

cation was not made regarding whether or not the model of
interest was stochastic or deterministic.
that one cannot make a determination

In the event

(at least from the

review of the literature), one course of action would be
to refrain from employing controversial methods or any
method at all.

In essence, this would amount to pursuing

a course of action recommended by the non-experimentalist
school and assumes

statistical techniques are not

permissible for deterministic models.
The researcher chose to adopt the alternate
position,

that is, such techniques are permissible,

or at

least, ought to be employed until such time as they are
proven to be inappropriate.

This,

in effect,

is an adoption

of the experimentalist's view and, while it is venturous,
there is at least opportunity for criticism.
to be of velue in and of itself,

This is held

thought it leads to the

59

second problem associated with utilization of these methods.
How then does one procede with design of the experiment
given no previous theory as a guide to follow and with the
understanding that such methodological use may be in error?
Naylor, et a l . (1968, p.

318) suggests a possible

strategy for design:
. . . we do not feel that the limited success achieved
thus far by computer simulation models in terms of
forecasting ability reflects some fundamental under­
lying deficiency in the technique itself.
Rather, we
strongly suspect the principal difficulty stems from
the limited experience that has been accumulated by
researchers using
this technique.
There is also the
further limitation imposed by the speed and memory
capacity of existing computer hardware.
However, we
remain optimistic on both of these points, con­
jecturing that these are short-run problems that man
is capable of dealing with in due time.
Design and procedures of the study will be elabo­
rated upon more fully

in a later part of

this study. How­

ever,

that the foregoing

discussion relates

it will be seen

directly to the nature of this study which involves a test
of the means of various forecasting techniques.

More will

be said of forecasting in relation to the information
needs of planners in the final section of this review
which follows.

Regarding the planned test of means,

McMillen and Gonzalez

(1965, p. 498)

state:

The use of classical analysis of variance seems
widespread in simulation, despite the awareness that
the null hypothesis may be improper, and that
independence of samples is often assumed when, in
fact, because of common starting conditions or because
of use of a common sequence of exogenous events,
dependence is the case.

60

Sterling and Pollack

(1968, pp. 499-500)

discuss

aspects of the assumptions underlying the use of classical
analysis of variance techniques and suggest the following:
The analysis of variance requires that the population
from which measurements are drawn be distributed
normally.
This latter assumption may be tested in a
number of ways.
The investigator could inspect a
histogram of his scores or even subject the frequency
distribution to a test of goodness-of-fit to the normal
distribution.
When the assumption of normality of
distribution is rejected, the investigator could take
recourse to "normalization" by a number of transfor­
mation functions (logs, square roots, arcsins, etc.).
It speaks for the robustness of analysis of variance,
however, that although normalcy of distribution is
required, the F ratio will not be affected appreciably
unless there is a considerable skew in the distribution.
One other assumption is that within the group variances
are of approximately equal size.
If variances should
differ considerably, it can be shown that the value of
F will be increased spuriously.
In summary, where statistical analysis of simu­
lation experiments is concerned,

there is divided opinion

regarding the wisdom of employing statistical procedures
or not analyzing the research at all.

If one adopts the

position that such experiments should be analyzed,

if for

no other reason than to provide a subject for criticism,
then a review of previous works is necessary.

The review

has revealed that most reported efforts deal with stochastic
not deterministic simulations or do not clearly indicate
which is the case.

Lacking a documented base from which

to procede two alternatives were considered.

The investi­

gator adopted the alternative of employment of statistical
analysis if only to provide a basis for future criticism.
In this respect,

the design of the study may be viewed as

61
venturous but it is contended that such a step is necessary
at this point in the resolution of the problem and may be
beneficial to future efforts.

Organizational Planning
An important part of the overall effort of this
study relates to improved rational planning in educational
systems.

Specifically,

if one assumes that student popu­

lation levels act as a primary demand for certified
professional staff, what can the analysis of student
population levels provide in terms of information about
the number of trained professional staff that will be
needed.

In this regard,

it was believed that a review of

literature related to this topic was necessary in this
study.

The objectives of this part of the review were:

to examine the nature of planning;
techniques employed in planning;

to review specific

and to examine previous

efforts which had utilized similar methods of forecasting.

The Nature of Planning
A number of authors
Ratoosh,

(Blalock,

1969; Churchman and

1959; Johnson, et a l ., 1967; McNamara,

and Mauch,

1962)

function.

Johnson, et a l . (1967, pp.

1971;

deal with various aspects of the planning
23-24)

state:

With a more dynamic environment and large, complex
units operating in the face of many forces restricting
flexibility, the planning function becomes critical
and must be thought of on a total-systems basis.
Herein lies the primary contribution of the application

62

of the systems concept to planning; the organization is
viewed as an entity, its major responsibility one of
planning the integrated activities of all the sub­
systems .
Mauch

(1962, p. 158)

contributes the following:

A school system is rationally organized to the extent
that it allocates resources among possible alternative
uses in such a way as to get the most highly valued
return for the resources expended.
One possible way
to get more from our educational resources— that is,
to increase efficiency--is to compare alternative
methods of reaching a goal.
Finally, McNamara

(1971, p. 421)

concludes:

. . . the primary purpose of educational planning is
to design educational policy, studies in this area
include such diverse topics as curriculum selection,
design of physical facilities, resource allocation
strategies, cost accounting, salary schedule and
analysis and student population projections.
Johnson, et a l . (1967, p. 21) provide additional
insight regarding functional aspects as they contend:
Although all the managerial functions (Planning,
Organizing, Communicating, and Controlling) are
interrelated and the manager undoubtedly performs each
at one time or another any given phase of organi­
zational activity must start with planning.
Planning
is the process by which the system adapts its resources
to changing environmental and internal forces.
McNamara,

(1971, p. 420)

however, presents an updated,

composite view of planning which differs from that taken
by Johnson,

et a l . (1967):

Characteristic of most recent descriptions of edu­
cational planning, however, is that planning was
presented as a process of preparing information in
the form of a set of alternatives (with estimates of
their consequences) to aid decision-making for
management policy formation and administrative action.
In summary, Johnson, et a l . (1967)

suggest that

the wholistic or systems approach to planning is a viable

63

strategy and Mauch

(1962)

speaks to the issue of rationality

in allocation of resources among alternative choices.
Finally, McNamara's

(1967)

interpretation is considered

the more useful for the purposes of this study and is
additionally, more representative of current thinking.

Johnson, et a l . (1967, pp.

40-41)

speak to the

importance of heuristic devices capable of reducing the
search for solutions.
Much of the progress in the application of computers
to decision-making has been through utilizing
algorithmic methods for finding problem solutions.
Algorithmic methods call for the total, systematic
search for solutions and have been described as the
"brute-force method" of problem solving.
Increasingly,
interest has grown in the application of heuristic
methods in decision-making.
A heuristic is a strategy,
rule of thumb, simplification, or any other device
which drastically limits search for solutions to a
reasonable process.
Given the great complexity of
planning and decision-making in complex organizations,
the development of knowledge about heuristic processes
and the creation of computer programs utilizing
heuristic rather than algorithmic methods offer very
interesting possibilities.
The development and testing of computer simulation
models is important because it is a heuristic device and
because it is one of the few methodological approaches
which can encompass the dynamic aspect of time series
analysis.

Such a device makes possible a forecasting

technique which is capable of handling the mathematical
analysis which may otherwise be intractable and which
permits forecasting which is not purely mechanical but

64
predictive in the sense that it is derived from grounded
theory.
The appeal of more mechanistic devices is their
inherent simplicity.

Heald and Moore

(1968, pp.

282-84)

discuss several methods of population forecasting that are
recommended to practicing educational administrators for
planning purposes.

Salzman

(1968) presents a thorough

discussion of commonly accepted forecasting methods which
have been employed extensively in economics.
particularistic sense, Costa

In a more

(1970) has employed the

method of moving averages and exponential smoothing to
predict teacher turnover in selected schools in Iowa.
Because these two methods

will be used in

may be useful to consider

them further.

Costa
averages as,
equal
is,

(1970, p.
" . . .a

weight to

6) defines the method of moving
forecasting technique which gives

as many previous years as desired."

a three year moving

F

where

this study it

That

average may be defined as,

L t-2 + L t-1 + L t
(3) = — — -- ^------ “
—

(L) is the level of magnitude of the variable of

interest at three successive time periods
t) respectively.
be derived.

In this

(t-2, t-1, and

way, a series of forecasts

can

65

F 1 (3) =

Costa

L t-2 + L t-1 + L t

L t-1 + L t + L t+1
-----—

F 2 (3) =

—

F3(3)

L

=

—

* t-Y+l

+ - L

t+,
2

(1970) adopts a definition of exponential

smoothing as follows:

ETt = a * (ET t_ 1 ) +

(1-a)

* ET

x

where E T fc is the desired current estimate of turnover at
time

(t), (a) and

(1-a) are weighting factors,

(ET

the actual turnover one time period in the past.
method is called exponential smoothing
pp.

9-10),

^) is
The

(Costa, 1970,

" . . . because of the fact that with increasing

time over successive periods the effect of earlier fore­
casts diminishes exponentially."
The critical problem in employment of these
methods as opposed to those suggested by Heald and Moore
(1968)

is that they forecast only one time period in

advance and then must be given an update of new infor­
mation.

In this respect,

unless they can be modified they

are of little use to planners whose needs may range from
five to ten years

(long-term planning).

Fortunately,

there are modifications of both methods which are sim­
plistic and which effectively combat the tendency of

66

moving
a

averages

static

new

level

and
if

exponential

given

the

smoothing

most

recent

to

tend

forecast

toward
as

the

update.

As a last consideration related to population
forecasting, one must consider what variables are impor­
tant if simulation is employed as one strategy for
achieving predictions?

Blalock

(1969, pp.

37-38) offers

insight to this problem in concluding that:
. . . p o p u l a t i o n c h a n g e is a s i m p l e a d d i t i v e f u n c t i o n
of four variables:
b i rth rates, death rates, and
rates of immigration and emigration.
The major
t h e o r e t i c a l t a s k i n e x p l a i n i n g p o p u l a t i o n c h a n g e is
that of finding the d e t e rminants of each of these
intervening variables.
In
sidered

summary,

the

facilitate
function
there

are

jections,
are

in

return

viewed
is
and
in

importance
the

as

theory

of

planning

of m a n a g e r s

of

complex

a number
most

of

in

methods

which

the

Most
for

of

range

methods

the

known

a trade-off.

of
are

though

this

projection
the

of

heuristic

of

accepted,
range

section

needs

limited

obtained.

this

are

the

devices

and which

for

is
in

benefits

and

is,

to

can
accepted

At

some

of

of

can

being

present,
pro­
which

be

utilization

of

problem,

derived.

con­

future

complexity

addition
be

an

Simulation

a one-time

to

is

that

simplicity

limitations.
That

which

attaining

projections

offer

has

organizations.

mechanical

of

review

is

development
accuracy

grounded

67
Summary
An extensive review of the literature was necessary
because of the large number of salient aspects of simu­
lation research, the short period of time in which
development has occurred,
efforts,

the large number of recent

and the fact that few aspects have been covered

in-depth.

