i JJJJJJJJJJJJ JJJJJJJJ JJJJ JJJJJJ 310559 6799 J This is to certify that the thesis entitled THE EFFECTIVENESS OF COLOR DOT MAPS IN REGION PORTRAYAL presented by Jill Patricia Eilertsen has been accepted towards fulfillment of the requirements for Masters degree in Geo graphx [EM/{Zane Major professor 0-7639 OVERDUE FINES: 25¢ per day per item ‘ RETURNING LXBRARY MATERIALS: J M 5331-”; j Place in book return to move ‘I. _. , Kn} «w»: .4 charge fro-i circulation accords Wm AUG 1 91997 I”; THE EFFECTIVENESS OF COLOR DOT MAPS IN REGION PORTRAYAL By Jill Patricia Eilertsen A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Geography 1980 ABSTRACT THE EFFECTIVENESS OF COLOR DOT MAPS IN REGION PORTRAYAL By Jill Patricia Eilertsen The ability of map readers to perceive regional information on multipattern dot maps which employ color to differentiate distributions, was examined in this study. The color dot mapping technique was compared to the conventional method of single distribution black and white dot maps, evaluating their effectiveness to commu- nicate regions with transitional boundaries. The effec- tiveness of each mapping technique was assessed in a psychophysical experiment in which subjects drew regional boundaries around perceived areas of distribution homo- geneity and mix. Two quantitative measures were employed to compare the responses; (1) the consistency with which subjects located regions within the map, and (2) the accu- racy of dot composition within perceived regions. The region drawing responses indicated that the color dot map was slightly more effective in terms of both consistency and accuracy, however the differences were not statisti- cally significant. It was concluded that the color dot map technique is at least as effective as single distribu- tion black and.white dot maps. ACKNOWLEDGMENTS I would like to express my appreciation to those professors and friends who assisted me in the completion of this study. Special thanks are due Dr. Richard Groop who provided assistance, advice and needed encouragement throughout the project. I owe him more for his help during my program at Michigan State than I can express here. I also wish to thank Dr. Richard Smith for his editorial assistance, and additional ideas and guidance. Finally, I thank my friends and fellow students, especially Debbie Sadler and Robin Walker, for their help, encourage- ment, and understanding during my temporary moments of insanity while counting dots. ii TABLE OF CONTENTS LIST OF TABLES , LIST OF FIGURES, CHAPTER I. INTRODUCTION. Background and Development of the Research Problem . Problem Statement . II. EXPERIMENTAL DESIGN AND METHODOLOGY . Introduction. . Design of the Experimental Maps Testing Methodology . . . . Task Design . . . Test Administration . III. DATA ANALYSIS . Introduction. . Consistency within the Map. Variance Standardization. Variance Ratio Comparisons. Accuracy within Regions . Additional Data Analysis. IV. SUMMARY AND CONCLUSIONS Summary of the Research . Conclusions APPENDIX A Test Instructions BIBLIOGRAPHY . iii Page iv l4 16 16 29 29 36 38 38 38 . 44 . 49 . 51 . 62 . 66 66 71 73 LIST OF TABLES Color Choices for Jenk's Color Dot Map . Color Choices for Color Dot Test Map Comparison of Variance Ratios. Comparison of Mean Error and Standard Deviation. Analysis of Variances F Test . Student's t Comparison of Means. Average Number of Regions Outlined per Subject . . . . . . . . . Responses to Multiple Choice Questions iv Page 11 29 49 57 60 62 63 65 Figure 5. (a-C) 6. 7. LIST OF FIGURES Example of Well-Defined Regional Boundaries. Four Definitions of the Great Plains Region. Example of a Conventional Black and White Dot Map . Examples of Region Drawing Responses Black and White Test Maps. Color Dot Test Map . Black and White Maps of the Combined (a- b) Dot Distributions . 8. 10. ll. 12. l3. 14. 15. 16. Sample Response of Perceived Homogeneous Regions . Sample Response of Perceived Mixed Regions . Consensual Response Map - Region A, Color Dot Map . . . . . . Relationship between Region Drawing and Variance. . . . . . . . . Region Perception Variability Visualized as Three-Dimensional Frequency Surfaces Frequency Surface of the Consensual Response Map Presented in Figure 10 . Total Subject Consensus in Regional Boundary Placement. Triangular Graph Used in the Accuracy Analysis . . Sample Triangular Graph — Region A, Color Group . . . . . Page 2 4 20 23-25 26 30-31 33 34 . 4O 42 . 43 . 45 46 53 55 CHAPTER I INTRODUCTION The concept of the region is central to geographic understanding. Although the definition of the term 'region' has been subjected to continual debate, "regions continue to remain one of the most logical and satisfactory ways of organizing geographical information" (Haggett, et a1. 