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This is to certify that the

thesis entitled

USING ANIMATION TO IMPROVE THE COMMUNICATIVE ASPECTS
OF CARTOGRAMS

presented by

Jennifer Alea Ware

has been accepted towards fulfillment
of the requirements for

M. A. degree in Geography

>214 (‘69 )7/2 O {Ta-c‘yk

Maer professor

Date /O/=’7-///7 3

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

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DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1m COW“

USING ANIMATION TO IMPROVE THE COMMUNICATIVE ASPECT
OF CARTOGRAMS

BY

Jennifer Alea Ware

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF ARTS
Department of Geography

1998

ABSTRACT

USING ANIMATION TO IMPROVE THE COMMUNICATIVE ASPECT
OF CARTOGRAMS

BY

Jennifer Alea Ware

The message of a cartogram is often lost if the reader
is unfamiliar with the underlying base map. The question
asked in this research is whether allowing the reader to
view and control the cartographic transformation between
geographic space and cartogram space aids in conveying
information.

In this study, cartograms of a familiar region and an
unfamiliar region. were presented. in three formats:
traditional (static), automatic animation, and. ‘user-
controlled animation. Subjects were asked questions about
the transformations occurring in each cartogram.

The results showed that familiarity was most important
when using cartograms in time still format. The animated
formats produced higher mean scores than the still format,
and there was a significant interaction effect between
familiarity and format. The greatest improvement was
between the mean scores for the unfamiliar region’s still

and animation formats.

Copyright by
JENNIFER ALEA WARE
1998

To my husband Rob Blanchard,
for his unceasing love and support.

iv

ACKNOWLEDGEMENTS

First and foremost I would like to acknowledge the
efforts of my advisor, Dr. Judy M. Olson. Her extensive
cartographic knowledge base as well as her editing skills
greatly improved this paper. I would also like to thank
Dr. Jack Williams and Dr. Assefa Mehretu for serving as my
committee members.

I thank my parents, John and Jacqueline Ware, for
instilling in me the importance of education and for their

support and encouragement in all my endeavors.

TABLE OF CONTENTS

List of Tables
List of Figures

Chapter I

Introduction
Introduction
Types of cartograms
Animation and cartograms
Overview of the research

Chapter 2

Literature review
Brief history of cartograms
Shape recognition . .
Cartograms and communication
Animation and maps .
Problem statement and hypotheses

Chapter 3

Methods
Overall design and expected results
Selecting the regions to map
Selecting the attributes to map
Constructing the cartograms
Creating the cartogram test
Selecting the questions to ask
Scoring the test .
Pretest and posttest questionnaires
Testing procedure
Statistical methods

Chapter 4

Results
Description of subjects
Prior knowledge of cartograms
Familiarity with each region
Practice materials
Processing the test scores
Main results
Posttest questionnaire results

vi

viii

.ix

\OCDUJH

.10

10
. ll
.12
.17
.18

.20

. 20
.22
26
31

. 35
.46
.48
50
50
52

.53

53
. 53
.55
.56
.57
.62
.67

Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . .74
Discussion

The subjects and their previous knowledge . . . . . 74
Expected results vs. statistical results . . . . . .77
Subjects’ posttest questionnaire responses . . . . .79
Weaknesses of the research . . . . . . . . . . . . .81
Broader implications . . . . . . . . . . . . . . . .84
Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . .86

Summary and conclusions

Appendices
Appendix A - Avenue code for creating cartograms
in ArcView . . . . . . . . . . . . . . 90
Appendix B - Text of cartogram test . . . . . . . . 95
Appendix C - Pretest and posttest questionnaires . 104
Appendix D — Sample mental maps . . . . . . . . . .108
Bibliography . . . . . . . . . . . . . . . . . . . . . .114

vii

LI ST OF TABLES

United States data.

China data.

Rank correlation of variables.

Raw results of cartogram test.

Rank and percentage differences for areas A and B.
Adjusted results of cartogram test.

Repeated measures ANOVA results.

Numerical results of posttest.

Average times.

viii

10.

ll.

12.

13.

14.

15.

16.

17.

18.

19.

20.

LIST OF FIGURES

Example of a linear cartogram.
Example of a noncontiguous cartogram.
Example of a contiguous cartogram.
Dent’s model.
Test cartograms.
Geographic map of the United States.
Geographic map of China.
Cartogram of population, United States.
Cartogram of cattle, United States.
Cartogram of population, China.
Cartogram of cattle, China.
Still format.
Play format (zero iterations).
Play format (final iteration).
Slider format (zero iterations).
Slider format (final iteration).
Mean scores.
Sketch map of the United States (1).
Sketch map of the United States (2).

Sketch map of the United States (3).

ix

21. Sketch map of China (1).
22. Sketch map of China (2).

23. Sketch map of China (3).

 

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Chapter 1

I NTRODUCT I ON

Introduction

 

Computer technology has opened the door to new
possibilities in the realm of geography, especially in the
cartographic field. Manual methods of mapmaking are
effectively obsolete, given the automation capabilities of
the computer. Olson (1997) writes that “computer usage in
mapping has become the norm, it is considerably easier than
mapping with manual methods, and it is at least of
comparable quality.” The question remains, however, have
any real advances been made beyond the shortening of time
needed to make a map?

In the early 19903, researchers felt that the computer
continued to be used to replicate manually made maps with
all their inherent limitations (Peterson 1993). Karl (1992)
stated, “the use of computers in cartography offers new
forms of information display. However, because we are still
fixated on the traditional map, we overlook this potential
and use computers predominately to mimic manual methods.”

Today, in the late 19908, the proliferation of the
World Wide Web and the availability of multimedia facilities
have created new territory in cartography. The computer is

used to make maps that are designed to be seen and used

(g

f :

 

primarily on the computer screen. Monmonier (1985), in
writing about the technological transition in cartography,
said that “maps should be viewed as software rather than
material objects.” To some extent, this belief has been
accepted.

Though maps are now being made specifically for use on
computers, exploration of the computer’s ability to add new
dimensions, such as animation, to maps has been slow.
Campbell and Egbert (1990) reviewed the evolution of
animated cartography and discussed its stunted progress. A
few notable historical examples of animated maps include
Tobler’s (1970) growth of a city, Moellering's (1973)
traffic accidents, and Weber and Buttenfield’s (1993)
surface temperatures in the U.S. More animated maps are
being produced now than in the past, but they are still not
commonly seen and used. Research needs to be done with
different map types to determine their possibilities for
cartographic .animation. (Karl 1992). Little research. has
been done with cartograms.

The construction (n5 cartograms through. computer
algorithms has received some attention (Tobler 1973,
Dougenik et a1. 1985, Gusein-Zade and Tikunov 1993, Jackel
1997a), but once completed, the final product is no
different from a manually constructed cartogram. Jackel

(1997b) has experimented with animating cartograms, but

 

 

 

 

 

 

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adding animation to cartograms is an exception rather than
the rule. Adding animation moves beyond using the computer
to create a traditional cartogram product. The purpose of
this research is to determine if adding animation to
cartograms is an appropriate and advantageous use of the

computer’s capabilities.

Types of cartograms

 

To understand the different types of cartograms, one
must first have an understanding of the general form. A
cartogram is a map on which distances or areas are
proportionate to some variable of interest other than
geographic distances or areas. A transformation occurs
between geographic space and cartogram space. “In these
abstractions from reality, ordinary geographical area,
orientation, and contiguity relationships are lost. The
reader is forced to look at a twisted and distorted image
that only vaguely resembles the geographic map” (Dent 1993).
As a result, cartograms are often difficult to interpret.
Visual cues that may' help the reader include labels on

places or enumeration units and an inset of the geographic

base map.
Cartograms can take several different forms . At the
most basic level is the linear vs. areal distinction. On

linear cartograms, distances represent something other than

earth distance. The most commonly known examples of linear
cartograms are subway maps and some road maps (Kadmon 1982).
Geographic accuracy is sacrificed in favor of an abstract
though topologically correct rendition (Figure 1).

On an areal cartogram, areas represent something other
than earth area. Areal cartograms are more prevalent, and
they can be either contiguous or noncontiguous.
Noncontiguous cartograms retain the shapes of the individual
enumeration. units, changing only" their size (Figure 2).
They are much easier to construct, requiring only linear
scale changes, but they' do not preserve boundary
relationships (Olson 1976). Contiguous cartograms maintain
boundary relationships, but the shapes of individual
enumeration units are distorted (Figure 3). 'The ‘major
difficulty in using contiguous cartograms is that the
distortion may make it difficult for the reader to make the
connection back to geographic space, even with the addition
of visual cues (Dent 1993).

Cartograms are used most effectively when they differ
greatly from the underlying geographic map. Their main
advantage: is that they' abrogate the 'visual dominance «of
larger enumeration units (Olson 1976). They allow the data,
rather than land area, to determine the importance of each
enumeration unit. However, this neans tflmn: their success

depends on readers’ familiarity with the geographic map.

 

 

 

 

 

 

Figure 1. Example of a linear cartogram"
Based on a map of the Washington D.C. Metrorail system
created by the Washington Metropolitan Area Transit
Authority. Simplified by the author.

NUMBER OF PERSONS 66 YEARS OF AGE AND OVER: 1970

C] 100.000 Persons
86 and over

 

Source: U.S. Bureau at the Census

Figure 2. Example of a noncontiguous cartogram.
Created by Judy M. Olson.

 

On

 

 

 

 

Figure 3. Example of a contiguous cartogram»
Map showing the number of births in New England.
Created by the author.

The fact that Maine is much smaller than Massachusetts
on this cartogram of births can have little impact on a
reader who is not aware of the states’ actual geographic
size.

The term “cartogram” in the remainder of this thesis
will refer to the contiguous value—by-area cartogram, where

the enumeration units retain their topological relationships

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and the area of the enumeration unit represents the value of

the attribute being mapped.

Animation and cartograms

 

Animation is generally used in cartography to represent
change over time. For example, a series of maps showing
population at discrete points in time can be rapidly
displayed in sequence to portray the illusion of movement of
the population. Migratory patterns of distribution can be
detected. Peterson (1993) states that although
“cartographic animation is predominately associated with the
representation. of change over time...[it is] useful for
other purposes as well, such as depicting the deformation
caused by a map projection.” A cartogram by its nature
undergoes such deformation, and animation can show the
change from geographic map to cartogram and vice versa.

The deformation of a geographic map into a cartogram
can be called a metamorphosis. Gersmehl (1990) describes
metamorphosis as “defining an object with a series of points
and placing those points in their appropriate starting and
ending positions...The computer’s job is to calculate the
position for each ‘in—between’ frame of an animation.” This
process of creating in-between frames is called “morphing.”
Through animation, the geographic map will appear to morph

into the cartogram.

Overview of the research

 

This research is primarily concerned with testing the
communicative aspects of contiguous cartograms that may be
affected by adding animation. It is not concerned with
developing a new way to construct cartograms, since
automation of that process has already been developed.

Griffin (1983) states that “the full communicative
impact of a cartogram will be achieved only if the users are
able to relate cartogram space to geographic space.” This
process is especially difficult with contiguous cartograms.
Allowing the reader to view and control the transformation
between cartogram space and geographic space with the use of
animation may lead to greater comprehension of the
cartogram’s message. The general idea of this research is
that the addition of animation to a cartogram will improve
its communicative function, especially' with non-familiar
regions. If this hypothesis can be supported, it will mean
that cartograms may be used more often and with a wider

variety of regions.

Chapter 2

L I TERATURE REVI EW

Brief history of cartograms

 

It is difficult to determine when cartograms first came
into existence. Kadmon (1982) cites the Peutinger Map, a
ijh century copy of a Roman road map dating from the fourth
century, as one of the oldest known examples. Cartograms
came into general use in various European countries in the

late nineteenth century, as reported by Hunter and Young

(1968) . They are known by different names in different
countries: the French “anamorphose,” the German
“Kartogramm,” and the Russian “varivalent projection”

(Kadmon 1982, Tobler 1986).