Thus,

it was necessary to consider many aspects

as opposed to a brief survey of the field and intense
focus on the primary topics.
Examination of the theory of general systems
provided a framework for conceptualization of the organi­
zation as system.

The theory included a number of

concepts which were pertinent to the central interest
of this study.

In particular,

"stress" was operationalized

as a primary drive in the organization and the "process"
by which the organization adapted to this stress became
the aspect of reality which was to be simulated.
Extensive review of the technological aspects of
computer simulation provided a foundation for model
development and computer programming.

Until the model

was under construction it was impossible to ascertain
which particular analytical procedures would be employed
nor from what alternatives the choices would be made.
Finally,
planning.

it was necessary to deal with rational

Planning is a primary function of management

in any organization.

Simulation as a tool of analysis

68
permits wholistic analysis encompassing the many variables
of the system.

Therefore, predictive information attained

through simulation was expected to be at least as accurate
as forecasts achieved by other methods.

In addition,

there is evidence to indicate that simulation models can
provide insight into complex organizational process.
The procedures of the study to be presented in
Chapter III make use of the findings of the review of
literature as a foundation for design and development of
the model and as a guide for analysis.

CHAPTER III

TECHNIQUES AND PROCEDURES

Chapter III presents a description of the tech­
niques and procedures that were employed in this study.
Organization of the chapter follows the nine steps
identified by Naylor
of the literature.

(1968)

and discussed in the review

Because of the developmental nature of

the study and the tool of analysis employed,

the Naylor

schema was found to be a useful format for reporting the
techniques and procedures of this study.

Formulation of the Problem
Conceptualization of the system of interest and
determination of the level of aggregation were major
concerns in the formulation of the problem.

In this

respect, the university model developed by Koenig,

et a l .

(1968, p. 9) was useful as a means of suggesting primary
components of educational systems.

Appendix A provides a

schematic of the model presented in the authors'

69

report.

70

As suggested by Elton, et a l . (1971)

and Hopkins

(1971), reduction of the focus of the study was mandatory.
Therefore,

the university model was modified and the

schematic representation was reformulated to provide the
representation which is included as Appendix B.

The four

components depicted in the modified schematic were initially
considered for inclusion in the study and were subsequently
rejected as still exceeding manageable proportions.
Therefore, attention was ultimately focused on that portion
of the system included within the area defined by the
dotted line

(see Appendix B) and the remainder of the

system was left for future efforts.

The components of

interest were therefore limited to the student population
component and the professional staff component.
The determination of the level of aggregation was
based on three considerations.

First, development of a

system of education is constitutionally the responsibility
of the state.

Policies developed at this level are

uniformly applied in all districts thus eliminating a
problem of inter-system variation.

Further,

insofar as

the process model was representative of a particular
school district it would be representative of all local
school districts.

Second, the State Department of Ed u ­

cation offered the advantage of providing a large body of
standard data requisite to development of the simulation
(McNamara,

1971).

Third,

if the study had been focused

71
on the local district level with its considerably reduced
body of data

(in comparison to the state public school

system as a w h o l e ) , the question may have been raised
regarding whether mathematical analysis as opposed to
simulation might not have been more efficient.

In this

regard, the capacity of modern computers for massive data
storage and computational performance is a technological
resource particularly suited to a problem aggregated at
the state level.
At this point in problem definition,

two possible

orientations existed as alternatives to simulation
development

(Cooper and McGillem,

1967, p. 9).

That is,

one might have elected systems analysis which would focus
interest on an attempt to identify the organizational
process which relates given inputs to outputs.

Or, one

might have elected the course of systems design in which
attention would be concentrated on development of an ideal
process to achieve desired outputs given stated inputs to
the system.
In this study, the investigator elected the course
of systems analysis.

Attention was thus focused on the

existing process within and between the student population
and professional staff components as sub-systems of the
state public school system in Michigan.

Furthermore,

was necessary to invoke the assumption regarding the
"block-recursive" nature of the organizational system

it

72

which was discussed by Blalock

(1969)

in the review of

the literature.
Pheiffer

(1968)

concluded that identification of

the boundaries of the system of interest was a pre­
requisite to problem definition.

Blalock

(1969)

suggested

that population change is an additive function of birth
rates, death rates, and rates of immigration and emi­
gration.

Since the components of interest were both

population sectors,

i.e.,

student population and p r o ­

fessional staff population,

Blalock's suggestions were

employed in this study with few modifications.

These are

discussed in the section which deals with formulation
of the model.

Collection and Processing
of Data
The collection and processing of data had impli­
cations for both problem formulation and formulation of
the model.

That is, collection and processing of data

completed an iterative loop which at certain stages
resulted in problem clarification or modification and, at
other times identified a need for additional empirical
evidence necessary to further progress in model formu­
lation.

This frequently occurred during model formulation

as attempts were made to decrease the difference between
simulated response and real world behavior.

73

Michigan birth rate data was obtained from the
Michigan State Department of Health.

The data was obtained

for the years 1940 to 1971 inclusive and is presented in
Appendix C.

Age specific death rates were obtained from

the Commissioner1s Standard Mortality Table
included as Appendix D of this study.

(1958)

and are

The age specific

death rates as given by the table are not computed for
specific geographic regions

(states)

and were not weighted

or altered to allow for a primarily rural or a primarily
metropolitan state.
For the purposes of computer simulation it was
necessary to consider birth data since 1940 because the
simulation program required at least seventeen years of
compressed time model operations to produce a simulated
K-12 school population.

This procedure yielded a K-12

student population by 1957.

For the experiment,

K-12

simulated population levels were required for 1959-1968.
Student population data for the public elementary
and secondary schools in the State of Michigan were
necessary as a standard against which the model could be
verified.

For this purpose,

Fourth Friday Report data

the investigator utilized

(1950-1957) made available by

the State Department of Education in Michigan

(MSDE).

Data associated with the professional staff
component were derived from several sources.

First,

currently employed totals of professional staff were

74

available from the State Department of Education in
Michigan

(MSDE)

Personnel Report

and had been derived from the annual
(1950-1970)

required of all public

school districts in Michigan.

Second, data related to

the production of professional staff by certificate area
was obtained from a series of three reports produced by
the State Department of Education in Michigan
Further,

(1968-69).

the MSDE had produced a study of teacher supply

and demand

(1971).

Data from this study was useful in

establishing net in/out migration estimates of certified
professional staff and one estimate of the functional
supply-demand rate for currently employed professional
staff.

Formulation of the Model
Formulation of the model was appreciably dependent
upon identification of the elements of mathematical models
defined by Naylor, et a l . (1968), upon the critical vari­
ables in population studies as identified by Blalock

(1969),

and upon the clarification of types of simulation models
as presented by Cooper and McGillem

(1967).

All of the

aforementioned were discussed in the review of the liter­
ature .

Model Characteristics
First, the system of interest as previously defined
was conceptualized as discrete,

linear, dynamic,

and

75

deterministic.

While to some extent the "Whorfian

Hypothesis" may have been active the assumptions are not
without some basis.
A discrete model was planned because the real
world system of interest reports data for major variables
on an annual basis and the amount of change in these
variables for shorter time periods was considered
n e gligible.
Linearity was assumed for the sake of simplicity
even though considerable evidence would suggest that
populations,

in particular,

by exponential
assumption,

(non-linear)

are more appropriately described
functions.

In support of this

a Pearson Product-Moment correlation was

computed and revealed a correlation of

(.93) between

reported student census data and reported professional
staff for similar years
coefficient was

(1959-1970).

The linear regression

.0171 with a sample standard error of

estimate of 2,990.

Procedures recommended by Hays

(1963)

were employed in the analysis.
The model incorporated time as a basic system
parameter

(the dynamic aspect)

in order to take advantage

of a primary benefit of simulation.

That is, most static

models employ computed survival ratios or a similar
scheme which circumvents the necessity of considering the
time dimension;

thereby,

avoiding the large number of

76
computations that are necessary when time is taken as a
parameter of the system.
Finally,

the model was conceptualized as a

deterministic system because the basic problem of required
planning predictions dictated a need for point estimates
over the planning period as opposed to interval estimates.

Component Elements
Naylor,

et a l . (1968)

defines the elements of

mathematical models as the components,
(status, exogenous,

and endogenous),

the functional relationships.

are births, deaths,

the parameters,

Blalock

that where populations are concerned,

the variables

(1969)

and

suggests,

the primary variables

and in/out migration.

Identification

of the system required that these two sets be associated
and specifically identified for each component of the
system.

Specific identification of model elements and the

operating characteristics will be discussed under model
validations in Chapter IV.

Estimation of Parameters
Estimation of parameters for the purposes of this
study included both identification and estimation.

In all

cases, parameters were estimated from empirical evidence.
However,

some parameters were subsequently adjusted during

later stages of model development when the technique of
sensitivity analysis was employed

(see Figures 1 and 2

for examples of the effects of parameter c h a n g e s ) .

77

No attempt was made to review the sources and
methods of estimating all model parameters for two reasons.
First,

sources employed were discussed under a previous

section entitled "Collection and Processing of Data."
Second,

for the purposes of study replication the computer

program is readily available and within that program exact
values of the parameters are stated.

Thus,

exact study

replication is always possible and parameter values may be
extracted and compared against real world standards for
evaluative purposes.

Model Evaluation
In this study, model evaluation

(verification) was

accomplished only after system components and elements had
been identified and a basic computer program had been
written to generate K-12 school-age populations given
calendar year birth data

(1940-1971)

and age specific

death ratios.
The computer program was designed to generate
school-age

(5-18)

through 1974-75.

populations for the years 1957-58
After generating the population estimates,

the technique of sensitivity analysis was employed using
the mathematical equations which represent the system to
test the effects of various combinations of parameter
values and to compute the magnitude of differences between
simulated and real time series data.

78

Given parameter values that had been identified
from previous studies

(MEA, 1971; NEA, 1970)

from empirical evidence

or estimated

(Fourth Friday Enrollment data;

Professional Personnel Data)

as initial statements about

the real world, an iterative process of parameter mod i ­
fication and solution of the mathematical model attempted
to achieve successively better approximations of real
world behavior.

The objective of this effort was to test

the mathematical model for relative accuracy prior to
final computer program formulation,

thereby avoiding

extensive reprogramming.
Model verification procedures consisted of
alternately adjusting system parameters and testing the
simulation output which consisted of the primary endogenous
variable response

(employed professional sta f f ) .

The

statistic employed was Thiel's U which was used in a
similar fashion by Tsao and Day

(1971, p. B - 6 0 3 ) .

Thiel's U is a variation of the standard goodnessof-fit test.

That is, the statistic varies in value from

zero to one.

The closer the value is to zero, the stronger

is the inference that the computer generated time series
approximates the desired real world response.
Day

(1971)

Tsao and

selected a particular value of the statistic

as an a priori criterion of model acceptance.