1977). In very general terms, a region is an area with characteristics of internal homogeneity within measured or theorized geographic distributions. Regions are defined by boundaries and, therefore, the map is the most suitable and most used description of regions. Two kinds of regions are frequently portrayed by map makers. The first type are regions with sharp, well- defined boundaries. The division of the United States and Canada into states and provinces for political administra- tive purposes are familiar examples. Other examples in— clude merchandising districts established across the coun- try by sales companies, or the division of the United States into commercial-financial regions by the Federal Reserve Bank (Figure 1). These types of regions are pre- cisely defined and can be delimited.on a map with a single line. Their portrayal causes few problems for the 1 THE FEDERAL RESERVE DISTRICTS 0 BANK CITY OF EACH DISTRICT 1 Boston 7 Chicago 2 New York 8 St. Louis 3 Philadelphia 9 Minneapolis 4 Cleveland 10 Kansas City 5 Richmond 11 Dallas 6 Atlanta 12 San Francisco Figure 1. Example of Well-Defined Regional Boundaries. (From Murphey, An Introduction to Geography, 1971) cartographer. The second type of region geographers and cartogra- phers must frequently portray are those with transitional boundaries. Regional characteristics of certain geographi- cal distributions change gradually over space between one homogeneous region and another, rather than ending abruptly. The American South and the Corn Belt for example, are regions whose identity depends on characteristics more strongly and unanimously present in central parts of the region than in peripheral areas. The portrayal of these regions which merge in hazy transition zones presents the cartographer with difficult communication problems. 3 The subject of this research is an empirical examina- tion of the effectiveness of an unconventional thematic mapping technique, multipattern color dot maps, in communi- cating regional information to the map user. The purpose is to determine whether or not multicolor dot maps offer the cartographer an effective solution to the problem of representing regions with transitional boundaries. This chapter presents a discussion of the development of the research problem, including a review of previous cartogra- phic literature pertaining to color dot maps. Two research questions are introduced relating to the effectiveness of color dot maps in region communication. Background and Development of the Research Problem Jenks (1953) states that cartographers frequently rely on mapping techniques which promote misinterpretation of areal relationships on the part of the map reader. One such technique involves the use of bold contrasting lines to represent boundaries which are transitional in nature and, therefore, based upon interpretation. Jenks suggests that these errors result in poor communication of the map message from the map maker to the map reader. While the cartographer who drew the boundary meant it to represent the middle of a much wider zone of transition, the average map reader often misinterprets a line as an abrupt change in regional characteristics. Comparison of the four maps in Figure 2, borrowed from an introductory geography text, illustrates this Figure 2. Four Definitions of the Great Plains Region. (From Broek and Webb, A Geoggphy of Mgrkind, 1973, p.13) 5 problem in region communication. Each of these maps repre- sents a definition of the Great Plains region, symbolized by a closed, bounding contour and uniform.shading within the boundary. However, no two maps fully agree to the area's exact extent because each author has defined the essential feature of the region from a slightly different perspective. If a map user were to view only one of these representations, it is likely he would misinterpret the boundary as an abrupt change in all essential features of the region, without understanding the varying transitional patterns of the many Great Plains characteristics. Although the method often results in poor communica- tion of the map message, cartographers have continued to use bold contrasting lines to represent regions with transi- tional boundaries for two reasons. First, the method is accepted, and precedent is hard to break. Second, it is much easier for a cartographer to draw lines around areas and fill these areas in with solid patterns or colors, than it is to compile and produce a more appropriate map by transitional pattern or color blending (Jenks, 1953, p.4). However, these reasons fail to provide an excuse for, or a solution to, this cartographic problem in region portrayal. The traditional dot map method of thematic mapping offers a partial solution to the cartographic problem of portraying homogeneous regions separated by transition zones. On a simple black and white dot map, spatial data are symbolized by varying numbers of uniform dots, each HOGS, NORTH CAROLINA (1967) ' . ' 5- f : :-'..’ 9133535: . . - ~ :s-:'=-.-.;--. \ o .. . .20....0..e. o 0'... co. . e ...0:o...e':'.°.. " .0. .:0:3 '3'... ‘3'... .0. ..:.o.o .. :.:.. I. :-.‘s‘:' :' Rita-‘53:... ::{:‘. 333:“: 19,..- °e .fi'.' .0“: 0.0.0 0.. :"fion ‘ .0". .e‘ . o . . .. ‘.."'o: ‘00": .0 o . o o O o o O o ' eh'.'. 0:... g .353.