In the 19308 Edwin Raisz was one of the first American
cartographers tx> make Luxa of cartograms. Raisz’s (1934)
rectangular cartograms of the United States were contiguous,
maintaining boundary relationships but not retaining shapes
of individual enumeration units. Text labels were required
to denote specific units; otherwise the reader would have no
way of determining which rectangle corresponded to which
state. Raisz’s focus was not on comparing the cartogram to
geographic space; he did not view the cartogram as a true
map but as a simple geometric design to visualize spatial

relationships in statistical data.

10

Until the 19508, cartograms were seen as a combination
of maps and graphs, showing both comparative proportion and
relative position of enumeration units. Several researchers
suggested that it might be possible to preserve the
approximate shape of individual units while maintaining
topology (Harris 1955, Tobler 1963), and rough
approximations had been attempted (Woytinsky and Woytinsky
1953). Briefly, topology is the configuration of nodes,
lines and connections, which means that.cx1.a topologically
correct area cartogram, an enumeration unit has all the same
neighbors that it has on the earth’s surface. The idea of
truly maintaining topology, however, produced a severe

challenge for maintaining recognizability of shapes.

Shape recognition

 

Since the sizes and possibly positions of enumeration
units in a contiguous cartogram are changed from geographic

reality, it is important that the shape of the unit remain

recognizable in order to facilitate communication. Olson
(1976) writes, “the success of the visual
representation...depend8, in fact, on the reader’s
recognition of the units shown.” Shape has been primarily

used as a descriptive device in geography (Boyce 1964).
Various approaches have been. taken towards 'understanding

two-dimensional shape recognition (Quinlan 1991).

11

Conflicting theories (Attneave 1954, Kennedy and Domander
1985) exist about whether the most useful aids in the
recognition of shapes are the points of maximum change or
the points of minimum change.

Cartographers giving attention to the matter have
concluded that the points of maximum change are most
important to shape recognition, at least on maps. In 1972,
Borden Dent studied the importance of shape, specifically in
relaticwi to cartogranl communicatitnL Dent’s experiments
revealed that map readers mentally' generalize shapes by
using “information points,” places on the outline where the
shape changes direction. He concluded, “those elements of
the original shapes that truly define it should be preserved
to give the map reader the visual cues necessary to identify
the new shape. In this way, mental transferal from
previously-learned shapes to the more unconventional ones of

the cartogram will be easier and more reliable” (Dent 1972).

Cartograms and communication

 

Cartograms have been used to map a wide variety of
topics, including population, economic variables, and
electoral vote distribution (Raisz 1934, Getis 1963, Dorling
1994). They can be seen in atlases, textbooks and magazine
articles. However, few researchers have assessed the

communicative success of the cartogram.

12

In 1975, Dent focused on the communicative aspects of
value—by-area cartograms. Subjects were asked to evaluate a
proportional circles map and a cartogram, each displaying
the same information, by using a semantic differential test.
Using polar opposite words or phrases (such as easy to read
vs. hard to read, innovative vs. conventional) in three
categories (general attitudes, appearance, and readability),
subjects marked on a continuum where they judged each map to
fall. The results were surprising. Though cartographers
feel, according to Dent, that the proportional circles map
is a conventional technique, subjects felt both it and the
cartogram were innovative and unusual. Subjects also felt
both maps communicated their messages effectively and
symbolized the information well, but the cartogram was rated
harder to read than the proportional circles map.

Dent’s (1975) model of cartogram communication between
cartographer and reader (Figure 4) lends itself to the goals
of this paper. He outlines six steps taken by the reader
and six corresponding steps taken by the cartographer. In
animating the cartogram, the problem of subjects’ not
adequately or correctly performing the mental
transformations necessary to cartogram interpretation is

eliminated through the modification of several steps.

13

Reader Tasks

Cartographer Tasks

 

 

Understand
map purpose.

Provide total map
organization to
suit purpose.

 

 

l

I

 

 

 

Recognize
statistical
units.

 

 

Provide shapes
with meaningful
cues from original
geographic shapes.

 

 

l

l

 

 

Use mental map
of mapped area.

Provide an inset
map of geographic
base to augment
mental map.

 

 

l

 

 

Make magnitude
estimations of
statistical areas.

Use straight line
segments for
areas and provide
a legend.

 

 

1

l

 

 

Compare mental
map of geographic
area and
cartogram.

 

Use other
cartographic
language elements
efficiently.

 

 

l

l

 

 

 

Respond to
cartogram message.

 

 

Be willing to
restructure map
to effect desired
response.

 

 

Figure 4.

Dent's model.

14

 

 

 

If

r

 

 

 

 

In step 3, the readers will not be required to have a
mental map of the area, since they will be able to view the
geographic area at the scale of the cartogram instead of
using an inset map at a different scale. Step 4 as an
explicit task has been eliminated in the research design;
the readers will not be required to make absolute magnitude
estimations of statistical areas. In step 5, the
cartographer will use animation instead of traditional
cartographic language elements to facilitate comparison
between the geographic area and the cartogram.

T.L.C. Griffin in 1983 “examine[d] the user’s ability
to achieve the intellectual transformation so essential to
cartogram use.” Griffin tested subjects’ ability to
recognize areal units on topological (contiguous, value-by-
area) cartograms. Subjects were shown a geographic map of
the electoral subdivisions of .Adelaide, Australia, or a
cartogram where the subdivisions had been spatially
transformed according to population values. For each round
of the experiment, one map, either the geographic map or the
cartogram, was designated the task display. The opposite
one was designated the target display. Certain units were
marked with letters on the task display, and subjects were
required to find the corresponding unit on the target

display. Griffin recorded both correctness and location of

15

the response. Location was measured angularly from the
centroid of each correct unit.

Although the error rate in responses was high at 23%,
the spatial pattern of the errors revealed that two map
transformation qualities were affecting the responses:
change in angular location of units and change in each
unit’s shape. The subjects were able to locate faster the
units on the cartogram when first shown the map than they
were able to locate units on the map when first shown the
cartogram.

It is not surprising that angular and shape changes
affected. speed, but the reason for the cartogram-to-map
difficulty is not easily explained. Griffin suggested the
subjects were not adequately compensating mentally for the
cartogram distortion. If this factor can be alleviated or
controlled, cartogram communication should improve.
Allowing the reader to view and control the transformation
between geographic space and cartogram space through the use
of animation will obviate the need for the reader to
mentally visualize the distortion transformation.

More recently, Rittschof et al. (1996) demonstrated
that familiarity with the geographic area depicted in a
cartogram is a vital part of the cartogram's ability to
communicate. Subjects were asked to reconstruct geographic

maps and cartograms of a familiar region and an unfamiliar

l6

region after being shown these maps for a brief period of
time. Short—term familiarity with a region, as defined by
viewing a geographic map immediately preceding a cartogram,
resulted 111 less accurate recreations tfluni long-term
familiarity. Rittschof et a1. concluded that the “true,
earth—centered scale” of a region, such as an inset map,
should be provided to prevent subjects’ mental maps from
becoming distorted by viewing the cartograms. Since the
geographic map will morph into the cartogram in this
research, subjects will be able to view the geographic map
as many times as necessary and in conjunction with the
cartogram. Long-term familiarity with the geographic area
is not expected to be a requirement due to the use of

animation.

Animation and maps

 

The first suggestions that animation might be useful
when combined with maps came from Thrower (1959). Examples
of animated maps are varied (Tobler 1970, Moellering 1973,
Weber and Buttenfield 1993). Progress has not been as
smooth as one might expect, hindered by factors such as
costs to produce, difficulty in distribution, and the
complexity of conditions involved in proper and effective
use of animation. Progress in animating maps is also

closely tied to development of the proper technology

17

 

 

S

 

(Campbell and Egbert 1990). There are still many issues to
explore in animated cartography. DiBiase et al. (1992)
suggested that animation could be used to complement
spatially abstract maps, such as cartograms.

In the more general literature, much experimentation
has been done to investigate how animation affects
comprehension and learning. 1%) clear case for or against
animation has emerged, possibly due to the wide variety of
conditions and topics for which animation is used (Park and
Hopkins 1993). However, some standardization of the
guidelines for using animation has occurred. One pertinent
guideline states that animation should be used “when the
instruction requires visualization, particularly’ with
spatially oriented information” (Milheim 1993). .A seminar
study with a physical geography animation supported this
conclusion; the only question on which subjects performed
significantly better was one that required visualization of
movement (Ware 1997). Maps by definition contain spatially
oriented information, and cartograms by their nature require

visualization of the transformation from geographic space.

Problem statement and hypotheses

 

Cartograms have traditionally been viewed as difficult
to interpret and as a result are rarely used. This research

is attempting to alleviate the difficulties caused by

18

readers’ inability to adequately perform mentally the
transformation between geographic space and cartogram space
by allowing the reader to view and even control the
transformation in the form of an animation. The problem is
to determine whether adding this animation to a cartogram
will improve its communicative function over the traditional
presentation of such. maps, and. whether the addition. of
animation is even more effective with a map of an unfamiliar
region.

Dent (1975) states that “it is only by recognizing the
discrepancy between [the cartogram] and geographic reality
that the reader is able to absorb the map message.” Griffin
(1983) also states that “the full communicative impact of a
cartogram will be achieved only if the users are able to
relate cartogram space to geographic space.” The hypothesis
of this research is that allowing the reader to view the
transformation of a cartogram through animation will improve
its communicative function, especially with non-familiar
regions. Cartograms may become more widely used if they can

communicate more effectively.

l9

Chapter 3

METHODS

Overall design and expected results

 

It will be useful to give an overall picture of the
design of the experiment and the expected results first.
Each set of choices in the experimental design will then be
discussed in turn.

To test the effects of animation on the communicative
aspects of cartograms, a set of twelve cartograms was
created (Figure 5). TWO regions were selected, a familiar
area and a lesser—known area. Two variables were chosen to
be mapped. Three formats were used to present the
cartograms: a still or non-animated layout, automatic
animation through the use of a “play” button, and manual
animation through the use of a slider bar. Three questions
were asked of each cartogram and the response and response
time were recorded for each question.

The familiar region was expected to have higher overall
mean scores than the unfamiliar region, especially on the
still format questions. For each region, the best
performance was expected on questions following the use of a
slider bar to present the cartograms because this format
gives the reader both the ability to view the transformation

and to control its speed and direction (forward or reverse).

20

Presentation Formats

 

 

 

 

 

 

 

 

 

Still Play Slider
Familiar
Region:
United Population Population Population
States
Cattle Cattle Cattle
Unfamiliar
Region:
China Population Populat1on. Population
Cattle Cattle Cattle
Figure 5. Test cartograms.

The lowest performance was expected on questions using

the still format to present the cartograms because this

Jflbrnat requires the reader to nentally perform the

tIEansformation and. gives no other 'visual aids or cues.

21

Overall, higher scores were expected on the animated
questions than the still questions.

The addition of animation to a cartogram of an
unfamiliar region was expected to have more of an effect on
cartogram communication than the addition of animation to a
cartogram of a familiar region.

Subjects were expected to feel they spent less time
answering the questions for animated cartograms than they
spent answering the questions for still cartograms. In
reality it is likely that the subjects would spend more time
answering the questions for animated cartograms because they

had the ability to play and replay the animation many times.

Selecting the regions to map

 

To appreciate the distortion occurring in a cartogram,
the reader must have some knowledge of the geographic base
map. If this knowledge is ingrained, that is, if the reader
has a strong mental image of the geographic map, then
conventional wisdom suggests that the only requirement is to
look directly at the cartogram. The reader should be able
to visualize the geographic map and mentally compare it with
the cartogram. This process may not be as automatic as
might be expected. It is possible to see an object and
recognize that some aspect has changed but be unable to

pinpoint the exact nature of the change. In the same

22

fashion, a reader might lock at a cartogram and recognize
that it looks different from a geographic map but be unable
to determine in what way it is different. In other words,
it is only a hypothesis and not a foregone conclusion that
familiarity with the geographic area makes reading a
cartogram easier.