This study

used successive values of the statistic as a guide to
determine when parameter modifications were effective,

79

such as, resulting in lower values of the statistic indi­
cated when modifications were ineffective.

Time and

resources were the ultimate constraints on sensitivity
analysis and the particular value of the statistic that
was accepted prior to conduct of the experiments.
Formulation of the Computer Program
The review of the literature revealed two alterna­
tive courses of action regarding programming.

That is, one

could employ any one of the numerous special purpose
simulation languages

(GASP, Simscript,

could employ a standard language

and others)

or one

(Fortran, Cobol, A P L ) .

The decision to employ Fortran IV in this study was based
entirely on the fact that most hardware systems will have
a fortran compiler.

Therefore,

the program could be

adapted to the greatest number of systems given that
adequate storage and central memory were available.
The system on which programming was completed
consisted of the Michigan State University, CDC-6500
system which has the capacity for Model 33 teletype
terminal interaction.

Programming and testing used the

remote terminal because this permitted minimum turn­
around time and increased overall programming efficiency.
A minimum number of library sub-routines

(such as square

root) were employed so that modification for use on other
systems would be minimal.

80

Finally, where possible modular construction of
the simulation vehicle was employed.

That is, interaction

within and between components and sub-routines related to
model evaluation were kept separate wherever possible.
The final product was a program consisting of only the
simulator and the model elements previously discussed
(see Appendix E ) .
(birth data)

Given a particular array of inputs

the program will generate a deterministic set

of outputs representing employed professional staff and
required staff replacement estimates.

Model Validation
The problem of model validation as discussed by
Clarkson

(1962)

is more appropriate to the following

chapter which deals specifically with analysis.
the approach suggested by Schechter

However,

(1971) was employed.

That is, the mathematical representation was related to
real world components and elements and a rationale
presented in support of the mathematical relationships
included in the model.

The questions that are pertinent

to the analysis are as follows:
1.

What assumptions are inherent in the model and
what are the implications of these assumptions
for the study?

2.

What components of the system of public school
education in Michigan have been incorporated in
the model?

81

3.

What variables have been defined as

exogenous?

4.

What variables have been defined as

endogenous?

5.

What are the operating characteristics of the
system?

Particularly, what are the relationship(s)

that unite distinct components of the system?
6.

What are the status variables which

represent the

state of the system over time?
7.

To what extent was the design limited by factors
beyond the control of the investigator?

(For

example, the choice of values of a particular
parameter when real world data was not available.)
8.

What is the nature and extent of any departures
from intended design and/or the real world;

and,

what implications do these departures have for
the simulation?

Design of Simulation Experiments
Two experiments were conducted to test the
capability of the model to provide more accurate planning
information than that which could be obtained through use
of conventional methods,
averages

(2 years)

such as, the method of moving

and exponential smoothing

(a = .8).

The latter techniques are currently used primarily by
economists to make predictions for the business sector.
Design of both experiments employed a one-way,
fixed effects analysis of variance

(Hays,

1963).

82

Treatments were simulation, moving averages,
ponential smoothing.

The dependent variable was pr o ­

fessional staff population levels
treatments,
years.

and ex­

i.e., methods)

(as forecast by different

and the experimental unit was

The critical level of alpha was selected at

(.05)

since the risk of error for the purposes of this study was
considered to be a minimum problem with few accompanying,
serious consequences.
For the first experiment,

the hypothesis to be

tested was:

There is no difference between the predictions
generated by a simulation model and those
achieved by moving averages and exponential
smoothing.

There is a difference between the predictions
generated by a simulation model and those
achieved by moving averages and exponential
smoothing.

Both the method of moving averages and exponential
smoothing have serious limitations in terms of ability to
provide long range predictions for planning purposes
despite the current popularity and ease of use of these
methods.

That is, both methods can predict only one year

in advance and then must be given a new information update.
The first experiment was a test of ability to provide
short-range planning forecasts.

The experiment offered

every possible advantage to the conventional methods by
providing a true information update each year for a ten

83

year period

(the planned duration of the collapsed time

e xperiment).

In so doing,

the experiment was planned as

a maximum test of the simulation vehicle.
The second experiment assumed that ten years of
planning data was required and that each of the methods
would be compared without special advantages.

That is, a

modification of the two forecasting techniques was
necessary in order to provide such data.
Modification of the forecasting techniques was
achieved by providing an update based on the last forecast
increased by the mean gain over the five years prior to
the experimental period

(1954-1958).

Justification of

such a procedure was based on retention of the ease of
use provided by each of the conventional methods.
contrast,

In

simulation requires a long period of development

and considerable resources.

The essence of the second

experiment was related to the capability of one or more
of the methods to provide more accurate planning data.
It is believed that a better decision could be made
regarding which method to employ given the relative
accuracy of each of the methods,
advantages and disadvantages.

as well as related

Design of the second

experiment was similar to the first.

The hypothesis to

be tested was:

H^:

There is no difference between predictions
generated by simulation and those achieved by
modified forecasting methods.

84

12 :
^

There is a difference between the predictions
generated by simulation and these achieved by
modified forecasting methods.

The use of analysis of variance to examine the
hypothesis of equal means in each experiment required
consideration of three underlying assumptions.

The F

statistic is robust to violations of the assumptions of
normal distribution and equality of variance for the
dependent measure.
of variance

However,

the FMax test for equality

(Walker and Lev,

1953, pp. 191-95) was used

(alpha = .05) to examine the strength of the latter
assumption.
The third assumption of independence was con­
sidered questionable and therefore,

the following linear

transformation of dependent measures was used:

d j_(t) - P i (t) - A (t)
where,

d^(t)

represents the difference between the

predicted score derived from a particular treatment and
the actual real world value for a given year.

If the

null hypothesis was rejected in either experiment,
pair-wise comparisons were planned to examine the
differences between means using the Scheffe method as
described by Hays

(1963).

85

Summary
The procedural plan of this study involved five
sequential steps.

First,

the development of the model

which included problem formulation,
processing of data,

collecting and

system identification

(formulation of

the mathematical m o d e l ) , and estimation of parameters and
operating characteristics.
computer program.

Third,

Second,

formulation of the

evaluation of the model

(veri­

fication) which employed sensitivity analysis and the use
of Thiel's U statistic as a guide to model improvement.
Fourth, validation of the model accomplished through a
series of questions formulated to provide an analysis of
model structure in terms of the related real world system.
Finally,

two experiments were planned to compare the

accuracy of the predictive capacity of the model against
two conventional forecasting techniques.
The procedural plan followed the nine step schema
proposed by Naylor, et a l . (1968)
The ninth step, however,

almost without exception.

dealing with the analysis of

simulation data was postponed to Chapter IV of this study.

CHAPTER IV

REPORT OF FINDINGS

The report of findings is organized around three
topical areas as suggested by Fishman and Kiviatt

(1968)

followed by a summary which relates the three areas.
Validation of the model is the first area and involves a
review of the development of the model followed by an
explanation of structural elements and relationships in
terms of real world correspondence.

The second area is

model verification which concerns the simulated response
of endogenous variables as compared to real world behavior.
The third area is an analysis of findings for two experi­
ments which were conducted using the simulation vehicle.

Model Validation
Model validation concerns a presentation of the
model accompanied by appropriate explanation of the
elements of the model in terms of real world counterparts.
For the purposes of this section the development will be
described first.

Next, variables and operating character­

istics will be defined.

Finally, the mathematical model

86

87

will be presented with accompanying explanations and
previously formulated questions will be answered regarding
the model and the real world system of interest.

Model Development
The development of the model and the planning and
conduct of this study was not a straightforward procedure
as might be inferred from the carefully constructed schema
suggested by Naylor

(1968).

That is, at some time or

another the study progressed through each of the identi­
fied stages.

However,

the development of the model often

required looping back to previous stages in order to
attain subsequent refinements or to implement desired
modifications.

A brief review of these developmental

phases may be useful to future efforts.
The public school system in Michigan was first
analyzed from a wholistic point of view.
of time,

Over a period

important components became distinguishable and

attempts were made to diagram the components and hypothe­
sized relationships between components

(see Appendix B ) .

The foregoing iterative sequence was replaced by a similar
loop which first examined individual elements within
components followed by tentative formulation of hypotheses
about the nature of relationships between elements within
a particular component.

This process was followed by a

more detailed diagram of systemic relationships.

88
As components and elements of the system were
identified, time series data related to important elements
of the system were collected and analyzed.
Product-Moment correlation

A Pearson

(r = .93) was calculated to

examine the nature of the relationship between student
populations and teacher populations which was critical to
this study.
The next phase was formal identification of the
system and development of the mathematical model.

First,

elements within components were given variable names and
defined.

Second, equations were formulated that closely

corresponded to the former hypotheses about the nature of
relationships.

Third,

an attempt was made to test the

equations for correspondence to real world behavior.
some cases,

In

the functions were rejected and subsequently

reformulated.

In other cases, new data were collected to

provide required input to the model.

Finally,

different

relationships were peremptorily tested to provide expla­
nation of inter-component behavior.

At this point,

the

model had been completely identified and formulated,
though a number of iterations were subsequently necessary
to reach the final stage.
Development of the computer program using
Fortran IV proceded rapidly because of the mathematical
nature of the model; at least one complete program was
rejected before the final program was formulated and

89

tested.

Use of the computer terminal for program testing

was especially efficient,

since considerable turn-around

time between computer runs was avoided.
The last phase of development was concerned with
achieving successively improved performance.

Once again,

a number of iterations were necessary as parameters were
altered and time series data were re-generated and
compared with real world data.

Final comparisons indi­

cated that the model was performing satisfactorily and
the two, planned experiments were conducted.

Variable Definitions and
Operating Characteristics
In the process of model identification the
following elements were identified and given specific
variable names.
1.

Student population component.
a.

Birth(t)— birth rates for years 1940-1971

b.

Surv(t)— surviving population after death
losses

c.

Dth(a)— age specific death rates

d.

SPOP(t)— student populations for grades
(K-12) by years

e.

PI— net in/out migration factor

f.

P2— private school population factor

g.

P3--drop out factor

90

2.

Professional staff

(teacher)

component.

a.

AvStf(t)— total available staff

b.

InProd(t)— number of teachers produced by
training institutions per year

c.

InPool(t)— number of teachers qualified to
teach but remaining inactive by choice

d.

Attr(t)— losses due to death,

retirement,

and for other reasons
e.

NMigr(t)— number of teachers who migrate in
or out of the State of Michigan

f.

TPOP(t)— number of teachers currently employed

g.

NStaff (t)— number of teacher replacments needed

h.

ElmStf(t)— number of elementary replacements
needed

i.

SecStf(t)— number of secondary replacements
needed

3.

j.

P6— elementary replacement rate parameter

k.

P7— secondary replacement rate parameter

Interdependency Parameter.
a.

4.

P4— approximate student/teacher parameter

Operating characteristics.
a.

Student sector—
SPOP(t)

= SPOP' (t) + Pl*SPOP'(t)
...