“ “5-. :fiw-gr o .0... :g: 0.0.. :0 2%? U9 inununu ---.3. Figure 3. Example of a Conventional Black and.White Dot Map. (From.Jenks, "Visual Integration in Thematic'Mapping - Fact or Fiction", 1973) representing the same amount of a given phenomenon (Figure 3). The dots are placed as near to the actual location of the phenomenon as the map scale and the detail of the data allows. While preserving much of the detail of the original spatial distribution, the dot map performs several impor- tant comparative functions. A dot map shows the location of individuals and clusters in a distribution, as well as the extent of the phenomenon over space. The approximate Egggg of the phenomenon can be determined by following the outer edge of the dot distribution. Through variations in the spacing between groups of dots, subpatterns can form reflecting the structure of the distribution (Turner, 1977). 7 In addition, the dot map provides the reader with a visual impression of relative density from place to place. Varia- tions in the dot density over space indicate trends in the rate of change of the distribution in various directions (Robinson, 1978). With a simple dot map, map readers are able to understand the transitional nature of distributions more clearly since the form.and extent of the distribution are defined by changes in the 'textural' detail of dot loca- tion and density, rather than by sharply defined boundaries. The dot map technique avoids the misleading effects of boundary lines used in regional representations. A limitation of the simple black and.white dot map method of region portrayal, however, is that only one dis- tribution can be shown on each map. This is a disadvantage since, in many instances, it is necessary that the map reader areally compare distributions of a number of related geographic phenomena to fully understand a particular re- gional concept. By comparing several dot patterns, a map reader may gain a better understanding of why a distribu- tion has the form.it does. Although map readers may be partially successful in mentally evaluating the spatial associations between individually mapped dot distributions, it seems probable that the communication of regional pat- terns and relationships would be improved if individual distributions of related phenomena were recorded in the same map space (Turner, 1977). Results of a study by McCarty and Salisbury (1961) in which the ability of map 8 readers to visually compare isopleth maps was examined, supports this idea. Responses to their psychophysical test indicated that visual comparisons of maps did not provide an effective means of determining the degree of association between individually mapped distributions. It is possible to represent several distributions on one map if differences in color, size, tone or shape are used to distinguish the various dot patterns. Multipattern dot maps have two potential advantages over single distri- bution dot maps. First, the multipattern technique reduces the number of individual maps required to portray a regional message. In addition, the method allows the map reader to make judgements about the association of various distribu- tions without having to mentally superimpose them.from separate maps. The multipattern dot map is the only sta- tistical mapping technique in which more than two distri- butions can be overlayed without considerable complexity and clutter (Turner, p.63). However, perceptual and physi- cal limits obviously restrict the cartographer in the number of distributions he can effectively represent on one map. To date, only a few attempts have been made to experi- ment with and assess the potential of displaying multiple data sets on a single map using dot-like symbols. Because color and shape are most frequently used to represent nomi- nal differences among point symbols (Robinson, et a1, 1978), it is likely that these visual variables would be most 9 effective in representing nominal differences between dot patterns. As a result, cartographic techniques employing color or shape distinctiveness have been the topic of li- mited research pertaining to multipattern dot maps. In one such study, Turner (1977) evaluated the role of shape as a variable for distinguishing between point- symbol patterns on black and.white maps. Based on psycho- physical testing, Turner established a set of three symbol pattern groups from 24 geometric shapes which viewers judg- ed to be maximally different from one another. He recomr mended that a single symbol could then be selected from each group to distinguish distributions on multipattern dot maps. From these results, Turner attempted to iden— tify any relevant dimensions which might be controlled in order to improve pattern discrimination. Examination of the symbol groups showed that the dimensions of (1) tonal contrast (percent of area inked) and (2) contour variation (complexity) were most important in a symbol's discrimina- bility (Turner, p. 122-3). To a limited extent, Turner also investigated the degree to which subjects were able to