If knowledge of the geographic space is not ingrained,
that is, if the reader does not have a strong mental image
of the geographic map, then additional visual cues are
required to facilitate comparison with the cartogram. The
most common visual cue is an inset of the geographic map.
The reader is required to perform eye movement between the
inset map and the cartogram, as well as process a mental
scale change if the inset map is different in size from the
cartogranu These additional tasks presumably' make
interpretation slower and possibly less correct when a
cartogram depicts an unfamiliar region. If the reader were
able to view the transformation between geographic space and
cartogram space, with both depictions at the same scale,
perhaps comprehension. would. be faster' and interpretation
more correct.

This research is taking place in the United States and
the majority of the subjects are likely to be long-term
residents of the U.S. As such, they have probably had

lengthy exposure to its geographic map and the shapes of

23

individual states. For this reason, the continental United
States was chosen as the "familiar" region (Figure 6).
Subjects were expected to have a strong mental map of the
United States. The term "states" will refer to states and
the District of Columbia.

The country of the People’s Republic of China,
hereafter referred to simply as “China,” is approximately
the same area as the United States, and it has a similar

administrative hierarchy. China's mutually exclusive set of

provinces, municipalities and autonomous regions, are
parallel to American states. The term “provinces” will
collectively apply to this set of divisions. While some

subjects may have a strong mental map of China as a whole,
they are unlikely to have a strong mental map of China's
individual provinces. China was chosen as likely being
“unfamiliar” to subjects (Figure 7).

The base map of China was obtained online from the
China Data Center at the University of Michigan (Liu, Xurong
and Lavely et al., 1996) in ArcInfo export format. The map
was downloaded and imported into ArcView, then converted to
a shapefile. The base map of the United States was obtained
online from the National Oceanic and Atmospheric
Administration (1996) in shapefile format. The map was

downloaded and brought into ArcView.

24

 

Figure 6. Geographic map of the united States.
Map shows the forty-eight continental states and the
District of Columbia.

Figure 7. Geographic map of China.
Map shows the thirty provinces, municipalities and
autonomous regions.

25

Selecting the attributes to map

 

Selecting attributes for cartogram representation
requires careful thought. The essence of the cartogram is
its distortion from the geographic map. If little or no
distortion occurs, the purpose of the cartogram is lost.
Analyzing the data prior to cartogram construction prevents
this unwanted result. A simple correlation analysis can be
performed between the rank orders of the land area
percentage of each enumeration unit and its attribute
percentage. Using the total amount of land area and the
total amount of the attribute, each enumeration unit is
assigned a percentage according to its proportion of the
total. If the rank orders correlate, then the attribute is
inappropriate, as the cartogram will look very similar to
the geographic map.

In this particular testing environment, an additional
criterion needed to be met. Two variables were used in the
testing program. The two variables were required to produce
a sample, albeit small, of different-looking cartograms;
therefore, the attribute percentages could not have rank
correlations with one other that were close to 1.00.

Population was the most obvious attribute to select,
since it does not generally correlate with land area.
Selecting a second attribute that met all the above criteria

was run: an easy task» Various possibilities were

26

 

considered, including per capita income, number of
illiterate persons, and acres of cropland” Eventually,
number of beef cattle was chosen. The data did not exactly
compare across the two countries because China recorded the
number of cattle slaughtered while the United States
recorded the number of beef cattle. This was accepted as a
close enough match for the purposes of this research, and
the attribute was given the common name "number of cattle."

The attribute data for the United States were obtained
online from the U.S. Census Bureau (1992) and the National
Agricultural Statistics Service (1992) (Table 1). The
attribute data for China were obtained online from the China
Data Center (Skinner et a1. 1997) and the Agricultural
Statistical Database of the People’s Republic of China
(Colby, Cook and Webb, 1998) (Table 2).

The Spearman’s rank order correlation test was
calculated on the ranked percentages of area, population,
and cattle. Not surprisingly, area and cattle were the most
highly correlated, but none of the variables were strongly
correlated (near 1.00) with each other in either region

(Table 3) .

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1. United States data.

Name Population Cattle

Alabama 4040587 771151
Arizona 3665228 292848
Arkansas 2350725 826306
California 29760021 862971
Colorado 3294394 900347
Connecticut 3287116 6878
Delaware 666168 2856
District of Columbia 606900 0
Florida 12937926 962527
Georgia 6478216 599899
Idaho 1006749 565016
Illinois 11430602 447201
Indiana 5544159 293836
Iowa 2776755 1065744
Kansas 2477574 1434017
Kentucky 3685296 1088532
Louisiana 4219973 441725
Maine 1227928 11412
Maryland 4781468 51676
Massachusetts 6016425 7347
Michigan 9295297 116106
Mississippi 2573216 588920
Missouri 5117073 1876845
Montana 799065 1506445
Nebraska 1578385 1857341
Nevada 1201833 265690
New Hampshire 1109252 3727
New Jersey 7730188 12280
New Mexico 1515069 631738
New York 17990455 72971
North Carolina 6628637 385428
North Dakota 638800 837716

 

28

 

Table 1 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Name Population Cattle

Ohio 10847115 272920
Oklahoma 3145585 1728273
Oregon 2842321 629625
Pennsylvania 11881643 157773
Rhode Island 1003464 967
South Carolina 3486703 222566
South Dakota 696004 1604838
Tennessee 4877185 988550
Texas 16986510 5186359
Utah 1722850 356971
Vermont 562758 11812
Virginia 6187358 674068
Washington 4866692 310554
West Virginia 1793477 197886
Wisconsin 4891769 195810
Wyoming 453588 746789

 

29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2. China data.

Name Population Cattle

Anhui 56181005 968000
Beijing 10819414 69000
Fujian 30048275 96000
Gansu 22371086 508000
Guangdong 62829737 452000
Guangxi Zhuang 42244884 553000
Guizhou 32391051 383000
Hainan 6182833 146000
Hebei 61089196 780000
Heilongjiang 35215953 577000
Henan 85534200 2208000
Hubei 53970501 241000
Hunan 60561433 265000
Jiangsu 67056812 165000
Jiangxi 37710277 270000
Jilin 24659785 560000
Liaoning 38930683 417000
Nei Mongol 21456518 737000
Ningxia Hui 4655445 54000
Qinghai 4456952 755000
Shaanxi 32882286 338000
Shandong 84392104 1673000
Shanghai 13341852 1000
Shanxi 28758846 258000
Sichuan 107218310 933000
Tianjin 8785427 52000
Xinjiang Uygur 15156883 819000
Xizang 2196029 472000
Yunnan 36972587 383000
Zhejiang 41635642 59000

 

 

30

 

Table 3. Rank correlation of variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

Region Variable 1 Variable 2 Spearman’s r
United States Area Population 0.110
Area Cattle 0.698

Population Cattle 0.133

China Area Population 0.187
Area Cattle 0.541

Population Cattle 0.257

 

Constructing the cartograms

 

Currently, the author is aware of no commercial
software program on the market that constructs cartograms.
Custom programs have been written in various languages
(Tobler 1973, Dougenik et al. 1985, Gusein-Zade and Tikunov
1993, Jackel 1997a). The method chosen for this project was
Jackel's 1997 program, which translates the Dougenik et al.
1985 contiguous cartogram algoritmn into the Awenue
programming language for use in the ArcView GIS environment
(Appendix A).

The program calculates the force exerted by the
centroid or center point of each polygon on each perimeter
point in each polygon and adjusts each perimeter point's

location accordingly. The force, based on gravitational

31

 

pull, is dependent on the polygon's attribute value and the
distance between the centroid and each perimeter point. A
centroid has a stronger effect on nearer points than on
farther points. The user chooses the number of iterations
to perform. As the number of iterations increases, the
error between the desired area and the actual area
decreases. Eventually, a limit is reached where performing
more iterations will not produce visible distortion and will
not lower the error by any meaningful amount. The output is
a standard ArcView shapefile produced at the conclusion of
each iteration.

The program requires the geographic data to be in the
form of an ArcView polygon shapefile as well. Since the
program computes the force on each point individually, the
program is extremely calculation intensive, and the more
points a shapefile has, the longer it will take to process.

The GIS data from which the United States and China
shapefiles originated had a much higher resolution than was
needed for the test maps. The shapefiles contained well
over 100,000 points each, too many to run the cartogram
creation program in a feasible amount of time. The
shapefiles were generalized in ArcInfo using the
"GENERALIZE" command with the "BENDSIMPLIFY" option.

The preservation of the shapes of individual

enumeration units is a key factor that enables cartograms to

32

communicate their messages (Dent 1972). Although topology
or contiguity is maintained perfectly, the size of the unit
is changing to reflect data values, and the better the shape
is maintained the easier it is to recognize identity of
units. To neintain shape in the cartogram transformation,
the geographic base map must start with well—defined shapes.
A balance must be struck between reducing the number of
points to take the map to a manageable level, and
maintaining good shape for each enumeration. unit. The
tolerance in the “GENERALIZE” command was varied until the
number of points was substantially reduced, yet recognizable
enumeration units were retained.

The United States shapefile was reduced to
approximately 9,000 points and the China shapefile to about
25,000 points. Even with this significant decrease in the
number of points, running the program took about four and
six hours for the United States and China respectively.

The attribute values must also meet certain guidelines
(Dougenik et al. 1985). No polygon may have a value of
zero. The District of Columbia has zero cattle, but its area
was merged with Maryland for the construction of the cattle
cartogram. If an enumeration unit is made up of more than
one polygon (for example, the state of Michigan, which has

an Upper and Lower Peninsula), then its attribute value must

33

be distributed among its polygons proportionate to the area
of each polygon.

Though China has thirty provinces, the shapefile
contained 298 polygons. Most of the coastal provinces are
made up of a large mainland and many smaller islands. These
islands would not be visible at the scale of the test maps
and were deleted. Two provinces had multiple polygons that
were large enough to be retained, for a total number of
thirty-two polygons in the shapefile. The continental
United States has forty-nine states, but the shapefile
contained 1268 polygons. Again, many small islands were
deleted. Three states had multiple polygons large enough to
be retained, for a total number of fifty—two polygons in the
shapefile.

If the data have too wide a range between extremes,
then the polygons with the smallest data values may have
problems distorting correctlyn The distortion. of their
points may be so great that the polygon overlaps itself. If
this happens, then the program treats this newly created
sliver as the enumeration unit. The program completes its
iterations, Inn: for some indiscernible reason, 1x3 further
distortion occurs. This problem occurred several times, but
was eliminated by making slight adjustments to the locations

of several points in the shapefiles.

34

Creating the cartogram test

 

A total of four cartograms were created in the PC
ArcView environment (Figures 8-11). For the population
cartograms, the number of iterations needed was twelve. For
the cattle cartograms, the number of iterations needed was
eight. An extra cartogram of births in the New England
region of the United States (Figure 3) was created for the
introduction. This cartogram required twelve iterations.
The output for each cartogram was a series of shapefiles,
one per iteration. Each shapefile was imported into
Macromedia Freehand where its size was reduced to 75% to fit
on the testing screen. The shapefiles were then exported as
GIFs and imported into Macromedia Director.

Macromedia Director was chosen as the software with
which to design the cartogram test because of its
multimedia, animation and interactive capabilities as well
as its availability at Michigan State University.
Macromedia Director is commonly used for a wide variety of
multimedia applications. Director also has the ability to
create “projectors” which run independently of the Director
software, allowing products to be used even on computers

that do not have Director installed.

35

 

Each shapefile was a “cast member” or a unique bitmap
graphic and was placed in its own frame or cell. When
viewed in rapid succession, the geographic map appears to be
morphing into the cartogram. The more frames, the smoother
the animation appears. With limits of twelve and eight
frames, the animations were not as smooth as intended, but
definitely sufficient to portray a visible morphing effect.