- P 2 * S P O P ' (t ) -

- P 3 * S P O P 1 (t)

91
b.

Professional staff sector—
AVSTF(t)

= InProd(t)

+ InPool (t) - Attr(t)

... + NMigr(t)
c.

+ ...

+ TPOP(t)

Supply-Demand function—
TPOP(t)

= P4 * SPOP(t), where P4 = .036

Model Identification
A sub-routine of the model permits calculation of
a

(20x31)

survivor matrix by interacting birth data with

age-specific death rates.

The unrefined sum of

(K-12)

student population for a given year was then obtained by
summing across 13 columns beginning with students of the
1940 birth group who were 17 years old in 1957, e.g.,

SPOP'(t)

= 171940 + 161941 + 151942 + ••• + 6i95i + 51952
= SPOP' (1957), the first possible

(K-12)

population given 1940 birth data

The unrefined sum of age-specific populations for each
year from 1957 through 1975 is then entered into the
operating characteristic of the student population sector
(see above)
populations.

to provide a refined estimate of student
Parameters PI, P2, and P3 were initially

estimated at .11,

.15, and .16 respectively.

These were

changed very little in subsequent refinements of the model.
The operating characteristic for the professional
staff sector relates important variables suggested by

92

Blalock

(1968) as does the operating characteristic for

the student population sector.

However, no data was found

from which an estimate of the inactive pool of teachers
InPool (t) could be obtained.

Thus, this function is

presently not operative though it has been included in
the program and could be made operative simply by providing
the required estimates of population dynamics.
To circumvent this problem a different approach
was taken.

That is, an annual estimate of required

teacher replacements

(.065) was computed to generate a

time series for a new variable NStaff (t) from annual
estimates of TPOP(t).

The relation used was:

NStaff(t)

= P5 * TPOP(t)

where the parameter P5 is a multi-factor point estimate
of several factors including attrition, production,

and

movement both into and out of the inactive pool.
Given this addition to the model it was possible
to generate a time series which represented professional
staff needs based on actual birth data for all years from
1957 to 1975.

Further,

given this time series it was

possible to estimate from data

(see Appendix F) the

proportion of replacment needs by certificate type.
functions that produce these estimates are:
1.

ElmStf(t)

= P6 * NStaff(t), where P6 = .485

2.

SecStf(t)

= P7 * N S t a f f ( t ) , where P7 = .515

The

93

Parameters P6 and P7 were derived from the data in
Appendix F after elimination of other types of certifi­
cates that are not expected to be used as new certification
rules come into effect.

The reduction of replacement needs

by certificate type results in a certain amount of error
for estimates prior to 1972 but seems justified in the
sense that predictions of greatest interest derived from
the model will be post 1972.
Examination of potential relationships which could
be used for the function uniting the primary components
(the supply-demand function)

employed a modified version

of a Fortran program formulated by Salzman

(1968).

The

program has the capability of generating polynomial,
logarithmic,

and exponential equations given time series

data for corresponding years on two variables of interest.
In addition,

a linear regression equation which had been

a by-product of the Pearson Product-Moment correlation
(Hays, 1963) was tested.

In all, the best fit was obtained

by calculating a rate parameter

(P4 = .036)

to represent

the approximate student/teacher ratio of 24:1 as suggested
by the Michigan State Department of Education study
(1971).
The full simulation model,

as defined, accepted

birth data beginning with the year 1940 and generated
estimates of student population levels from 1957 to 1975.
From these estimates the supply-demand function produced

94

estimates of the levels of employed professional staff for
similar years.

Finally, the model had the capability of

translating estimates of new staff needed for replacement
into needed certificate types.

Model Validation Questions
In Chapter III, eight questions were formulated
regarding the validity of the model in terms of the real
world system it purported to represent.
re-stated below,
1.

Each question is

followed by the answer for that question.

What assumptions are inherent in the model and
what are the implications of these assumptions for
the study?
Two assumptions were stated in the beginning of

the study.

The first adopted the position that student

population levels presented a major stress
within the system.

(drive impetus)

This assumption is basic to the model

and is the primary basis for derivation of all values of
endogenous variables.
is in error,

To the extent that this assumption

the values of all response variables would be

in error.

Since relatively close values were ultimately

predicted,

the assumption was held valid.

The second assumption concerned the block recursive
nature of the system.

That is, the system as represented

at the state level is assumed to be relatively unaffected
by behavior at either the local district or federal

95

level.

No way was found to assess the amount of error that

such an assumption contributes to derived response levels.
Again,

since derived values were considered acceptable,

it

is contended that the amount of error was negligible.
Other assumptions were made in the course of
development of the model.
(linear, discrete,

That is, the design criteria

dynamic, and deterministic)

as well as

the adopted values of certain influential parameters
migration, private school population,

(net

and drop-out rates)

have certainly contributed to error in the simulation
vehicle.

Again,

since simulated behavior closely

approximates real world behavior,

it is contended that the

total magnitude of such error was within acceptable
limits.
2.

What components of the system of public school
education in Michigan have been incorporated in
the model?
Only two components of the public school system are

represented in the model,

such as, the student population

sector and the professional staff sector
3.

(see Appendix B ) .

What variables have been defined as exogenous?
Within the student population component, Birth (t)

representing the number of births per year was the only
exogenous variable.

In the professional staff component,

the original plan would have required that InProd(t)

_

and

96

possibly InPool(t) be represented as exogenous variables
with accompanying input data.

However,

as previously

explained, the lack of data forced abandonment of this
scheme of representation.
4.

What variables have been defined as endogenous?
Within the student population component SPOP (t)

is both endogenous and a status variable.

Others such as

high school graduates, private school population,

and

number of drop-outs could easily be derived but were not
necessary for the purposes of this study.
Within the teacher population component,

there are

three endogenous variables for which time series data is
provided by the computer program.

NStaff(t)

provides

point estimates of required annual staff replacements
based on 6.5 per cent of currently employed staff.
ElmStf(t)

provides point estimates of the annual need for

new staff with elementary certificates.
SecStf(t)

Similarly,

provides estimates of the annual need for new

staff who are certified for secondary.

TPOP(t)

is the

primary endogenous variable of interest and is also the
status variable for the professional staff sector.

Time

series data is available for this variable also and is
used extensively in the two experiments.
5.

What are the operating characteristics of the
system?

Particularly, what are the relationships

that unite distinct components of the system?

97

These have been previously identified in the
section which dealt with model identification.

The supply-

demand function that unites the two distinct components of
the system as well as the operating characteristics for
each sector are linear in nature.

The supply-demand

function in particular is dependent upon stability of the
student/teacher ratio.
6.

What are the status variables which represent the
state of the system over time?
Within the student population component,

the state

of the system is represented by the number of clients to
be serviced by the public school system in Michigan,
SPOP(t).

i.e.,

S P O P (t) is important both in terms of the demand

for professional staff that it represents and also the
demand that is posed for other resources of the system
(physical facilities and financial resources).
In the professional staff component, TPOP(t)

is

the important status variable which represents the level
of employed staff over time.

Somewhat unrealistically,

TPOP(t)

is totally dependent on SPOP(t)

model.

The dependency of TPOP(t)

in the present

will change as future

expansion of the model is realized.
7.

To what extent was the design limited by factors
beyond the control of the investigator?

98

The most serious limitation was the lack of data
for the variable that represented the inactive pool of
teachers.

This prevented generation of point estimates

for the number of available staff over time.

The loss

detracted from the potential of the full model since
AvStf (t) is believed to be a useful variable in terms of
better understanding of the need for new staff on an
annual basis.

Of related importance is the need to begin

compiling data for both variables InPool (t) and NStaff(t)
so that related measures such as AvSTF(t)

may eventually

be obtained.
8.

What is the nature and extent of any departures
from intended design and/or the real world;

and,

what implications do these departures have for
the simulation model?
The limitation discussed in answer to the previous
question was the only departure from intended design.
The implication of this departure has also been discussed.
There were no departures from the real world insofar as
all parameter estimates and input for exogenous variables
were derived from empirical findings.

The assumptions

previously discussed were the primary departures and these
were not happenstance.

99

Model Verification
As time series data was generated for an increasing
number of variables,

correlations were derived to examine

the relative ranking of both simulated time series with
real world counterparts and one simulated variable with
another.

As a result,

obtained for the years

the following incomplete matrix was
(1959-1968).

The figures in

Table 1 indicate how closely the relationships agree among
actual time series and simulated time series for different
variables,

such as, teacher population levels

student population levels

(SPOP(t))

(TPOP(t)) and

respectively.

The

first correlation as previously discussed was obtained
prior to the beginning of model development to examine the
nature of the relationship between primary variables in
each of the two components which were to be simulated.

TABLE 1.— Relationships Between Actual Teacher Populations
and Actual and Simulated Teacher, Student
Populations.

Variable Time Series

Actual TPOP(t)

Actual SPOP(t)

.976

Simul.

SPOP(t)

.917

S i m u l . TPOP (t)

.937

Table 2 compares response value for simulated
teacher populations

(TPOP(t))

achieved at three separate

points in the overall process of sensitivity analysis.

TABLE 2.— Actual and Simulated Response for TPOP(t).

1st Sim.
Run

2nd Sim.
Run

Dif f 2

3rd Sim.
Run

Dif f 3

1959

58,251

64,811

5,610

59,825

1,574

55,857

2,394

1960

60,394

67,278

6,977

62,103

1,708

59,405

989

1961

63,271

70,029

6,829

64,642

1,371

63, 362

91

1962

66,024

73,255

7,255

67,620

1,596

68,002

1,978

1963

68,099

76,398

8,398

70,521

2,422

72,521

4,422

1964

69,380

78,422

9,122

72,389

3,009

75,432

6,052

1965

72.935

79,596

6,696

73,474

538

77,121

4,186

1966

76,047

80,885

2,570

74,664

1,384

78,974

2,927

1967

80,637

82,015

2,240

75,707

4,931

80,599

38

1968

85,346

82,703

2,597

76,342

9,005

81,589

3,757

100

Actual
TPOP

Dif f ^

Year

It is clear that observation of the difference scores
would have been sufficient guidance in the early stages
of model refinement.

However,

experience has shown that

in the latter stages of development some guidance technique
was necessary to distinguish improvements.

Thiel's U

statistic was employed as a guide in sensitivity analysis
once a complete functioning model and computer program had
been attained.
Table 3 provides a comparison of the value of the
U statistic computed for each of the foregoing simulated
time series as well as the values of relevant parameters
used in the model to achieve that series.

The computer

program for the revised model from which the third time
series

(above) was generated was used in the experiments

which are discussed in the last section of this chapter.
It is important to note that the relatively low values of
the U statistic were not expected and that this factor
almost as much as time expenditure caused early curtailment
of the process of sensitivity analysis.

Further,

a scheme

ought to be devised and employed to rapidly examine
various combinations of different parameter levels.
space of all possible combinations of parameters
at approximately 1,000 in this model)

The

(estimated

should have been

systematically examined for possible improvement of the
primary endogenous variable TPOP(t).