determine the spatial relationship between multiple black and white patterns dis- tinguished by shape. Test subjects were asked to perform a comparison task on target patterns presented alone and later with one and three other symbol patterns. Various combinations of symbol types and pattern densities were tested. The results indicated that people were able to 10 discriminate a target pattern in a mix of up to four dis- tributions differentiated by dissimilar shapes (Turner, p. 186). In an earlier study, Jenks (1953) experimented with color in an attempt to find a more satisfactory method of blending patterns to represent regions with transitional boundaries. Jenks' work with color was based on the tech- nique of 'pointillismT or juxtapositional color mixture. Color psychologists have demonstrated through experimenta- tion that if a color is broken up into its component parts, and these component colors are presented in small dots, the sensation of the original color will be obtained if the dots are viewed at a distance. In adapting this idea to cartography, separate colors are assigned to each phenome- non mapped on a multipattern dot map. As the mapped dis- tributions of the phenomena change, so does the balance between different colored dots. Ideally, if the color dot map is viewed at a distance, a new distinctive color will be perceived in each map area having its own distributional pattern. Theoretically, juxtapositional mixture of color dots should result in the map readers' perception of larger areal patterns, and provide a possible solution to the car- tographic problene of transitional shading and the communi- cation of transitional boundaries. Jenks experimented with the cartographic application of pointillism.by producing a unique map of crops harvested in the United States in 1949. The sample map employed ll eleven different colors to represent the dot distributions of eleven major crops. Colors were chosen to represent each crop based on three factors. First, colors should remind the map reader of the crop they represent. Second, high value, low acreage crops sudh as tobacco or truck farming crops, should be a more intense hue than the widely grown crops. Finally, selected minor crops which tend to change the crop character of broader areas should be repre— sented by colors of moderately high intensity (Jenks, 1953, p.5). Table 1 lists the colors which were chosen to repre- sent each major crop. Table 1 Color Choices for Jenks' Color Dot Map Yellow - small grains Brown — peanuts Orange - corn Red - tobacco Tan - sorghum Purple - fruit Light green - hay Black - truck crops Light blue - cotton Gray - other crops Dark green - soybeans The map was constructed at a scale of l:2,500,000 allowing acreages for each crop to be plotted at the county level. Each dot on the map represented 10,000 acres of a harvested crop. Although Jenks found that his color dot map of crop production demonstrated color blending at various viewing distances, he encountered a number of design and production problems requiring further examination. First, Jenks 12 suggested that the technique might be improved by experi- menting with different colors. With his choice of pastel colors for some crops, the loss of color intensity was too great in areas where dots were isolated. Additionally, he suggested the map might be more effective if the number of distributions was reduced from eleven. As is the case with gray tone shadings, there is a perceptual limit to the numr ber of colors that viewers can distinguish in a map reading context. Jenks also believed that the scale of the map was too large, causing extreme detail to distract from.the per- ception of larger areal patterns. Finally, Jenks' greatest criticism of the map resulted from problems in the printing process. The technique requires extremely accurate regis- tration, especially if four-color process printing is used. Poor registration was a problem on the crop map, as well as a lack of consistency in the hues and values of the printed colors. Despite these design and production problems involving color selection, scaling,and difficulties with the printing process, Jenks recommended further experimentation with the color dot map technique because it fulfils several differ- ent needs of the map reader. Color dot maps provide ex- cellent detail about distributions when viewed close enough so individual dots are clearly visible. Transitions bet- ween distributions are also accurately rendered by changing balances of dots, portraying the larger areal pattern and offering a possible solution to the problem.of representing 13 regions with transitional boundaries. It was Jenks' belief that, "the technique could do much to improve the map user's understanding of both interpretative boundaries and the transitional nature of many distributions" (Jenks, 1953, p.5). In the 27 years since Jenks completed his initial re- search and recommendations, multipattern color dot maps have received minimal attention in cartographic literature. While this