The test was designed to present the cartograms in
three formats for purposes of comparing each format’s
effectiveness in communication (Figures 12-16). All formats
displayed a basic layout consisting of the geographic base
map and the cartogram at the same scale on the same screen.
A "still" format was the basic layout only, where the
cartogram was displayed in its final iteration (Figure 12).

A "play" format was the basic layout with the addition
of "play" and "rewind" buttons. The cartogram was first

displayed at zero iterations, matching the base map on the

other side of the screen (Figure 13). The reader was able
to click "play" to watch the cartogram automatically
transform in a continuous, relatively smooth movement. The

end display was the cartogram in its final iteration (Figure
14). The reader was also able to click "rewind" to watch

the transformation in reverse and return to the zero

iteration. This format allowed the reader to view the

38

transformation in either direction, but did not allow
control of the speed of the transformation.

A "slider" format was the basic layout with the
addition of a slider bar, containing a draggable icon that
gave the reader control over the viewing of the
transformation. The cartogram was again first displayed at
zero iterations (Figure 15). The reader was then able to
drag the icon to view the cartogram at any intermediate
stage between the base map and the cartogram in its final
iteration (Figure 16). This arrangement allowed the reader
to control both the speed and direction of the
transformation.

The cartograms and geographic maps were given titles to
distinguish between them and to tell the reader what
variable was being presented. No other labeling, such as of
individual states or provinces was provided on any of the
maps. The maps were displayed as black-and-white linework.
Using a color scheme would have provided the reader with an
unwanted (in this research) additional visual cue. bk)
legend was given, because subjects were not asked to obtain
absolute quantitative data from the maps.

A total of twelve cartograms were used in the test

program . Two cartograms were created of each region, the
United States and China, using the two variables of
population and cattle. Each region and variable was

39

presented in each one of the three formats: still, play
animation and slider animation. The twelve cartograms were
divided into two sets by region. The United States
cartograms were seen first, the China cartograms second.
The United States cartograms were always seen first so that
the subjects might not be too intimidated or frustrated by
starting out with the unfamiliar region. Also, by keeping
the cartograms grouped by region subjects could maintain
focus on one region at a time.

Three tests were used, where the order of cartograms
within each region group varied according to format. In one
test, the order was still—play—slider. In the second test,
the order was play-still—slider. In the third test, the
order was slider-still-play. In this way, any learning
effect that might occur from seeing the earlier cartograms
was spread evenly over the three formats for the test group

as a whole.

40

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45

Selecting the questions to ask

 

As stated. in the literature review, Griffin’s 1983
research discovered that two map transformation qualities
were affecting the responses of the subjects: change in
angular location of units and change in each unit’s shape.
Subjects were not adequately mentally performing the
transformation between geographic space and cartogram space.
The hypothesis of this research is that allowing the reader
to view the transformation in an animation will alleviate
this problem. Therefore, the test questions were designed
to focus on the transformations that the animation might aid
in understanding. With areas “A” and “B” labeled on the
geographic map only, subjects performed three tasks with
each cartogram:

J” Find the state/province on the cartogram that
corresponds to state/province A on the geographic map.

2.Find the state/province on the cartogram that
corresponds to state/province B on the geographic map.

23.Using the cartogram, determine which state/province, A
or B, has the greater value.

The first two tasks were patterned after Griffin’s
experimental design. They directed the subject to locate a
corresponding area on the cartogram, given a labeled area on
the geographic base map (Figures 12 and 14). Results of
these tasks determined if the subject could understand the
transformation and recognize the same area on the base map

and the cartogram. The states and provinces chosen for the

test were selected based on two criteria of change: each had

46

a noticeable amount of shape distortion between the base map
and the cartogram, and each moved angularly from its base
map location.

The third task required the subject to compare sizes of
the two areas on the cartogram and determine their rank

order (Figure 16). Results of this task determined how well

the subject could interpret the data on the cartogram. Even
if the subject incorrectly located A and/or B, a correct
answer to the third question was still possible based on the
relative sizes of the areas chosen for that task.

The correct responses to the third task were determined
based on ranks of the data values of the areas. “Greater”
areas differed by at least ten rank positions. The
difference in size was easily discernible. To be considered
“equal," areas had to be within two rank positions of each
other.

To answer the questions implied in the first two tasks,
the subject clicked on the corresponding area on the
cartogram. For the third task, the subject clicked on one

of three radio buttons: A is greater, B is greater, or A and

B are equal. The still format displayed the cartogram in
its final iteration only. The subject answered directly
from that screen. The play and slider animation formats

started off with the cartogram at zero iterations, and the

subject had to first view the animated transformation at

47

least once before being able to answer the questions. The
ability to answer the questions by clicking on the map or
the radio buttons was not activated until the final
iteration was displayed.

The text of the cartogram test in its entirety can be

found in Appendix B.

Scoring the test

 

The cartogram test program was designed to record a
navigational log of the subject's movements through. the
program. The log also recorded the subject’s answers to the
test questions and the time spent on each question. The
output was a text document.

Because of Macromedia Director’s idiosyncrasies, the
easiest way to record the subject's answers to the first two
questions was to register the coordinate location of the
mouse click on the screen. Further processing was needed
after completion of the test to match each coordinate with a
specific state or’ province. The time was recorded in
Director’s unit of measurement, the tick, or one-sixtieth of
a second. The recorded times were divided by sixty to get
the number of seconds.

One preliminary hypothesis of this research was that
the response time for questions with animated cartograms

would be shorter than that for questions with still

48

cartograms. By the time the test program was completed, it
had become clear that response time was actually likely to
increase, given that the subject could play and replay the
transformation again and again, taking more time than on a
still format cartogranu Increased time had become the
hypothesis, then; however, it was also predicted that
subjects’ perception of time might be reversed because
viewing the transformation was expected to increase
comprehension and lessen frustration. The subject may feel
less time is taken on the animated cartograms than the still
cartograms because the animated cartograms were understood
with more ease, when in fact more time was taken by
continually reviewing the animation.

The time was recorded from the instant a subject
entered a question screen to the instant the subject exited
the screen by answering the question. The measure included
time spent viewing the basic screen layout, reading the
questions, and. performing animations. The average time
spent on each question was compared to subjects’ perceptions
of time, and observations were made of several subjects
while they were taking the test to see what behavior took

place during the elapsed time.

49

Pretest and posttest questionnaires

 

Pretest and posttest questionnaires on paper (Appendix
C) were developed in conjunction with the computerized
cartogram test. The pretest questionnaire was designed to
determine the depth and breadth of subjects’ prior exposure
to cartograms. In addition to answering questions, subjects
were to sketch mental maps of the continental United States
and China, determining if the United States was the more
familiar region as presumed. Blades (1990) has shown that
sketch maps are a reliable source of data about readers'
mental representations of areas. The posttest questionnaire
asked the subjects to evaluate their testing experience, the
design and navigability of the program, and the three
different presentation formats -- still, play animation and

slider animation.

Testing procedure

 

Testing took place in a computer laboratory. Upon
receipt of approval from the University Committee for
Research Involving Human Subjects, recruitment of subjects
commenced. Announcements were made in geography classes and
volunteers were solicited from among geography' graduate
students. Fourteen test sessions were held over a two—week

period. One to six subjects were tested in each session.

50

An oral overview of the testing procedure was given and
a written consent form was obtained from each subject. The
next step was the pretest questionnaire, taken with paper
and pencil. The pretest was the most time-consuming part of
the entire test, asking the subjects to construct the two
mental maps. A guideline of twenty minutes was given for
completing this step. However, the limit was flexible; as
soon as all subjects in a particular session had indicated
their completion of the pretest, they were all able to move
on.

The subjects were then directed to individual computers
on which the cartogram test program was installed. The test
program was designed to be self-sufficient, running
independently of the Director software and containing its
own instructions. The researcher remained in the room for
technical support but did not control any aspect of the test
program itself. Subjects were allowed as much time as
needed to complete the cartogram test. They were not told
that the time spent on each question would be recorded.

As soon as individuals finished the cartogram test,
they moved to the final step, the posttest questionnaire,
again taken with paper and pencil. They were allowed as
much time as needed to complete this step as well. At the
completion of the three tests, subjects were paid five

dollars as compensation for their participation.

51

Statistical methods

 

The experiment was planned. as a factorial repeated
measures design. There 'was (nu: categorical independent
variable or factor, REGION. REGION could be one of two
categories: the familiar region.<n: the unfamiliar region.
The dependent variable was FORMAT. FORMAT had three levels:
still, play or slider: Each subject’s performance was
repeatedly measured while varying the level of format.
Since each subject was measured at every level, FORMAT was a
within-subjects or repeated measures variable. REGION was
used as a grouping variable.

A factorial repeated measures analysis of variance
(ANOVA) test was used to assess three hypotheses (Wilkinson
et al. 1996). The first hypothesis was that the familiar
region and the unfamiliar region had different overall mean
scores. The familiar region was expected to have higher
overall mean scores. The unfamiliar region was expected to
have lower mean scores.

The second hypothesis was that the different formats
had different mean scores overall. The animated formats
were expected to have higher mean scores than the still
format. The third hypothesis of the ANOVA test was that the
mean scores would be affected by the interaction between the
format and the region. The animation was expected to have

more of an effect on responses to the unfamiliar region.

52

Chapter 4

RESULTS

Description of subjects

 

All subjects were students at Michigan State
University. IX total of thirty-three subjects participated
in the study. The navigational log file for one of the

subjects was found to be corrupt for some unknown reason and

could not be used. Thirty—two subjects, then, were used in
the analysis . Of the thirty-two subjects, fourteen were
male and eighteen were female. The ages ranged from

nineteen to fifty-two, with a median age of twenty-two.
Subjects were asked to complete the paper-and-pencil

pretest questionnaire in twenty minutes. Subjects generally

took about fifteen to twenty minutes to finish. One subject

took about twenty-five minutes.

Prior knowledge of cartograms

 

The first two questions on the pretest questionnaire
(Appendix C) asked if the subject had ever heard of a map
called a cartogram and if so, to provide a definition.
Nineteen subjects of the thirty—two (59.4%) claimed to have
heard of a cartogram, but only six subjects of the nineteen
(18.8% of the total test pool of thirty—two) were able to

provide an accurate definition. Eight of the nineteen gave

53

an incorrect or vague definition, and five of the nineteen
stated they did not know the definition. Thirteen subjects
of the thirty—two (40.6%) had never heard of a cartogram.

The subjects were asked if they had ever seen a
cartogram in any of a list of contexts. Twelve subjects of
the thirty-two (37.5%) had never seen a cartogram. One of
the subjects who had never heard of a cartogram did not
answer this question, but it was assumed that having never
heard of a cartogram, the subject had also never seen one.
The answers of the thirteen subjects who claimed to have
heard of a cartogram but were unable to provide an accurate
definition were not tallied because the subjects were not
able to prove sufficiently their ability to recognize a
cartogram.

Of the six subjects who provided a correct definition,
two had seen a cartogram in an atlas, five in a textbook,
five in a classroom (used by a teacher as a visual aid), and
three in a journal, newspaper or other printed media. One
had seen a cartogram on the Internet, television or other
electronic media, and one on a postcard.

The subjects were asked if they had ever used a
cartogram in any of a list of contexts. Nineteen subjects
of the thirty-two (59.4%) had. never 'used (nus. Of the
remaining thirteen subjects, seven were in the group unable

to provide an accurate definition. Again, their answers

54

were not tallied. Of the six subjects who had provided a
correct definition of a cartogram, three had used a
cartogram in a classroom exercise or lesson and four had
used a cartogram to answer a test question. Two had used a
cartogram for their own personal reference. No subjects had
included someone else’s cartogram in a paper or project, and

no subjects had created their own.

Familiarity with each region

 

To assess whether the United States was the familiar
region and China the unfamiliar region as presumed, subjects
were asked to draw and label as many individual states or
provinces as they could using only their memory (Appendix
D). Correct shape and location of states or provinces was
not evaluated; only the total number of labeled ones.