TABLE 3.— U Statistic and Parameter Values for Separate Simulation Estimates of
TPOP (t).

Simulation
Series

U
Statistic

Values of Relevant Parameters
-----------------------------------------------Net Migr.
Priv. Schl.
Drop-out
PI
P2
P3

T/'S Ratio
P4

First Run

.03538

.11

.15

.16

.037

Second Run

.02589

.14

.13

.15

.039

Third Run

.02298

.14

.13

.15

.036

The parameter estimates used for the first simu­
lation run represented mean estimates of true population
parameters.

That is, the estimate of net in/out migration

which was obtained from data in Meyers and Van Meer
was estimated at approximately
populations

(11%).

(1966)

Private school

(MEA, 1971) averaged approximately 275,000 per

year which was initially stated as
population of survivors.

(15%) of the total

Employment of a point estimate

for the private school population parameter
the fitting of a curve)

(as opposed to

is believed to have contributed

substantially to error in the model since this particular
variable oscillates from year to year and currently
exhibits a clear pattern of population decrease.

A better

scheme for representation of the model would have been to
fit a curve to the data and then to extrapolate future
predictions from the function of that curve.
Some attention ought to be devoted to the process
of curve fitting which represented three restrictions for
the purposes of this study.

Bertalanffy

(1968) has noted

that such activity is no more than intellectual play.
That is, curve fitting permits access to more exact point
estimates but the parameters of the function will likely
have no meaning in the real world.

Second,

functional

representation of the parameters in this study would
possibly have yielded a non-linear function for at least
one of the parameters thereby exceeding a design

104

limitation which clearly specified a linear model.

Third,

functional representation of parametric effects requires a
knowledge of contributing variables, data related to those
variables,

and adds additional complexity to the model.

The alternatives for this study were parsimony or increased
accuracy.

In this case, a parsimonious model was elected

especially in view of the low value of the U statistic
which was obtained.
Table 4 provides a comparison of the means,
standard deviations,
series

and variances for the two time

(actual teacher population levels and final-run

simulation values of that variable for the years 1959-1968).

TABLE 4.— Simulated and Actual Teacher Population Parameters
(1959-68).

Time Series Identity

Mean

s .d.

Variance

Actual No. of Teachers

70,038

8,751

76,580,001

Simul. No. of Teachers

69,729

5,889

34,690,321

The agreement in level

(the mean)

is noteworthy,

though

the difference in standard deviation is indicative of
considerable variation in point by point comparisons as
well as in the overall configuration.

Figures 1 and 2

which follow illustrate these observations.

Figure 1 is

a comparison of first-run simulation values for TPOP(t)
with actual values of teacher population levels for the

105

85 •

Teacher Pop.

(1,000's)

°

X

x

x

o

x

80 *
X

X

75
X

70

o
o

65 *

Parameter Values
60 *
PI
P2
P3
P4

=
=
=
=

.11
.15
.16
.037

55.

— t—

'59

Figure 1.

'60

— ... > — ..■ >

'61

'62

1

'63

■ ■>

'64

|

'65

m

'66

(t)
— — -

1

'67

'I

'68

Comparison of actual and simulator predicted
teacher populations (1959-1968).

Note:

o Actual teacher populations.
x First simulation run-predictions.

106
Teacher Pop.

(1,000's)

85 -

X
X

80
X

X

o
75o

X

70
o
X

o

65
o
X

o

60

Parameter Values

X

°

PI
P2
P3
P4

x
55

=
=
=
=

.14
.13
.15
.03

(t)
4

• -

'59

Figure 2.

'60

'61

'62

'63

'64

'65

'66

'67

'68

Comparison of actual and simulator predicted
teacher populations (1959-1968).

Note:

o Actual teacher populations.
x Simulation predictions of teacher
populations-final run.

107

years

(1959-1968).

The observed mean was 75,540 for this

simulated time series.

Figure 2 is a comparison of the

final-run of the simulation vehicle with population
levels.
In summary, no previously specified value of
Thiel's U statistic had been selected as the threshold of
model acceptance.

Instead,

successive values of the

statistic were employed to guide subsequent modifications
of model parameters.

It was planned that sensitivity

analysis would terminate when time and resources dictated
or when further adjustments achieved no improvement in
performance of the model.

The unexpectedly low values of

Thiel's U contributed as much to the termination of
sensitivity analysis as did the contraint of time.

This

prohibited a more complete exploration of the parameter
space in search of a combination which would minimize
the disparity between actual population levels and simu­
lated levels.
In view of the extremely low value of Thiel's U
(.023)

and the relative agreement of the two time series

in mean value, the performance of the model in relation to
real world behavior was considered acceptable.

Model Experimentation
Experimentation with the simulation vehicle was
planned to test the ability of the model to provide
accurate planning estimates of the expected level of

108

teacher employment over a ten year period

(1959-1968) .

Two distinct experiments were planned and they are
discussed separately in this section.

Experiment One
The first experiment was concerned with the accuracy
of different methods for one year at a time forecasts.
The experiment was planned as a maximum test of the
accuracy of the simulation vehicle.
method of moving averages
exponential smoothing

(2 years)

That is, both the
and the method of

(a = .8) were given the required,

annual update of true information necessary.

The

question was:
Is there a difference between simulation forecasting
and forecasting which employs either moving averages
or exponential smoothing?

:

There is no difference between the method of
forecasting by simulation or forecasting by
moving averages or exponential smoothing.

There is a difference between the method of
forecasting by simulation or forecasting by
moving averages or exponential smoothing.

Results of the statistical analysis pertinent to
the stated question are presented in Table 5.
Application of the FMax test indicated that
homogeneity of variances for forecasts existed for differ­
ent forecasting methods.

The mean square ratio for

109

TABLE 5.— Fixed Effects ANOVA for Teacher Population
Predictions By Separate Forecasting Methods.

Source

d. f .

SS

MS

F (.05)

Treatments

13,567,587

2

6,783,794

2.79

Error

65,701,139

27

2,433,375

. .

Total

79,268,726

29

treatments

•

•

•

•

(2.79) did not exceed the tabled value of F

at the .05 level of significance for 2 and 27 degrees of
freedom respectively.

The null hypothesis was retained

and follow-up tests were not conducted.

It can be

tentatively assumed that there is no significant differ­
ence between accuracy of forecasts between different
methods of forecasting.
Table 6 is a ceil summary for the first experiment.

TABLE 6.— Cell Summary for Experiment One.
Types

N

Mean

Variance

Standard
Deviation

Simulation

10

2,683

35,010,972

1,972

Moving
Averages

10

4, 328

16,993,614

1,374

Exponential
Smoothing

10

3,575

13,696,552

1,233

110

Experiment Two
Experiment two was designed to test the accuracy
of the simulation vehicle against both methods of moving
averages and exponential smoothing given that ten years
of planning data was desired.

The conventional forecasting

methods were not permitted a true information update

(as

would be the case if actual predictions were desired)
instead were modified by other means

(see Chapter III)

order to achieve long range forecasts.
For long range forecasts,

but
in

The question was:

is there a difference

between simulation forecasting and forecasting which
employs either a modified form of moving averages or
a modified version of exponential smoothing?

:

There is no difference between the method of
forecasting by simulation or forecasting by
modified versions of the method of moving
averages or exponential smoothing.

There is a difference between the method of
forecasting by simulation or forecasting by
modified versions of the method of moving
averages or exponential smoothing.

Results of the statistical analysis pertinent to the above
question are presented in Tables 7, 8, and 9.
Application of the ^ ax test indicated that
homogeneity of variances for predictions existed for
different forecasting methods.
treatments

(9.85)

The mean square ratio for

exceeded the tabled value of F at the

Ill

.05 level of significance for 2 and 27 degrees of freedom
respectively.

The null hypothesis was rejected in favor

of the alternative and follow-up tests were conducted.
Of the three pair-wise comparisons,

two were found

to be significant using the Scheffe procedure.
difference

(2,683)

The mean

for simulation forecasting was signifi­

cantly smaller than the mean difference

(8,309)

for moving

average predictions.

Similarly,

exponential smoothing

(4,059) was significantly smaller

than the mean difference

the mean difference for

(8,309)

for moving averages.

Significant differences between mean differences for simu­
lation and for exponential smoothing did not exist.
These findings indicated that more accurate
forecasts could be obtained by simulation and/or e x ­
ponential smoothing than could be obtained by moving
averages.

TABLE 7.— Fixed Effects ANOVA For Teacher Population
Predictions By Separate Forecasting Methods.

Source

SS

d. f .

MS

Treatments

172,052,177

2

86,026,088

Error

235,889,300

27

8,736,640

Total

407,941,477

29

*Significant at F (>Q5) (2f2?)

F (. 0 5)

9.85*
*

112

Table 8 provides a cell summary for the second
experiment.

TABLE 8.— Cell Summary for Experiment Two.

Types

Standard
Deviation

N

Mean

Variance

Simulation

10

2,683

35,010,972

1,972

Moving
Averages

10

8,309

166,030,791

4,295

Exponential
Smoothing

10

4,059

34,847,536

1,967

Table 9 provides a summary of the follow-up tests
for the second experiment.

TABLE 9.— Post-Hoc Comparisons

Simulation

Simulation

for Experiment T w o .

Moving
Averages

-5,627*

Moving
Averages

Exponential
Smoothing

-1,376

4,251*

Exponential
Smoothing

*Significant at the .05 level.

113

Summary
This chapter was concerned with three distinct
parts of simulation research:
validation,

model verification, model

and experimentation.

Model validation required an explanation of the
simulation model accompanied by a rationale in support of
design and structure.
and judgmental.

Acceptance of the model is heuristic

That is, it remains for the observer to

decide for himself,

if the model is representative of the

purported system of interest.

This study, presented

definitions of the elements of the model,
of all functional relationships,
accompany each.

specific examples

and explanations to

Of particular importance to the process

of validation is the necessity to understand the basic
assumption upon which the model was constructed.

That is,

that students provide the primary demand for system
resources.

This assumption provided the functional basis

for construction of the model.
Model verification required a two-phase,
procedure.

iterative

The process of sensitivity analysis was

employed to achieve successively better approximations of
simulated performance.

Thiel's U statistic was used as

a guide to indicate when a particular modification of the
model improved the performance.

No a priori value of the

statistic was specified as an acceptance threshold.
attained value of U

(.02298) was the final congruence

The

114

measure after numerous modifications and in terms of
performance, the model was accepted.
Two questions were addressed in separate experi­
ments and concerned the accuracy of simulation forecasting
for short- and long-range planning purposes in comparison
to the accuracy of conventional methods
and exponential smoothing).

(moving averages

The null hypothesis was

retained in the first experiment which was planned as a
maximum test of the simulation vehicle.

It was concluded

that with regard to short-range planning all of the methods
are equal in accuracy of forecasts.

Differences in the

means of each series of forecasts were noted and it was
observed that simulation forecasts were more accurate.
In the second experiment the null hypothesis was
rejected at the .05 level of significance.

The

test

indicated equality of variance among treatment methods
and follow-up tests employing the Scheffe procedure were
conducted which identified the nature of treatment differ­
ences.

It was concluded that with regard to long-range

planning simulation forecasts and predictions attained
from a modified version of exponential smoothing were
more accurate than predictions obtained from a modified
version of the method of moving averages.

Differences in

the means of each prediction series were observed and
simulation forecasts were observed to be more accurate.

CHAPTER V

SUMMARY AND CONCLUSIONS

This chapter provides summaries of the purpose of
the study, the techniques and procedures employed, and the
findings which concern model development, model validation,
model verification,

and experimentation.

The last section

is concerned with the conclusions from this study and
suggested areas for future research.

Purpose of the Study
It was the purpose of this study to examine the
student population and professional staff components
the public school system in the State of Michigan.

of
Simu­

lation was selected as the appropriate tool for wholistic
analysis.

The following objectives,

evolved from the

stated purpose of this study and provided guidance for the
work:
1.

Development of a simulation model.

2.

Development of a functional computer program
embodied the simulation model.

115

which

116

3.

Validation of the model.

4.

Verification of the simulation model.

5.

The completion of two experiments using the model to
compare the accuracy of the simulation vehicle
against conventional forecasting methods for the
purpose of deriving short
range

(ten year)

(one year)

and long-

planning information.

Given that the model could be developed,

programmed,

and successfully tested it was expected that the model
would prove to be more accurate in forecasting future
professional staff needs than conventional methods,
moving averages and exponential smoothing.

such as,

In addition,

it was believed that wholistic analysis followed by
synthesis of system elements to form a mathematical model
would provide greater insight regarding complex inter­
actions within the public school system.

Techniques and Procedures
Data was accumulated for annual levels of two
primary variables,

student populations and teacher popu­

lations of the public school system in Michigan.
correlation coefficient

A

(r = .93) was computed to provide

an indication of the nature of the relationship between
the two variables.

Since each component comprised a

population sub-system,

additional system elements were

identified using a scheme suggested by Blalock

(1968) .

117

Additional data for these elements
migration,

attrition) were located.

(births,
Then,

in/out
a mathematical

model of the system as identified was constructed and a
computer program was written representing the model of the
system.
Model validation followed and entailed a three
part procedure.

First,

model were defined.

all elements of the simulation

Second, the elements were presented

as related by operating characteristics of the system and
the supply-demand function which unites the student popu­
lation component with the professional staff component.
A discussion of the functional relationships in terms of
the real world system of interest accompanied the expla­
nation of the mathematical model.

Third,

(which had been previously formulated)

eight questions

regarding the

nature of the model were presented and answered.
Procedures employed in model verification were
based on an iterative scheme.

Sensitivity analysis and

Thiel's U statistic were alternately employed to achieve
successively better approximations to the final system.
The model was accepted when Thiel's U statistic reached
.023 for a comparison of the simulator generated endogenous
variable TPOP(t) with the corresponding time series of
actual values.

The foregoing procedure constituted

verification of the model as opposed to selection of an
a priori value of the U statistic as the acceptance
threshold.

118

Finally,

two experiments were planned and conducted

which compared the accuracy of simulation forecasting with
the method of moving averages
smoothing
similar.

(a = .8).

(two years)

and exponential

The design of both experiments was

A fixed effects, analysis of variance was

employed to test the hypothesis of equal forecasting
accuracy between all methods.

A test of the hypothesis

of homogeneity of variance was planned for each experiment.
It was further planned that if the null hypothesis was
rejected the F ^ ^

test would be followed by post hoc

comparisons using the Scheffe procedure.
The first experiment was planned as a test of the
relative accuracy of each of the methods for short-range
planning,

i.e., year-to-year forecasts.

The second experi­

ment was planned as a test of the relative accuracy of
each of the methods for long-range planning,

i.e., ten

year forecasts.

Analysis of Findings
Model validation attempted to demonstrate and
explain elements of the model and wholistic representation
in terms of real world components.

Acceptance of the

model as being representative of the real world was a
judgmental decision.
in this study,

Of particular important to validation

is the basic assumption that student popu­

lation levels drive the system.

That is, public school

students present a primary demand for system resources.

119

This assumption provided the foundation for construction
of the model and is the method by which the concept of
"stress"

from general systems theory was operationalized.

Model validation is necessarily heuristic and judgmental
but has been called for by authorities in the field as
being an important component of simulation research.
Model verification entailed a decision to accept
or reject the model on the basis of performance,

i.e., the

ability of the model to approximate real world systemic
behavior.
criterion.

Thiel's U statistic was employed as the decision
The performance of the model,

as measured by

a simulated time series for the primary endogenous variable
representing professional staff levels over time, was
accepted after successive parameter modifications that
finally yielded U = .023.
Two questions were addressed in separate experi­
ments and concerned the accuracy of simulation forecasting
for short- and long-range planning purposes in comparison
with the method of moving averages and exponential
smoothing.

All statistical tests were conducted employing

an alpha level of .05.
The first experiment was a test of the fore­
casting ability of three methods
averages,

(simulation, moving

and exponential smoothing)

(year-to-year)

planning.

for short-range

The null hypothesis of no

differences between treatments was retained

(mean square

120

ratio = 2.79).

A test of the equality of variances

resulted in retention of the null hypothesis and indicated
the assumption of homogeneity of variance was valid.

The

results of the analysis were interpreted to mean that for
the purposes of short-range,

year-to-year planning either

of the three methods would product forecasts whose
accuracy in relation to the other two methods were about
equal.

It is interesting to note, however,

that differ­

ences in the means, were observed and that the mean of
simulation forecasts

(69,729) was considerably nearer

the mean of the actual time series

(70,038),

the means of the two conventional methods

then were

(65,710 and

66,463 respectively).
The second experiment was a test of the fore­
casting ability of three methods

(simulation and modified

versions of moving averages and exponential smoothing)
for long-range

(ten years) planning needs.

The null

hypothesis of no differences between means was rejected
(mean square ratio = 9.85)

in favor of the alternate.

Subsequent pairwise mean comparisons indicated that
simulation forecasts were significantly more accurate
than those attained by the method of moving averages and
that exponential smoothing forecasts were significantly
more accurate than moving average forecasts.

Significant

differences were not found between simulation forecasts
and exponential smoothing though once again differences

121
were observed and simulation forecasts were observed to
be more accurate.

Conclusions
The following conclusions are derived from the
findings of this investigation:
1.

It is possible to develop a valid simulation model
which is representative of the public school system
in the State of Michigan

(realization of the first

and fourth objectives).

Further,

it is believed

that the model as constructed is generalizable to
local school districts as well as to other state
systems if parameter values are adjusted to reflect
local conditions.
2.

The simulation model can be embodied in a computer
program and satisfactory response of the model

in

terms of functional performance of primary
endogenous variables was realized

(completion of

the second and third objectives).
3.

Future resource

(professional staff)

needs for

short-range planning purposes derived from the
model are not significantly different than fore­
casts obtained by the methods of moving averages
and exponential smoothing when the conventional
methods are given a true information update each
year.

However,

aside from this finding,

122
differences in the means were observed and the
mean of predictions obtained from the simulation
vehicle

(69,729) was noticeably more accurate than

the means of predictions obtained by the con­
ventional methods

(65,710 and 66,463 respectively)

in comparison to the mean of the real world time
series

(70,038).

Standard deviations for each

method were 1,972,
4.

Future resource

1,374,

1,233 respectively.

(professional staff)

needs for

long-range planning purposes derived from the model
were significantly more accurate than those
obtained by the method of moving averages.

Of the

three pairwise comparisons two were significant.
Both simulation and exponential smoothing forecasts
were significantly different from moving averages
which was least accurate.

There was no signifi­

cant difference between simulation predictions
and forecasts attained by exponential smoothing.
That is, given the modification of exponential
smoothing that was employed,
as accurate as the other.

either method is just

However, observation

of the mean of predictions by each method indicated
once again that simulation was observably more
accurate.

fluii

123

Implications of the Study
1.

Simulation is a viable tool of analysis insofar as
investigation of complex organizational systems on
a wholistic basis is the concern.

Simulation

permits functional integration of numerous,
empirically derived,

systemic variables and

provides unlimited opportunity for process
analysis all of which contributes to enlightened
understanding of the dynamics of the real world
system of interest.
2.

The concept of "stress" when operationalized as a
systemic demand and represented by the number of
public school students requiring system resources
(professional staff) provides an important
foundation for construction and development of
simulation models.

3.

The supply-demand function is a viable means of
representing inter-component interaction within
the overall organizational process.

That is, all

sub-systems of the organization are conceptualized
as "open systems" with identifiable
As such, the sub-systems
sector)

"boundaries."

(student sector,

staff

compete for organizational resources

(staff services, money, materials)
inputs to the sector.

as required

There appear to be at

least two sources of stress or demand.

As used

124

in this study, demand was a variable which
originated from a source external to the system,
that is, student population levels are a function
of external parameters.

It seems reasonable to

assume that stress in the form of interaction
demands could just as reasonably originate from
within the system,
Equilibrium,

from internal sources.

then could be operationalized as a

function of the totality of stress interactions
over time.

In this respect,

the supply-demand

function is useful as a way of depicting the
dynamics of "boundary exchange" either internally,
between components, or externally as between the
system and ancillary systems or between the
system and a supra-system.

Thus,

the demand for

trained professionals appears to be a function of
several intra-component variables such as attrition,
the inactive pool, and the deployment of staff
resources.

The model further suggests that the

demand for trained staff transcends variables
peculiar to the professional staff component and
is in fact traceable to the levels of students
requiring services and to the number of births.
4.

The inclusion of time as a basic parameter of the
simulation model in conjunction with the previously
mentioned supply-demand relationship permits

125

accurate prediction of professional staff needs at
least five years in advance of need.

Such

predictions provide sufficient lead-time to be
used as a guide for institutional production.
The net replacement estimate

(6.5%) or about

5.000 teachers per year in comparison with current
production rates

(estimated at approximately

17.000 annually inflated by net in/out migration
of approximately 4,500 entering teachers per year)
results in an estimated over-production of about
16.000 teachers per year.
The implication for higher education may be a
review of goal primacy and serious consideration
of expanded services to currently employed pro­
fessionals as opposed to continued production of
new professionals.
5.

The simulation model provides a viable foundation
for at least one component of a management infor­
mation system.

Such systems are presently under

pilot study in several states as a result of
recent contracts awarded by the United States
Office of Education.

Suggestions for Future Research
The simulation vehicle developed in this study
represents only two components of the public school
system in Michigan and is founded on the assumption that

126

the number of clients to be served
a primary drive for the system.

(students)

represents

However, within these

limitations there are virtually an unlimited number of
possible directions for future research.

A limited

number of suggestions are provided and incorporate a
suggested order of priority.
1.

The present study could not complete the pro­
fessional staff sector because of a lack of data
for important variables,
available staff.

the inactive pool and

Completion of this component of

the model and testing of all endogenous variables
by Thiel's U statistic or a more appropriate
congruence measure is a first order need.
2.