Twenty-eight subjects out of thirty-two (87.5%) were
able to identify at least half of the forty-nine continental
United States (forty-eight states and the District of
Columbia). Eighteen subjects (56.3%) were able to identify
over forty states, and no one identified fewer than eleven
states. Two subjects out of thirty-two (6.3%) were able to
identify at least half of China’s thirty provinces. Out of
the remaining thirty subjects (93.8%), no one was able to
identify' more than two provinces. Five of the thirty

identified Tibet and five of the thirty identified Mongolia

55

as provinces of China. Twenty—seven at least attempted to
draw an outline of the country. Two subjects left the area
completely blank.

These results indicated that every subject was familiar
with the United States, but not everyone was unfamiliar with
China. Both the U.S. and China were familiar to two

subjects.

Practice materials

 

The introductory part of the cartogram test program
first defined a cartogram, then displayed an example using a
cartogram of the number of births in New England. This
example cartogram was used throughout the introduction.
Subjects were next given a multiple-choice question to see
if they then clearly understood the definition of a
cartogram” Thirty-one subjects of tflua thirty-two (96.9%)
selected the correct definition. The subject selecting the
wrong definition chose the correct response on the second
try.

The introduction displayed the two formats of
animation, automatic and manual, and subjects were asked to
familiarize themselves with. both formats. Finally, the
introduction explained the basics of the test and displayed
three examples of test questions identical to those on the

test. Though the actual test questions appeared in all

56

three formats, the example questions portrayed the example
cartogram in still format only.

Results from the introductory part of the test showed
that subjects were able to familiarize themselves with the
test format and complete the tasks as instructed with little

difficulty.

Processing the test scores

 

The raw results of the cartogram test were tallied in
tabular form. The table lists each question by variable and
format, then gives the number of subjects who gave a correct
answer to that question and the average time taken to answer
for both regions (Table 4).

Upon examination of the raw results, an error in the
testing method was found. The answers to the third task,
comparing the sizes of areas A and B, had been determined by
the differences in rank of the data value of the areas.
Ideally, the sizes of the areas on the cartogram maintain
these rankings. However, due to varying forces of
distortion the enumeration unit may not end up with its area
corresponding exactly to its data value. Ranking the areas
according to actual cartogram area instead of data value
resulted in slightly different rankings for some of the

areas (Table 5).

57

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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60

When using the new rankings, the previously established
criteria for “greater” and “equal” were preserved for all
but four of the twelve comparison questions. Three of these
comparison questions had an original answer of “equal” and
one had an original answer of “A is greater.”

The areas involved in the “A. is greater" question
(China/Cattle/Play), when assigned the new ranks, only
differed by eight rank-positions instead of ten. The areas
were becoming too close in rank and actual size for one to
be considered greater. When the areas in the three “equal”
questions were assigned the new ranks, two of the questions’
areas differed by three rank—positions and one differed by
five rank—positions. Too much difference existed for the
areas to be considered equal in these three questions.

Comparing the percent size differences of each pair of
areas confirmed these figures (Table 5), especially for one
of the “equal” questions. The areas were too close in
percent size difference (only 3.76% different) to expect
subjects to discern any difference between them. For this
question (U.S./Cattle/Slider), all three answers (A is
greater, B is greater, A and B are equal) had. to be
accepted. Subjects’ answers to the four affected questions
were rescored. Tflme adjusted answers are reflected in the

text of the test (Appendix B).

61

Another adjustment to the scores was made based on
familiarity with the two regions. Two subjects evidenced
enough familiarity with China that it was not an unfamiliar
region to them. Therefore, their scores for the questions
using cartograms of China were considered “familiar region”
scores. Instead of naming the regions the United States and
China in the scoring, the regions were instead called
“Familiar” and “Unfamiliar.” The total number of answers
for the familiar region became 34 and the total for the
unfamiliar region became 30. The adjusted results of the

cartogram test were tallied in tabular form (Table 6).

Main results

 

Once the tests were rescored, statistical testing could
be performed. During the cartogram test, different subjects
viewed the twelve cartograms in different format orders.
Nine subjects saw the cartograms in still—play-slider order,
eleven in play-still-slider order, and twelve in slider-
still-play order. Although it would have taken equal
numbers of subjects viewing all six. possible orders to
completely balance the design, these selected orders did
prevent any one format from being consistently first or
last. Since approximately equal numbers of subjects saw the

cartograms in each of the three orders, any learning effects

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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63

caused by the earlier displays were assumed to be evenly
distributed over the three formats.

Though some test sessions contained multiple people,
each subject took the test independently from every other
subject. To make the assumption that mean values in samples
are normally distributed, the sample size should generally
be at least thirty. This experiment had a subject sample

size of thirty-two, and with multiple questions, sample size

in statistical tests became larger. With independence and
normality assumptions met, a parametric statistical
procedure could be used. A significance level of 0.05 was

selected for all tests.

All statistical analysis was performed using the
program SYSTAT. IX factorial repeated measures ANOVA test
was performed on the data. .ANOVA is based on the F
statistic. The first <questionq called. the “Familiarity”
question (Table 7), was whether the overall mean scores of
the familiar and unfamiliar regions were significantly
different when controlling for format. The null hypothesis
was that the mean scores were equal. The alternative
hypothesis was that the means for the familiar and
unfamiliar regions were not equal. The calculated F
statistic, 7.792, was greater than the rejection statistic
of 4.000 with. 1 and, 60 degrees of freedonu The null

hypothesis was rejected; there was at least one significant

64

Table 7. Repeated measures ANOVA results.

 

 

 

 

 

Question Confidence F statistic Probability
level
Familiarity 0.05 7.792 0.007
Format 0.05 22.933 0.000
Familiarity x
Format 0.05 9.009 0.000
(interaction)

 

 

 

 

difference in scores between the two types of regions. When
looking at the mean scores for each region in each format
(Figure 17), the greatest contrast is in the scores of the
still formats.

The second question, called the “Format” question
(Table 7), was whether the three formats had significantly
different mean scores. The null hypothesis was that the
mean scores for the different formats were equal. ‘The
alternative hypothesis was that the mean scores were not
equal. The calculated F statistic, 22.933, was greater than
the rejection statistic of 3.150 with 2 anui 60 degrees of
freedom. The null hypothesis was rejected. At least one
significant difference existed between.tflu3'mean scores for
the three different formats when controlling for familiarity
of region. A visual comparison of the mean scores (Figure
17) showed that for both regions, the play format had the

highest mean scores, the slider format had the next highest

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66

scores (very close to those for the play format), and the
still format (especially for the unfamiliar region) had the
lowest mean scores.

The third question of the ANOVA test, called the
“Familiarity x Format” or “interaction” question (Table 7),
was whether the format had a different effect on mean scores

for the familiar vs. unfamiliar region. The null hypothesis

was that there was no interaction. The alternative
hypothesis was that there was an interaction. The
calculated F statistic, 9.009, was greater than the

rejection statistic of 3.150 with 2 and 60 degrees of
freedom. The null hypothesis was rejected; a significant
interaction effect existed between the regions and formats.
Looking at the mean scores (Figure 17), the greater
improvement was in the mean scores for the unfamiliar
region. The still format had a much lower score than either
animation format. In contrast, the scores for the familiar

region are relatively consistent over the three formats.

Posttest questionnaire results

 

The paper-and-pencil posttest questionnaire (Appendix
C) asked subjects to evaluate several aspects of the testing

experience. Subjects were given as much time as needed to

complete the posttest but generally finished in about ten

67

minutes. The results, minus subjects’ comments in their own
words, were recorded in tabular form (Table 8).

First, several questions were asked about the
computerized testing. Six subjects of the thirty-two
(18.8%) had taken a computerized test like the cartogram
test before. Twenty-six subjects (81.3%) had not. Twenty-
nine subjects <3f time thirty-two (90.6%) felt comfortable
using the computer to take the test. Three subjects (9.4%)
felt neutral and no subjects felt uncomfortable.

A series of questions was asked about the design of the
cartogram test program. Twenty-nine subjects of the thirty-
two (90.6%) felt the introduction adequately prepared them
to take the test. Three subjects (9.4%) felt neutral and no
subjects felt the introduction did not adequately prepare
them.

Thirty-one subjects of the thirty-two (96.9%) felt the
definition of a cartogram was helpful. One subject (3.1%)
was neutral. This subject commented that it would have been
useful to see the definition again during the test, or to
receive an explanation before the test of why cartograms are
needed. No subjects felt the definition of a cartogram was

unhelpful.

68

 

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69

Thirty subjects of the thirty-two (93.8%) felt the
format examples of the automatic animation and the manual
animation were helpful. Two subjects (6.3%) felt neutral
and no subjects felt the format examples were unhelpful.

Twenty-eight subjects of tine thirty-two (87.5%) felt
the test question. examples ‘were helpful” Four' subjects
(12.5%) felt neutral and no subjects felt the test question
examples were unhelpful.

Thirty-one subjects of the thirty-two (96.9%) felt it
was easy to navigate through the testing program. One
subject (3.1%) felt neutral and no subject felt the program
was “not easy” to navigate.

The posttest questionnaire then asked which format
(still, play or slider) was easiest and fastest to use to
locate areas A and B. No subjects preferred the still
format. Eleven subjects of the thirty-two (34.4%) preferred
the play format, and twenty—two subjects (68.8%) preferred
the slider format. The total does not add up to thirty—two
because one subject chose both the play and slider formats.

Three subjects made specific mention of the fact that
the static format was difficult to use with China because of
their unfamiliarity with China’s geography. The most
prevalent comment of those who preferred the play format was
that they did not have to concentrate on moving the slider;

they could simply press one button and sit back to watch the

70

animation. Several subjects also noted that since the mouse
cursor was not in use during the transformation, it could be
used as a pointer to mark the position of the changing state
or province on the map or cartogram. Subjects who preferred
the slider format generally made some mention of the fact
that this format allowed them to control the speed of the
transformation.

The posttest questionnaire also asked which format
(still, play or slider) was easiest and fastest to use to

compare the areas of A and B. Four subjects of the thirty-

 

two (12.5%) preferred the still format. Nine subjects
(28.1%) preferred the play format, and nineteen subjects
(59.4%) preferred the slider format.

The four subjects who preferred the static format felt
that movement was not needed to compare sizes of areas. The
other subjects, no matter their preference for automatic
(play) or manual (slider) animation, gave generally the same
reasons for their preferences as they did in the pmevious
question.

Though a majority of subjects felt that the play and
slider presentation formats were easiest and fastest to use,
looking at overall average response times (Table 9) shows
that, as expected, subjects spent more time on these formats
than on the still format. The average time spent on all

still questions was 16.282 seconds, the average on all play

71

questions was 19.788 seconds, and the average on all slider

questions was 21.756 seconds.

Table 9. Average times.

 

 

 

 

 

 

 

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Slider 21.756

 

 

 

 

 

The final question on the posttest questionnaire asked
if the subject believed the cartogram could be a useful tool
for presenting spatial information. Twenty-six subjects of

the thirty-two (81.3%) answered yes. Five subjects (15.6%)

were neutral. One subject (3.1%) answered no and commented
that cartograms “could confuse learners of spatial
relations.”

One subject who answered that cartograms could be
useful then went on to say that “I have a hard time with
‘spatial comparisons’” but cartograms might work well for
others. Several subjects mentioned that they were visual

learners and that cartograms would be an ideal learning tool

72

for them. One subject wrote that cartograms “allow for
information to be presented with regard to data
representation rather than geographic boundaries.”

Subjects who felt neutral about the usefulness of
cartograms commented that without a detailed explanation,
cartograms could be difficult to interpret. Some stated
that their ambivalence came from the pmesentation format;
cartograms might be useful in an animated environment, but
“static environments can prove very challenging [when one is
faced with] unfamiliar areas.”

Subjects were given the opportunity to make any
comments they wished at the end of the posttest. The
prevailing response was that the cartogram test program was
fun and interesting and a good introduction to cartograms.
Overall subjects appeared to have a positive testing

experience.

73

Chapter 5

DISCUSSION

The subjects and their previous knowledge

 

The sample population, all college students, was
relatively homogeneous. Although a greater variety of
previous experiences with cartograms might have turned out
with a broader sample, the limitations seemed justified,
since college students are among those to whom a cartogram
might be useful. About equal numbers of males and females
took part, which means that skewing of the results due to
possible gender bias was unlikely.

The pretest questionnaire revealed that cartograms are
not well known to this population. Though over half the
subjects claimed to have heard of a cartogram, only about
one fifth could provide an accurate definition. A majority
of subjects reported having heard the word “cartogram”
before, but were unable to define it. Quite possibly, most
of the subjects would have been able to recognize a
cartogram if shown one. The pretest question was evaluating
mental understanding of a cartogram, not looking for simple
visual recognition.

Though only a small number of subjects were able to
describe: a cartogram. accurately, the most common. places

cartograms were seen were in educational settings, either

74

textbooks or classrooms. They were not often seen in
printed and electronic media. Since all subjects were
college students, the most likely' place they' would see
cartograms would be an educational setting. However, some
subjects were significantly older than the median age of
twenty—two and had more life experience; these subjects may
have had more opportunity to see cartograms in other
contexts. Perusal of the pretests proved this to be false,
but the population of “older” subjects was relatively small
in this experiment. A wider sample of “older” subjects may
have a different result.

The majority of the subjects had never used a
cartogram. Of the subjects who were able to correctly
define a cartogram, the most common uses were to answer a
test question or to support a classroom lesson; again,
educational settings were involved“ Not surprisingly, no
subject had ever used a cartogram in a paper or project, and
no subject had ever created one.

The United States was shown to be a familiar region to
most of the subjects. Most could identify at least half of
the states, and no one identified fewer than eleven.
Likewise, China was shown to be an unfamiliar region to most
subjects, but two were able to identify at least half of
China’s provinces. These two subjects were also able to

construct sufficient mental maps cm tine United States, so

75

the United States was not an unfamiliar region; instead,
both regions were familiar. The mental map task prevented
the assumption that the United States was the familiar
region and China the unfamiliar region for everyone. The
regions could be appropriately categorized as familiar or
unfamiliar for each individual subject. Without having
subjects sketch mental maps as a check on this assumption,
an error could easily have been made. This result is a
clear indication that familiarity assumptions should be
checked in any cartographic testing where it might have an
influence.

Even though the familiarity was readily classified, the
quality of familiar-area mental maps varied widely. Some
subjects were able to recreate shape, location and identity;
others only location and identity, drawing simple rectangles
instead of correct shapes. A few subjects did not attempt
to draw any sort of shape and simply wrote in state names in
the approximate locations. All subjects first drew outlines
of the countries and then attempted to fill in the
individual states or provinces, instead of drawing the
states and provinces first to create the outlines of the
countries. 'This response probably' results front greater
familiarity with country outlines than with their internal
subdivisions. Subjects have probably seen the United States

and China both with and without their respective

76

subdivisions, but are more likely to remember “wholes” than

“parts.”

Expected results vs. statistical results

 

The purpose of the research was to determine if the
addition of animation to cartograms improved the cartogram’s
ability to communicate, especially when the region was
unfamiliar: This idea was definitely supported. by' the
statistical tests.

Familiarity was shown to be a strong factor in
communication when the cartograms were shown in the still
format. This conclusion is already part of the general
literature on cartograms, often worded as a caution to the
cartographer not to use cartograms unless the depicted
region is familiar to the audience. It is often impossible
to test an audience’s familiarity level with a selected
region before creating the cartogram. Since cartograms have
been seen only in a still environment for nearly all of
their existence, the familiarity factor has hindered the use
of cartograms.

While the greatest contrast occurred between the still
format scores, the animated format scores for the two
regions were extremely close. Familiarity with the region
ceased to be a factor in both animated formats. Animated

cartograms may be used to depict a greater range of

77

geographic areas, then, since the audience’s familiarity
with the region is no longer a major concern.

Format was also shown to be a strong influence on
communication, but it is apparent once again that the still
format with the unfamiliar region is the one that differs
from the rest. The graph of the scores shows that overall
the play format had the highest mean scores and the still
format the lowest. The slider format’s mean scores fell in
the middle, but were much closer to the scores for the play
format.

The expected outcome was that slider would be the best
format, and this was supported by subjects’ two—to-one
preference for the slider format on all types of questions.
Subjects chose the slider format as easier and faster to
use, so presumably the slider format would. produce the
highest scores as well. However, the numerical results
showed the play format as having slightly higher scores.

Still, the difference in mean scores between the two
animated formats was not large enough to advocate use of one
method over the other. Both methods of animation achieved
higher scores than the still format, especially for the
unfamiliar region. Animation increased the effectiveness of
the cartogram’s ability to communicate, and the animated
versions were preferred. With the wide range of familiarity

even for the “familiar” area, the results provide a strong

78

case for the use of animation with cartograms of any region,
“familiar” or “unfamiliar.”

Finally, a significant interaction effect existed
between the two regions and the three formats, and the graph
clearly indicated that the greatest improvement with
animation came with the unfamiliar region. The mean scores
for the unfamiliar region across formats differed much more
than the mean scores for the familiar region. As expected,
the cartogram’s ability to communicate was most affected by
animation when an unfamiliar region was depicted, and
animation opens the door to effective cartogram

communication for any region.

Subjects’ posttest questionnaire responses

 

Readers’ perceptions of time and effort should be taken
into consideration when creating any kind of map. Readers
are not likely to opt for a map perceived to be difficult or
frustrating when a less difficult or less frustrating one is
available.

Subjects displayed a clear preference for the animated
formats over the still format. In their comments, they
recognized the benefits of adding animation to cartograms,
and even stated that cartograms might not be useful unless

animation is used. They also preferred the slider format,

79

as it gave them both the ability to view the transformation
and control its speed and direction.

Though subjects felt that the play and slider formats
were the “easiest and fastest” to use to answer both types
of questions, they spent on average up to five seconds more
on questions with these formats than with the still format.
The increased time was probably a result of replaying the
animation multiple times. Though the actual time spent on
animated cartograms was longer than that spent on still
cartograms, subjects’ awareness of the time spent was
apparently shorter. In all likelihood, the level of
concentration necessary was also lessened with the animated
maps. Combining “easiest” and “fastest” in the question may
have confused the issue somewhat, but it seems unlikely that
separating the ease and time components would have resulted
in different preferences.

The majority of subjects had never taken a computerized
test like the cartogram test before, but there was no fear
of the computer or uncertainty about the tasks. Most
subjects felt comfortable taking the test on the computer;
no one felt uncomfortable. The test was easy to take and
the tasks clearly defined. Whatever faults the test may
have had, lack of comfort and clarity for subjects was not

among them.

80

Weaknesses of the research

 

A major weakness of this experiment was the problem
with the ranking of the areas. The choices of areas in the
comparison questions were selected based on the ranked data
values. The areas produced by the cartogram do not always
conform to these rankings due to varying forces of
distortion. Depending on the distribution, one pair of
neighboring ranks might have very dissimilar values while
another pair of widely separated ranks might be close in
value. Even more important with the maps used here, the
rankings as pmoduced by the cartogram areas differed from
the data value ranks. The answers to the comparison
question should have been determined using the actual
cartogram area rankings instead of the data value rankings.
Unfortunately, this was discovered after the testing had
already taken place, and adjustment of scores was necessary.
The experimental design could have been stronger had the
problem been anticipated and more appropriate pairs of areas
been chosen.

The selection of enumeration units to be areas A and B
was a difficult one in any case. Criteria such as visible
distortion and angular movement from the original location
were used to select areas, but each cartogram provided a
multitude of possible choices that met these criteria. The

researcher then subjectively selected from these

81

possibilities. Had different areas been chosen, different
results could conceivably' have occurred, although it is
unlikely that the overall conclusions would have changed.

Another improvement on the design of this experiment
would be to have more test questions for each presentation
format. This design used six questions for each combination
of region and format for a total of thirty-six questions.
The mean scores for the different formats are all fairly
close. By themselves they' do not appear' to .have ‘much
variance, even though the .ANOVA test showed significant
differences because of poor performance with the unfamiliar
region in still format. A greater number of questions,
varying in difficulty, would allow for more variation in the
mean scores, and possibly a more visible difference.

An interesting observation about cartograms, still or
animated, is that different methods of construction will
produce different—looking cartograms from the same data.
Different-looking cartograms may send different messages,
even if they are displaying the same data. Identical tests
using cartograms created from the same data as these
cartograms, but constructed ‘using' different computer
algorithms, would contribute to knowledge of those
algorithms’ accuracy and effectiveness as well as strengthen
or modify the conclusions reached here. (Hue results from

this experiment must be tempered with the realization that

82

they are based on cartograms produced with this particular
method of cartogram construction.

No analysis was done specific to the type of task
(location and comparison) being performed. with the
cartograms because the total number of questions for each
region/format/task combination was so small (only six
questions total, four location and two comparison). Again,
a greater number of questions would allow for task-specific
analysis. However, subjects were asked which format they
preferred for each task. That subjects overwhelmingly chose
the animated formats for both tasks was not surprising.
Interestingly, while no subjects preferred the still format
for the location tasks, four subjects preferred it for the
comparison tasks. It may be that the format used to present
cartograms should be task—specific. Depending on the
purpose of the cartogram, perhaps animation may or may not
be necessary.

Due to time limitations and the necessity of
eliminating one subject, only thirty-two subjects were

included in the analysis. A larger number of subjects would

be more representative of the population. Also, a wider
range of people could be tested. All subjects in this
experiment were college students . Future research could

widen the recruitment scope to children, older adults, and

non-college students. It is suspected that testing subjects

83

from outside an educational setting may produce different
results, if only“ in the pretest questions dealing' with

exposure t0 cartograms.

Broader implications

 

Research with animated maps has had mixed conclusions,
partly because of the many conditions under which animation
is used. Though statistical analyses are often equivocal,
subjects usually' prefer' animation. to traditional, static
methods of presenting maps. Partly attributed to the
“novelty" effect, subject interest and motivation cannot be
discounted when assessing animation’s influence. Cartograms
themselves are novel approaches to data representation;
animated cartograms would seem to be doubling the novelty
effect, which may be adding to the animation’s
effectiveness.

Though animation is generally used in cartography to
represent temporal change, animation was used in this case
to represent a kind of spatial change. The three tasks
subjects were asked to accomplish focused on the spatial
transformations taking place in the maps. The way in which
animation was used and the purpose for which the maps were
used were directly connected. Another task often used with
cartograms is retrieval of quantitative data by estimating

the sizes of areas. This task requires a legend to which

84

the reader can compare sizes of areas on the map, and the
question arises of whether to incorporate a static legend
into an animated map. This dilemma exists not only for
cartograms but for other types of animated maps as well.
Perhaps animated legends are the answer, but the issue then
becomes how to design such legends and test their
effectiveness.

Now that animation has shown its effectiveness in one
dimension, that of spatial change, perhaps it can be useful
in two dimensions, combining spatial and temporal change. A
series of cartograms could depict an attribute over time.
Animation would allow the cartograms to morph either into
the geographic base map or into the next time-sequential
cartogram. Results from this research suggest that such
animated sequences should.1x2 effective, Inn: sound testing

should be used to provide a concrete answer.

85

Chapter 6

SUMMARY AND CONCLUSIONS

The purpose of this research was to determine if the
addition of animation to cartograms would increase the
effectiveness cflf the cartogram's communication, especially
with unfamiliar regions. A cartogram test was designed to
present cartograms of a familiar region, the United States,
and an unfamiliar region, China, in three formats. The
three formats were still, having no movement; automatic
animation through the use of a play button; and manual
animation through the use of a slider bar.