The present study did not systematically explore
all possible parameter magnitudes within specified
limits.

Thus, a different combination of parameter

values might provide more accurate predictions.
3.

The model should be expanded to provide for
inclusion of other system components such as the
physical facilities or financial resources
sectors.

These have been included in the schematic

of the system

(see Appendix B) but could not be

accommodated by the present study.

127

4.

Experiments should be designed to test the present
means of parameter estimation against results that
could be obtained if the parameters were repre­
sented by functions which could more appropriately
describe the effects of system parameters over
time.

5.

Exogenous variables such as Birth(t)

ought to be

represented stochastically to examine the
functional limits of the system under various
hypothesized stress forces.

How long,

for

example, does it require for institutional pro­
duction to recover from or respond to varying
rates of birth demand?

Or, what rate of increase

of births over time is required to exceed the
recovery capability of both the inactive pool,
InPool (t), and institutional production,
6.

InProd(t)?

Given that the model is both expanded and tested
for functional limitations
preferential condition)

(not a mandatory but a

experiments may be designed

to test the effects of alternative policies on the
system.

Thus, one might explore the effects of

different staffing patterns as an internal demand
for professional staff resources.

Or, one might

examine the effect of new certification rules
which would restrict or increase the supply of
professional staff.

Finally, one might be

128

motivated to study the effect of policies which
would limit the production rates of trained staff
by institutions of higher education.
7.

Finally,

it is possible to envision a time in the

near future when one simulation model will be
joined with others to facilitate representation
of systems of systems whose complexity and
magnitude may approach that of the real world.
One can anticipate that understanding may be
sacrificed for greatly enhanced prediction.

REFERENCES

REFERENCES

Abt Associates, Inc.
Report of a Survey of the State of
the Art:
Social, Political, and Economic Models
and Simulations. Cam b r i d g e , M a s s . : Abt Associates, 1965.
Alcorn,

Bruce L.
"The Concept of Total Systems In Edu­
cation."
Edited by Enoch Haga.
In Automated
Educational Systems. Elmhurst, 1 1 1 . : The
Business Press, 1967-

Andrew, Gwen.
"An Analytic System Model For Organization
Theory."
Academy of Management Journal (September,
1965).
Beck,

Isabel H . , and Munroe, Bruce.
"Some Dimensions of
Simulation."
Educational Tech n o l o g y , LX, No. 10
(October, 1969) •

Benchoff, Dennis L.
"A Simulation Approach to Military
Vehicle Design."
Unpublished M.S. dissertation,
Michigan State University, 1969.
Bennis, Warren G.
"The Coming Death of Bureaucracy."
In Systems, Organizations, Analysis, M a n a g e m e n t :
A Book of Readings. Edited by David I. Cleland
and William R. King.
New York:
McGraw Hill Book
Co., 1969.
Bertalanffy, Ludwig Von.
General System Theory:
Foun­
dations, Development, Applications. New York:
George Braziller, 1968.
Blalock,

Hubert M . , Jr.
Theory Construction:
From Verbal
to Mathematical Formulations. New Jersey:
Prentice-Hall, Inc., 1969.

Bordman,

Robert.
"The Theory and Practice of Educational
Simulation."
Educational Research, London (June,
1969) .

129

130

Boulding, Kenneth E.
"General Systems Theory— The
Skeleton of Science."
Management Science (April,
1956.
Bunge, Mario.
Scientific Research II:
The Search For
T r u t h . New York:
Springer-Verlag I n c . , 1967.
Campbell, Donald T.
"Temporal Changes in Treatment— Effect
Correlations:
A Quasi-Experimental Model for
Institutional Records and Longitudinal Studies."
(Proceedings), 1970 Invitational Conference on
Testing Problems'll P r i nceton, N . J . : Educational
Testing Service.
Carzo,

Rocco, Jr., and Yanouzas, John N.
Formal Organi­
zation:
A Systems A p p r o a c h . Homewood, 1 1 1 . :
The Dorsey Press, 1967.

Churchman, C. West, and Ratoosh, P.
M e a s u rement:
Definitions and Theor i e s . New York:
John Wiley
and Sons, Inc., 1959.
Clarkson, G. P. E.
Portfolio Selection:
A Simulation of
Trust Investment. Englewood Cliffs, N.J.:
Prentice-Hall, 1962.
Cogswell, John F.
"Systems Analysis and Computer Simu­
lation in the Implementation of Media."
Audio­
visual Instruction (May, 1965), 384-86.
Cohen, K. J . , and Cajert, R. W.
"Computer Models in
Dynamic Economics."
Quarterly Journal of Economics,
L X X X V , No. 1 (1961), 112-27.
Cooper, George R . , and McGillen, Clare D.
Methods of
Signal and System A n a l y s i s . New York:
Holt,
Rinehart, and Winston, 1967.
Costa, Christ Henry.
"Prediction of Teacher Turnover
Employing Time-Series Analysis."
Unpublished Ph.D.
dissertation, University of Iowa, May, 1970.
Cruickshank, Donald R.
"The Use of Simulation in Teacher
Education:
A Developing Phenomena."
Journal of
Teacher Education, XX, No. 1 (Spring, 1969).
Cunningham, Laverne, L.
"Simulation and the Preparation of
Education Administrators."
Paper read at the
University Council on Educational Administration
Conference, University of Michigan, October, 1966.

131

Cyert, Richard M . , Feigenbaum, Edward A., and March,
James G.
"Models in a Behavioral Theory of the
Firm."
Behavioral S c i e n c e , IV (1959), 81-95.
De Leeuw Frank, and Gramlich, Edward.
"Staff Economic
Study:
The Federal Reserve— MIT Econometric
Model."
Federal Reserve Bulletin, LIV, No. 1
(1968).
Dutton, John M . , and Starbuck, William H.
Computer Simu­
lation of Human Behav i o r . New York:
John Wiley &
S o n s , I n c ., 1971.
Elton, Martin, and Rosenhead, Jonathan.
"Micro-Simulation
of Markets."
Operational Research Quarterly,
XXII, No. 2 (June, 1 9 ? 1 ) , 117-44.
Entwisle, Doris R . , and Huggins, W. H.
"Simulated
Environments in Higher Education."
School Review
(1967), 378-91.
Entzioni, Amitai.
Modern Organizations.
Prentice-Hall, Inc., 1964.

New Jersey:

Farley, John U . , and Hinich, Melvin G.
"Detecting 'Small'
Mean Shifts in Time Series," XVII, No. 3 (November,
1970), 189-99.
Fishman, George S., and Kiviat, Philip J.
"The Statistics
of Discrete-Event Simulation."
Sci Simulation,
X, No. 4 (1968), 185-95.
Freidman, Monroe Peter.
"Using Simulation Techniques to
Predict the Behavioral Effects of New Laws:
The
Case of Truth-In-Lending Legislation and the
Consumer."
Journal of Applied Psychology, LIV,
No. 4 (August, 1970), 297-301.
Gregg, Lee W . , and Simon, Herbert A.
"Process Models and
Stochastic Theories of Simple Concept Formations."
Journal of Mathematical Psychology, IV (1967),
246-76.
Griffiths, Daniel E.
Administrative T h e o r y .
Appleton-Century-Crofts, 1959.

New York:

_________ . Behavioral Science and Educational Administration.
6 3rd Yearbook of the National Society for the
Study of Education.
Chicago:
The University of
Chicago Press, 1964.

132

Guetzkow, H . , Ed.
Simulation in International Relations;
Developments for Research and T e a c h i n g . Englewood
Cliffs, N.J.:
Prentice-Hall, 1963.
Gullahorn, John T., and Gullahorn, Jeanne E.
"Computer
Simulations of Role Conflict Resolutions."
In
Dutton and Starbuck, 1971.
Haga, Enoch, ed.
Automated Educational Syst e m s .
111.:
The Business Press, 1967.

Elmhurst,

Hallworth, Herbert J.
"Computer Simulation of Cognitive
Processes."
Educational T e chnology, LX, No. 10
(October, 1969), 60-63.
Hays, William H.
Statistics for Psychologists.
Holt, Rinehart and Winston, 196 3.

New York:

Heald, James E . , and Moore, Samuel A. II.
The Teacher and
Administrative Relationships in School S y s t e m s .
New York:
The MacMillen Company, 1968.
Heinkel, Otto A.
"Evaluation of Simulation as a Teaching
Device."
The Journal of Experimental Education,
XXXVIII, No. 3 (Spring, 1970), 32-36.
Hillier, Frederik, S., and Lieberman, Gerald J.
Intro­
duction to Operations Resea r c h . San F r a n c i s c o :
H o lden-Day, I n c ., 1967 .
Holland, Edward P . , and Gillespie, Robert W.
Experiments
on a Simulated Underdeveloped Economy; Development
Plans and Balance-of-Payments P o l icies. Cambridge,
Mass.:
The M.I.T. Press, 1963.
Hopkins,

David S. P.
"On the Use of Large-Scale Planning
Models for University."
Review of Educational
R e s earch, XLI, No. 5 (December, 1971), 467-78.

Johnson,

Richard A., Kast, Fremont E., and Rosenzweig,
James E.
The Theory and Management of S y s t e m s .
New York:
McGraw-Hill Book Co., 2nd e d . , 1967.

Katzenmeyer, William G.
Seminar on Management Information
Systems:
The State of the Art.
Duke University,
1969, p. 191.
Kelly, William F.
Management Through Systems and Pro­
cedures:
The Total Systems C o n c e p t . New York:
Wiley Interscience, 1969.

133

Kircher, Paul.
"Fundamentals of Measurement."
Management (October, 1955), 5-8.

Advanced

Koenig, H. E . , Kenney, M. G . , and Zemach, R.
A Systems
Model for Management, Planning, and Resource
Allocation m Institutions of Higher E d ucation.
Project C-518, National Science Foundation,
September 30, 1968.
Kuo, Fakun, ed.
System Analysis by Digital Compu t e r .
New York:
Wiley, 1966.
(Princeton Summer
Conference on Computer Science.)
Longhary, John W . , Friesen, Deloss, and Hurst, Robert.
"Autocoun:
A Computer-Based Automated Counseling
Simulations System."
Personnel and Guidance
Journal (September, 1966), 6-15.
McMillan, Claude and Gonzolez, Richard F.
Systems Analysis
A Computer Approach to Decision M o d e l s . Homewood,
1 1 1 .:
Richard D. Irwin, I n c ., 1965.
McNamara, James F.
"Mathematical Programming Models in
Educational Planning."
Review of Educational
Resea r c h , XLI, No. 5 (December, 1971), 419-46.
March, James G . , and Simon, Herbert A.
Organizations.
New York:
John Wiley and Sons, Inc., 1958.
Markowitz, Harry M . , Houser, Bernard, and Karr, Herbert W.
Simscript:
A Simulation Programming L a n guage.
Englewood Cliffs, N.J.:
Prentice-Hall, I n c . , 1963.
Mauch, James.
"A Systems Analysis Approach to Education."
In Phi Delta Kappan, XLIII, No. 4 (January, 1962),
158-62.
Michigan Education Association.
Actual and Projected Pupil
Population Public, Non-Public and Total Michigan
1961-62 to 1978 - 7 9 , 1971.
Michigan M a n u a l . Compiled and published by the Department
of Administration, Governor's Office, State of
Michigan, 1969-70.
National Association of Insurance Commissioners.
The
Commissioners Standard Mortality Table (1956).
Proceedings of the annual meeting of the National
Association of Insurance Commissioners, New
Orleans, La., I, pp. 181-294.

134

National Education Association.
Teacher Supply and Demand
in Public Schools, 1970.
Research Division, NEA,
1970.
Naylor, Thomas H . , Balintfy, Joseph L., Burdick, Donald S.,
and Chu, Kong.
Computer Simulation T echniques.
New York:
John Wiley and Sons, Inc., 1968.
_________, and Finger, J. M.
"Verification of Simulation
Models."
Management Science, XIV, No. 2 (1967),
92-101.
Parsons, Talcott.
The Social System.
Press, 1951.

New York:

The Free

Pfeiffer, John.
New Look at Education:
Systems Analysis
in Our Schools and C o l leges. New York:
Odyssey
Press, 1968.
Phiffner, John M . , and Sherwood, Frank P.
Administrative
Organization.
Englewood Cliffs, N.J.:
PrenticeH a l l , Inc., 1970.
Pool,

Rabow,

Ithiel de, Abelson, Robert P., and Popkin, Samuel L.
Candidates, Issues and Strategies. Cambridge,
Mass.:
The MIT Press, 1964.
Gerald.
The Era of the System:
How the Systems
Approach Can Help Solve Society's P r o b l e m s .
New York:
Philosophical Library, 196$.

Rao, Ambar G . , and Shapiro, Arthur.
"Adoptive Smoothing
Using Evolutionary Spectra."
Management Scie n c e ,
XVII, No. 3 (November, 1970), 208-18.
Rice, Arthur.
"Looking Forward."
Nation's Scho o l s ,
L X X I I I , No. 10 (June, 1964).
_________. "Simulation Is Big Word in Administrative
Training."
Nation's Schools (June, 1964), 10.
Sackman,

H.
Computers, System Science and Evolving
Society. New York:
John Wiley and Sons, 1967.

Salzman, Lawrence.
Computerized Economic A n a l y s i s .
York:
McGraw-Hill Book Company, 196 8.
Schechter, Mordechai.
for Research."
73-88.

New

"On the Use of Computer Simulation
Simulation and Games (March, 1971),

135

Schmidt, J. W. , and Taylor, R. E.
Simulation and Analysis
of Industrial Systems. Homewood, 111. : Richard D.
Irwin, Inc., 1970.
Schoderbek, Peter P.
Management Systems.
Wiley and Sons, Inc., 1967.

New York:

John

Scott, Andrew M . , Lucas, William A., and Lucas, Trudi M.
Simulation and National Development. New York:
John Wiley & Sons, Inc., 1966.
Smith, Karl U . , and Sussman, Harvey M.
"Delayed Feedback
in Steering During Learning and Transfer of
Learning."
Journal of Applied Psychology, LIV,
No. 4 (1970), 334-42.
Smith,

Robert D.
"Heuristic Simulation of Psychological
Decision Processes."
Journal of Applied P s ychology,
L I I , No. 4 (1968), 325-30.

State of Michigan, Department of Education.
"Supply and
Demand for Teachers in Michigan Until 1980."
Unpublished department report, 1971.
Sterling, Theodore, and Pollack, Seymour V.
Introduction
to Statistical Data Processing. New Jersey:
Prentice Hall, Inc., 1968.
Sybouts, Ward.
"Simulating Leadership in Vocational
Education."
NASSP Bulletin (February, 1968),
114-19.
Tocher,

K. D.
The Art of Simulation. London:
Universities Press, Ltd., 1963.

The English

Tsao, C. S., and Day, R. H.
"A Process Analysis Model of
the U.S. Steel Industry."
Management Scie n c e ,
XVII, No. 10 (1971) B :588-608.
Twelker,

Paul A.
"Designing Simulation Systems."
cational Technology, LX, No. 10 (October,
64-70.

Edu­
1969),

U.S. Department of Labor.
"Manpower Demand and Supply in
Professional Occupations."
A reprint from the
1970 Manpower Report of the President.
Washington,
D.C.:
Government Printing Office, 1970.

136

Van Dusen, George Merrill.
"Applications of a Computer
Simulation Model to Logistical Decisions in a
University."
Unpublished Ph.D. dissertation,
Michigan State University, 1969.
Walker,

Helen M . , and Lev, Joseph.
Statistical Inference.
New York:
Henry Holt and Co., 1953.

Websters New Collegiate Dictionary. 2nd ed.
M a s s . : G & C Merriam C o . , 1951.
Werner,

Springfield,

Roland, and Werner, Joan T.
Bibliography of
Simulations:
Social Systems and E d ucation.
Contract #OEC-l-7-071027-4273, Western Behavioral
Science Institute, 1969.

Wynn, Richard.
"Simulation:
Terrible Reality in the
Preparation of School Administrators."
Phi Delta
Kappan (December, 1964), 170-73.
Zymelman, Manuel.
"A Stabilization Policy for the Cotton
Textile Cycle."
Management Science, XI (1965),
572-80.

APPENDICES

APPENDIX A

THE MSU UNIVERSITY MODEL

The Koenig Model

|

Capital
Resources

(MSU-SIM)

|

Adm.
Control

Personnel
Sector

Phys.
Facilities
Sector

Non-Acad.
Production
Sector

Academic
Production
Sector

Student
Sector

Source:

Koenig,

et a l ., 1968, p.

137

21.

APPENDIX B

MICHIGAN PUBLIC SCHOOL SYSTEM
SIMULATION MODEL SCHEMATIC

Modified Version of the Koenig Model
Michigan Public School System Schematic

VBonds(t)

VMills(t)

STAID(t)

Financial
Resources
Sector
FACLOS(t)

S ’POP(t)

Student
Population
Sector

Physical
Facilities
Sector

SPOP (t)

GRADS(t)
InPROD(t)
AVSTAFF(t )
NMIGR(t)

Reduced Area
of Study
InPOOL(t)

138

TPOP(t)

APPENDIX C

MICHIGAN BIRTH RATES 1940-1971

TABLE C-l.— Michigan Birth Rates

(1940-1971).

Year

Births

Year

Births

1940

99,106

1956

206,068

1941

107,498

1957

208,488

1942

124,068

1958

202,690

1943

125,441

1959

198,301

1944

113,586

1960

195,056

1945

111,557

1961

192,825

1946

138,572

1962

182,790

1947

160,275

1963

178,871

1948

153,726

1964

175,103

1949

156,469

1965

166,464

1950

160,055

1966

165,794

1951

172,451

1967

162,756

1952

177,835

1968

159,058

1953

182,968

1969

163,811

1954

192,104

1970

170,546

1955

196,294

1971

161,163

Source:

Department of Public Health, Michigan.

139

140

C-2.— Age-Specific Death Rate Per 1,000 Individuals.

Age

Rate/1,000

Age

Rate/1,000

0

7.08

10

1.21

1

1.76

11

1.23

2

1.52

12

1.26

3

1.46

13

1. 32

4

1.40

14

1. 39

5

1. 35

15

1.46

6

1. 30

16

1.54

7

1.26

17

1.62

8

1.23

18

1.69

9

1.21

19

1.74

Source:

Commissioners Standard Mortality T a b l e ,

APPENDIX D

EDUSIM— COMPUTER PROGRAM

EDUSIM

100=
110=
120=
130=
140=
150=
160=
170=
180=
190=
200=
210=
220=
230=
240=
250=
260=
270=
280=
290=
300=
310=
320=
330=
340=
350=
360=
370=
380=

PR0GRAM EDUSIM(INPUT,0UTPUT)
DIMENSI0N TBL(21,50),DTH(20),SCHL(50)
DIMENSI0N TP0P(50),NSTAFF(50),ELMSTF(50),SECSTF(50)
DATA DTH/7.08,1.76,1.52,1.46,1.40,1.35,1.30,1.26,1.23,1.21,
+1.21,1.23,1.26,1.32,1.39,1.46,1.54,1.62,1.69,1.74/
READ 100,IBASE,N
100 F0RMAT(14,12)
READ 101,(TBL(1,I),I=1,N)
101 F0RMAT(10F6.0)
C
C PARAMETER INITIALIZATI0N PHASE
C
Pl=.14
P2=.13
P3=.15
P4=.036
P5=.065
P6=.485
P7=.515
C
C BUILD THE MATRIX 0F SURVIV0R P0PULATI0NS
C
D0 1 J=1,N
D0 1 K=2,21
IND=K-1
TBL(K,J)=TBL(IND,J)- ( (TBL(IND,J)/1000)*DTH(IND))
1 C0NTINUE
C
C GENERATE SIMULATED SP0P(T)=SCHL(J) AND TP0P F0R 1957 T0 1975

390=
400=
410=
420=
430=
440=
450=
460=
470=
480=
485=
490=
500=
510=
520=
530=
540=
550=

C
IK=N-13
D0 2 J = 1 ,IK
SCHL(J)=)
II=J+12
D0 3 K=J,II
I=20-K
3 SCHL(J )=SCHL(J )+TBL(I ,K)
SCHL(J)=SCHL(J)+ (P1*SCHL(J)) - (P2*SCHL(J))-(P3*SCHL(J))
TP0P(J)=P4*SCHL(J)
AVSTF(t)=INPROD(t)+INPOOL(t)-ATTR(t)+NMIGR(t)+TP0P(t)
NSTAFF(J)=P5*TP0P(J)
ELMSTF(J)=P6*NSTAFF(J)
SECSTF(J)=P7*NSTAFF(J)
2 C0NTINUE
IBASE =IBASE+17
D0 4 J = 1 ,IK
PRINT 102,IBASE,SCHL(J),TP0P(J),NSTAFF(J),ELMSTF(J),SECSTF(J)

560=
570=
580=
590=

102 F0RMAT(*0*,14,F13.2,4F10.2)
4 IBASE=IBASE+1
CALL EXIT
END

141

APPENDIX E

CERTIFICATE DISTRIBUTION FOR 1968

TABLE E - l .— Certificate Distribution for Reported 1968
Professional Staff in Michigan.

Certificate Type

Number

Percent

Elementary Provisional

15,657

18.45

Elementary Permanent

16,706

19.71

Secondary Provisional

17,279

20. 39

Secondary Permanent

17,602

20.77

Life

10,304

12.16

4,702

5.55

State Limited

176

.21

County Limited

166

.20

Provisional or Permanent
Not Required

2,110

2.49

Certificate Not Required

57

.07

84,759

100.00

Full Year Permit

Total

Source:

MSDE Personnel Report,

142

1968.