A test pool of thirty-two subjects was recruited from
the student population at Michigan State University.
Subjects were tested in groups of one to six; each subject
took the test independently and was paid five dollars as an
incentive to participate.

Pretest questionnaire results showed that very few
subjects were able to provide an accurate definition of a
cartogram. Familiarity with cartograms was very low.
Cartograms were most often seen and used in an educational
setting. Subjects’ mental maps indicated that the United
States could be considered the familiar region and China the
unfamiliar region for the majority of subjects, but two

subjects showed familiarity with both countries.

86

Results of the cartogram test showed that there was a
difference in accuracy between the familiar region and the
unfamiliar region. A look at the graph of all mean scores
shows that the greatest difference is between the mean
scores for the still format. Familiarity with the region
was very important with the still format questions. There
was a significant difference in mean scores between the
three formats as well, again because scores were so much
lower for the unfamiliar region in still format. Finally,
there was a significant interaction effect between
familiarity and format. The greatest improvement was found
in the difference between the mean scores for the unfamiliar
region’s still format and animation formats.

Posttest questionnaire results showed that though
subjects spent more time on the animated format questions,
they perceived that they spent less time. Subjects
preferred the slider format on all types of questions almost
two to one over the play format because the slider format
allowed. the subject both. to “view ‘the ‘transformation. and
control its speed and direction.

Overall, the results of the experiment indicated that
animation of the transformation between the geographic map
and the cartogram does have an effect on the cartogram’s
ability to communicate. Though it may take more time to

receive the message as the animated transformation is viewed

87

‘18.

 

repeatedly, subjects perceive that they actually spend less
time on the animated cartograms. They also overwhelmingly
preferred the animated formats.

Though this experiment could 'undergo some revision,
such as using a different method of constructing cartograms,
recruiting a larger number of test subjects from a wider
population, and asking a greater number of questions, the

results provide valuable information about the use of

animation in cartography. In the words of one subject, the
animations “[were] great for exposure to cartograms, even if
[the purpose] was nothing more than that." The higher level

of accuracy with the animated versions, the comparable level
of accuracy with both familiar and unfamiliar regions when
animation was used, and the interest that the animations
elicit combine to present a strong case for using animation

with cartograms.

88

APPENDICES

89

APPENDIX A

Avenue code for creating cartograms in ArcView

av.ClearStatus
theProject = av.GetProject
theView = av.GetActivedoc
thePrj = theView.GetProjection
if (thePrj = nil) then

hasPrj = false
else

hasPrj = true
end

theAttributeValue = nil
theCurrentThemes = theView.GetThemes
theGoTheme = Msgbox.Choice(theCurrentThemes, "Select a
theme: ", "Convert Theme to Cartogram")
if (theGoTheme = nil) then
exit
end

theTheme = theGoTheme
anFtab = theTheme.GetFtab
theFieldList = anFtab.GetFields

while (theAttributeValue = nil)
theAttributeValue = Msgbox.Choice(theFieldList,"Select an
attribute: ", "Selected Theme is”++theTheme.AsString).
AsString
theContents = anFtab.ReturnValue(anFtab.FindField
(theAttributeValue), 0)
if (theAttributeValue = "Area" or theContents.AsString.
IsNumber.Not) then
Msgbox.Info("Selecting"++theAttributeValue++"as an
attribute will not produce a cartogram.", "Select Another
Attributel")
theAttributeValue = nil
end
end

iteration = nil
while (iteration = nil)

iteration = Msgbox.Input("Enter number of iterations to
generate cartogram: ", "Iterations", "8").AsNumber

if (iteration < 1) then

90

MsgBox.Info("Cannot perform negative iterations. Try

again.", "Oops!")
iteration = nil
end
end
def = (theTheme.GetName.Left(3) + iteration.AsString +

"_cg.shp").AsFileName
tbl = anFtab

shpfld = (tbl.FindField("Shape"))

if (shpfld.IsVisible.Not) then
shpfld.SetVisible(shpfld.IsVisible.Not)
wasNotVisible = TRUE

else
wasNotVisible = FALSE

end

anFtab = tbl.Export(def, Shape, FALSE)
anFtab.SetEditable(TRUE)

if (wasNotVisible) then
shpfld.SetVisible(FALSE)
end

iterationCount = 1

PI = Number.GetPI
PolygonValueList = {}
TotalValue = 0
TotalPoints = 0
PolygonAreaList = {}
TotalArea = 0

for each xnum in anFtab
theShape = anFtab.ReturnValue(anFtab.FindField("Shape"),
xnum)
PointsInEachPolygon = theShape.AsList.Get(0).Count
TotalPoints = TotalPoints + PointsInEachPolygon
PolygonValueList.Add(anFtab.ReturnValue(anFtab.
FindField(theAttributeValue), xnum))
TotalValue = TotalValue + PolygonValueList.Get(xnum)
PolygonAreaList.Add(anFtab.ReturnValue(anFtab.
FindField("Area"), xnum))
TotalArea = TotalArea + PolygonAreaList.Get(xnum)
end

OutputFile = LineFile.Make("debug.dat".AsFileName,
#F I LE_PERM_WRITE)

while (iterationCount <= iteration)

91

av.Shostg("Distorting original polygons: iteration #" +
iterationCount.AsString)

PolygonAreaList = {}

CentroidList = {}

DesiredList = {}

RadiusList = {}

MassList = {}

SizeErrorList = {}

SizeErrorTotal = 0

count = 0

OutputFile.WriteElt("Iteration
#"++iterationCount.AsString++"of"++iteration.AsString)

for each xnum in anFtab

theShape = anFtab.ReturnValue(anFtab.FindField("Shape"),
xnum)
PolygonAreaList.Add(anFtab.ReturnValue(anFtab.FindField
("Area"), xnum))

CentroidList.Add(theShape.ReturnCenter)
end

OutputFile.WriteElt("Poly# Value Value% PolyArea Poly%
DesiredArea Desired% SizeError")

for each xnum in anFtab
PolygonValue = PolygonValueList.Get(xnum)
PolygonArea = PolygonAreaList.Get(xnum)
Desired = TotalArea * (PolygonValue/TotalValue)
DesiredList.Add(Desired)

Radius = (PolygonArea/PI).Sqrt
RadiusList.Add(Radius)
Mass = ((Desired/PI).Sqrt) — ((PolygonArea/PI).Sqrt)

MassList.Add(Mass)

SizeError = (PolygonArea Max Desired)/(PolygonArea Min
Desired)

SizeErrorTotal = SizeError + SizeErrorTotal

SizeErrorList.Add(SizeError)

OutputFile.WriteElt(xnum.AsString++PolygonValue.AsString++Po
lygonValue/TotalValue*100).AsString++PolygonArea.
AsString++(PolygonArea/TotalArea*100).AsString++Desired.
AsString++((PolygonAreaDesired).Abs/Desired*100).AsString++S
izeError.AsString)

end

MeanError = SizeErrorTotal/SizeErrorList.Count
ForceReductionFactor = l/(1 + MeanError)

for each r in anFtab

92

theShape = anFtab.ReturnValue(anFtab.FindField("Shape"),
r)

theListofPoints

theNewPointList

theShape.AsList.Get(0)
List.Make

for each OriginalPoint in theListofPoints
x = OriginalPoint.GetX
y = OriginalPoint.GetY
teme = x
tempY = y

for each centroid in anFtab
theCentroid = CentroidList.Get(centroid)
cx = theCentroid.GetX
cy = theCentroid.GetY
distX = x - cx
distY = y - cy
Distance = OriginalPoint.Distance(theCentroid)
Desired = DesiredList.Get(centroid)
Radius = RadiusList.Get(centroid)
Mass = MassList.Get(centroid)

if (Distance > Radius) then
Fij = Mass * (Radius/Distance)
else
Fij = Mass * ((Distance‘2)/(Radius*2))*(4-3*
(Distance/Radius))
end

Fij = Fij * ForceReductionFactor/Distance
teme = teme + (Fij * distX)
tempY tempY + (Fij * distY)

end

theNewPointList.Add(teme@tempY)

count = count + 1

av.SetStatus(100*(count/TotalPoints))
end

theNewShape = Polygon.Make({theNewPointList})

anFtab.SetValue(anFtab.FindField("Shape"), r, theNewShape)
theNewShape = anFtab.ReturnValue(anFtab.FindField
("Shape"), r)

theAreaField = anFtab.FindField("Area")
thePerimeterField = anFtab.FindField("Perimeter")
anFtab.QueryShape(r,thePrj,theNewShape)

theArea = theNewShape.ReturnArea

thePerimeter = theNewShape.ReturnLength
anFtab.SetValue(theAreaField, r, theArea)
anFtab.SetValue(thePerimeterField, r, thePerimeter)

93

 

end

def = (theTheme.GetName.Left(3) + iterationCount.AsString +
"acg.shp").AsFileName

iterationCount = iterationCount + 1
anFtab.Export(def,Shape,FALSE)

end

MsgBox.Info("The mean error is"++MeanError.AsString++".",
"Mean Error")

anFtab.SetEditable(FALSE)
av.ClearMsg
av.ClearStatus

fthm = FTheme.Make(anFtab)
theView.AddTheme(fthm)
theView.GetWin.Activate

First published in Cartography and Geographic Information
Systems, vol. 24, no. 2, 1997, pp. 101-109, and reproduced
with the kind permission of the author of the code, Charles
Jackel, and the publisher of CaGIS, the American Congress on
Surveying and Mapping; modified by Jennifer A. Ware.

94

APPENDIX B

Text of the cartogram.test

This appendix contains the text of the cartogram test
in its entirety. The names of the labeled enumeration units
for each task are displayed in brackets. The correct
responses to the third task are also displayed in brackets.
Obviously, this information was not included on the actual
test screen but is included here to inform the reader. The
order of the cartograms is only one of the three orders that
were used. All text remained the same for each cartogram,
no matter what order the cartogram appeared in.

To obtain a copy of the cartogram test program in its
original softcopy form, please contact the author at
warejen1@pilot.msu.edu. This email address is valid until
December 2000.

 

Frame 1. Cartogram Test. Click NEXT to continue.

Frame 2. A cartogram is a map on which enumeration units
such as states or provinces are drawn
proportionate to some variable other than
geographic space. The size of an enumeration unit
represents the data value of that enumeration
unit. For example, states may be drawn
proportionate to their population.

Frame 3. This is a geographic map of the New England region
of the United States, where the states are drawn
proportionate to geographic space.

Frame 4. This is a cartogram of New England, where the
states are drawn proportionate to the number of
births. Click BACK to compare with the geographic
map.

Frame 5. Now that you’ve been introduced to the concept of
a cartogram, answer the following question by
clicking on one of the circles to the left.

A cartogram is a map on which...

0 The sizes of the enumeration units are randomly
changed. Larger units have no real
significance.

0 The sizes of the enumeration units are the same
as on a geographic map. Larger units indicate
larger land area.

95

 

Frame 6a.

Frame 6b.

Frame 7.

Frame 8.

Frame 9.

Frame 10.

Frame 11.

Frame 12.

Frame 13.

o The sizes of the enumeration units represent
the data. Larger units indicate larger data
values.

0 The sizes of the enumeration units mean
nothing. Larger units are no different than
smaller units.

Oops! Try again. Go back and read the

definition.

Correct! You understand the definition. Please

continue.

Cartograms can be animated, allowing you to view

the transformation between the geographic map and

the cartogram. The following screens will display
examples of two different types of animation. Use
the “Auto Play/Slide Play button to explore both
formats as many times as you wish. Click NEXT
from either screen when you are familiar with both
formats.

Click PLAY to automatically transform the map into

the cartogram. Click REWIND to reverse the

transformation.

Click on the red diamond and drag it anywhere

within the white column to manually control the

transformation between the map and the cartogram.

The test will ask three questions about each of

twelve cartograms. You will be able to refer to

the cartograms while answering the questions. Be
sure to study the cartograms carefully. You will
get only one chance to answer each question. Once
you select your answer, you will move
automatically to the next screen. The following
screens show examples of the types of questions
you will be asked. Answer the questions as if you
were taking the test.

This is a sample test screen. Answer the sample

question.

Objective: Find the state on the cartogram that

corresponds to state A on the geographic map.

[Answer: Vermont]

Instructions: Click once on the corresponding

state on the cartogram.

This is another sample test screen. Answer the

sample question.

Objective: Find the state on the cartogram that

corresponds to state B on the geographic map.

[Answer: Massachusetts]

Instructions: Click once on the corresponding

state on the cartogram.

This is a third sample test screen. Answer the

sample question.

96

Frame

Frame
Frame

Frame

Frame

Frame
Frame

Frame

Frame

14.

15.
16.

17.

18.

19.
20.

21.

22.

Objective: Using the cartogram, determine which
state, A or B, has the greater number of births.
[Answer: B]

Instructions: Click on one of the following
answers.

0 .A is greater
0 B is greater

0 .A and B are equal

This ends the introduction. Do you want to view
the introduction again? Are you ready to begin
the test?

Cartogram 1 [United States/Population/Still]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Utah]

Instructions: Click once on the corresponding
state on the cartogram.

Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Arkansas]

Instructions: Click once on the corresponding
state on the cartogram.

Objective: Using the cartogram, determine which
state, A or B, has the greater population.
[Answer: Equal or adjusted answer B]
Instructions: Click on one of the following
answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 2 [United States/Cattle/Still]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Indiana]

Instructions: Click once on the corresponding
state on the cartogram.

Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Wyoming]

Instructions: Click once on the corresponding
state on the cartogram.

Objective: Using the cartogram, determine which
state, A or B, has the greater number of cattle.
[Answer: B]

Instructions: Click on one of the following
answers.

0 .A is greater
0 B is greater

97

Frame
Frame

Frame

Frame

Frame
Frame

Frame

Frame

23.
24.

25.

26.

27.
28.

29.

30.

0 .A and B are equal

Cartogram 3 [United States/Population/Play]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Kansas]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the
transformation. Repeat as desired. Then, click
once on the corresponding state on the cartogram.
Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Pennsylvania]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the
transformation. Repeat as desired. Then, click
once on the corresponding state on the cartogram.
Objective: Using the cartogram, determine which
state, A or B, has the greater population.
[Answer: B]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the
transformation. Repeat as desired. Then, click
on one of the following answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 4 [United States/Cattle/Play]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Kentucky]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the
transformation. Repeat as desired. Then, click
once on the corresponding state on the cartogram.
Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Nevada]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the

' transformation. Repeat as desired. Then, click

once on the corresponding state on the cartogram.
Objective: Using the cartogram, determine which
state, A or B, has the greater number of cattle.
[Answer: A]

Instructions: Click PLAY to transform the lower
map into a cartogram. Click REWIND to reverse the
transformation. Repeat as desired. Then, click
on one of the following answers.

0 .A is greater

98

 

 

Frame
Frame

Frame

Frame

Frame
Frame

Frame

Frame

31.
32.

33.

34.

35.
37.

38.

39.

o B is greater

0 .A and B are equal

Cartogram 5 [United States/Population/Slider]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Missouri]

Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click once on the
corresponding state on the cartogram.

Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Connecticut]

Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click once on the
corresponding state on the cartogram.

Objective: Using the cartogram, determine which
state, A or B, has the greater population.
[Answer: A]

Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click on one of the
following answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 6 [United States/Cattle/Slider]
Objective: Find the state on the cartogram that
corresponds to state A on the geographic map.
[Answer: Colorado]

Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click once on the
corresponding state on the cartogram.

Objective: Find the state on the cartogram that
corresponds to state B on the geographic map.
[Answer: Tennessee]

Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click once on the
corresponding state on the cartogram.

Objective: Using the cartogram, determine which
state, A or B, has the greater number of cattle.
[Answer: Equal or adjusted answers A and B]
Instructions: Click on the red diamond and drag
within the white column to transform the lower map
into a cartogram. Then, click on one of the
following answers.

99

Frame
Frame

Frame

Frame

Frame
Frame

Frame

Frame

Frame
Frame

40.
41.

42.

43.

44.
45.

46.

47.

48.
49.

o .A is greater
0 B is greater

0 .A and B are equal

Cartogram 7 [China/Population/Still]

Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Sichuan]

Instructions: Click once on the corresponding
province on the cartogram.

Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Shanxi]

Instructions: Click once on the corresponding
province on the cartogram.

Objective: Using the cartogram, determine which
province, A or B, has the greater population.
[Answer: A]

Instructions: Click on one of the following
answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 8 [China/Cattle/Still]

Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Fujian]

Instructions: Click once on the corresponding
province on the cartogram.

Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Henan]

Instructions: Click once on the corresponding
province on the cartogram.

Objective: Using the cartogram, determine which
province, A or B, has the greater number of
cattle. [Answer: B]

Instructions: Click on one of the following
answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 9 [China/Population/Play]

Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Qinghai]

Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.

100

Frame 50.

Frame 51.

Frame
Frame

Frame

Frame

Frame 56.

52.
53.

54.

55.

Then, click once on the corresponding province on
the cartogram.

Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Hunan]

Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.
Then, click once on the corresponding province on
the cartogram.

Objective: Using the cartogram, determine which
province, A or B, has the greater population.
[Answer: B]

Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.
Then, click on one of the following answers.

0 .A is greater
0 B is greater

0 .A and B are equal

Cartogram 10 [China/Cattle/Play]

Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Gansu]

Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.
Then, click once on the corresponding province on
the cartogram.

Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Hubei]

Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.
Then, click once on the corresponding province on
the cartogram.

Objective: Using the cartogram, determine which
province, A or B, has the greater number of
cattle. [Answer: A or adjusted answer Equal]
Instructions: Click PLAY to transform the right-
hand map into a cartogram. Click REWIND to
reverse the transformation. Repeat as desired.
Then, click on one of the following answers.

0 .A is greater
0 B is greater

0 .A and B are equal
Cartogram 11 [China/Population/Slider]

101

Frame 57. Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Yunnan]
Instructions: Click on the red diamond and drag
within the white column to transform the right-
hand map into a cartogram. Then, click once on
the corresponding province on the cartogram.

Frame 58. Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Jiangxi]
Instructions: Click on the red diamond and drag
within the white column to transform the right—
hand map into a cartogram. Then, click once on
the corresponding province on the cartogram.

Frame 60. Objective: Using the cartogram, determine which
province, A or B, has the greater population.
[Answer: Equal or adjusted answer A]
Instructions: Click on the red diamond and drag
within the white column to transform the right-
hand map into a cartogram. Then, click on one of
the following answers.

0 .A is greater
0 B is greater

0 .A and B are equal
Frame 61. Cartogram 12 [China/Cattle/Slider]
Frame 62. Objective: Find the province on the cartogram that
corresponds to province A on the geographic map.
[Answer: Shaanxi]
Instructions: Click on the red diamond and drag
within the white column to transform the right—
hand map into a cartogram. Then, click once on
the corresponding province on the cartogram.
Frame 63. Objective: Find the province on the cartogram that
corresponds to province B on the geographic map.
[Answer: Anhui]
Instructions: Click on the red diamond and drag
within the white column to transform the right-
hand map into a cartogram. Then, click once on
the corresponding province on the cartogram.
Frame 64. Objective: Using the cartogram, determine which
province, A or B, has the greater number of
cattle. [Answer: B]
Instructions: Click on the red diamond and drag
within the white column to transform the right-
hand map into a cartogram. Then, click on one of
the following answers.

0 .A is greater
0 B is greater
0 .A and B are equal

102

Frame 65. The test is now over. Thank you again for your
participation.

103

APPENDIX C
Pretest and posttest questionnaires

PRE - TEST QUESTIONNAIRE
Number Gender ( )M ( )F Age
General Experience with Cartograms

1” Have you ever heard of a map called a cartogram before?
( )yes ( )no

2. If yes, what is your definition of a cartogram?

Z3.Have you seen a cartogram in any of these contexts?
Check all that apply.
( )have never seen a cartogram
( )in an atlas
( )in a textbook
( )in a classroom, used by a teacher as a visual aid
( )in a journal, newspaper or other printed media
(
m
(

)on the Internet, television or other electronic
edia

)other - please describe:

44.Have you used a cartogram in any of these contexts?
Check all that apply.
( )have never used a cartogram
( )in a classroom exercise or lesson
( )to answer a test question
( )for personal reference
( )included someone else’s cartogram in your paper or
project
( )created your own cartogram for use in a paper or
project
( )other — please describe:

104

Checking Your Mental Maps of the United States and China

The following questions require the most time and effort.
You may take up to 15 minutes to complete these two
questions. Try to be as accurate as you can, but don’t be
embarrassed by your effort. You are not receiving a score
on this part of the test, and you will not be asked to
answer any other questions like these.

ES.Using only your memory, draw a map of the continental
United States with as many individual states as you can.
Please label as many states as possible.

EL Using only your memory, draw a map of the People’s

Republic of China with as many individual provinces as
you can. Please label as many provinces as possible.

105

POST-TEST QUESTIONNAIRE

Number

 

Assessment of the Testing Experience

1.Had you ever taken a computerized test like this one
before?
( )yes ( )no

2.Eud.you feel comfortable using the computer to take the
test?
( )yes ( )neutral ( )no

23.Did you feel the introduction adequately prepared you to
take the test?
( )yes ( )neutral ( )no

4. If you said no, in what way did you feel unprepared?

EL Was the definition of a cartogram helpful?
( )yes ( )neutral ( )no

€S.Were the examples of the different formats (automatic
animation, manual animation) helpful?
( )yes ( )neutral ( )no

'7.Were the examples of the test questions helpful?
( )yes ( )neutral ( )no

£3.Was it easy to navigate through the testing program?
( )yes ( )neutral ( )no

9.If you said no, what part of the program was difficult to
navigate?

10. Which format did you find easiest and fastest to use to
locate areas A and B?
( )static, no movement
( )automatically animated using the “play” button
( )manually animated using the slider bar

11. Why did you prefer your choice?

106

12. Which format did you find easiest and fastest to use to
compare the sizes of A and B?
( )static, no movement
( )automatically animated using the “play” button
( )manually animated using the slider bar

13. Why did you prefer your choice?
14. Do you think that cartograms could be a useful tool for
presenting spatial information?
( )yes ( )neutral ( )no

15. Why or why not?

16. Any other comments about cartograms or the testing
experience?

107

APPENDIX D

Samples of mental maps

 

 

 

 

 

 

Figure 18. Sketch map of the United States (1).
Forty—eight states were identified. States are generally in
the correct positions and care was taken to draw correct
shapes and maintain topology. All states were labeled
correctly, but labels were deemed indistinct for printing
purposes and removed from this copy.

108

 

 

 

h ,_ r ‘\"“!
‘ ‘ v in .‘i
# ) \3

 

 

 

 

 

 

 

 

Figure 19. Sketch map of the United States (2).
Forty-four states were identified. States are generally in
the correct positions, but less effort was taken with regard
to correct shape. Most states were labeled correctly, but

labels were deemed indistinct for printing purposes and
removed from this copy.

109

 
    
    
  

  

w DAxarA
S. DkflaTA

 

H.0mauwa

3: (Mun/4

Figure 20. Sketch map of the United States (3).
Twenty-nine states were identified. States are generally in
the correct positions, and some are the correct shape.
Others are noted only by name.

110

 

A“
t,\

Figure 21. Sketch map of China (1).
Twenty-seven provinces were identified. Provinces are
generally in the correct positions, but little effort has
been taken to maintain correct shape. Most provinces were
labeled correctly, but labels were deemed indistinct for
printing purposes and removed from this copy.

111

Figure 22. Sketch map of China (2).
Two provinces have been identified, one in the wrong
location. The general shape of the country is correct
though the province shapes are not.

amm

Figure 23. Sketch map of China (3).
No provinces have been identified. An attempt was made to
draw the correct outline of the country.

112

B I BLI OGRAPHY

113

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