technique may offer a possible solution to the problem of region portrayal, to date it has not been evalu- ated experimentally to determine whether it is an effective solution. The true value of the color dot map as a commu- nication device will only be realized after potential color problems and region perception problems are studied. Among the major color problems involved in multipat- tern dot maps is that of color selection. Thomas (1955) suggested that color dot maps may result in faulty visual impressions if three requirements necessary to maintain the proper relationships, or 'balance', between hues, value and chroma are not fulfilled. The requirements are: (1) each color must be distinctive (different in hue) and therefore easily differentiated from.surrounding colors; (2) contrast between each color and the background must be equal (identical value); and (3) all colors must be equally vivid (equal chroma) so that no color covering an area of the map can overpower other colors covering an equal area. As many as five colors can be selected.with essentially 14 the same visual impact for use on a color dot map. Thomas recommended the use of red, yellow, green, blue and purple hues, each with a value and chroma of 50 percent. He con- ducted an experiment with fifteen college students which indicated that these colors were balanced and met his re- quirements for use on multicolor dot maps. However, his precise recommendations have yet to be evaluated in a map context. Potential region perception problems must also be con- sidered with respect to the effectiveness of color dot maps. It is important to determine whether map readers are capable of seeing regions by recognizing variations in the balance of different colored dots across the map, and whether the maps communicate the transitional nature of distributions to the reader. In addition, if it is found that map readers do see regions, how consistent as a group are their perceptions, and do their perceptions correspond to the intent of the map message? Problem Statement This study examines the ability of map readers to per- ceive regions on multipattern dot maps which employ color to differentiate distributions. The innovative color dot mapping technique is compared to the conventional method of black and white single distribution dot maps, evaluating their effectiveness to communicate regional information, and the transitional nature of geographic distributions, to 15 the map user. Psychophysical testing techniques are em- ployed to measure and evaluate communication effectiveness. The examination of the mapping techniques focuses on two questions: (1) Does the average map reader see regions of homo- geneity better with single distribution black and.white dot maps, or with one multipattern color dot map? (2) With which of the two mapping techniques, black and white or color dot maps, does the average map reader more easily see regions of mix, or transition? Measures of consistency and accuracy in regional percep- tions are employed to evaluate the effectiveness of the two mapping techniques. Previous literature by Jenks (1953) and Turner (1977) suggests that map readers are likely to be more consistent and accurate in perceiving regional information with multi- pattern dot maps. Their reasoning is based on the fact that with multipattern maps the reader can make spatial associations without having to mentally superimpose differ- ent dot distributions from.separate maps. By addressing these two research questions in a psychophysical testing experiment, it is hoped to determine, if in fact, color dot maps are a more effective method of region communica- tion than the conventional black and white dot map. CHAPTER II EXPERIMENTAL DESIGN AND METHODOLOGY Introduction A number of different psychophysical testing proce- dures are possible, however, many of these are not fully understood and, therefore, have been misinterpreted and used inappropriately by cartographers. ‘McCleary (1975) believes that in many recent examples of cartographic research the investigators have begun by asking the wrong questions. He cites faulty procedures in a number of psychophysical experiments dealing with the establishment of gray scale curves and the study of graduated symbol size. The message of McCleary's discussion is that ques— tions asked in test tasks should not parallel the cartog- rapher's method for choosing or producing a symbol, but rather match what the user will do when he confronts the map. In other words, an experiment should be structured to approximate the map using situation with consideration given to the intent of the map message. In terms of region perception, this is a demanding requirement (Lavin, 1979, p.143). Thematic maps are designed to communicate two general classes of information to the map reader. The first is 16 l7 tabular information which can be extracted, fact by fact, from.individual map symbols. The second class of informa- tion which can be transferred is the integrative type. This information is not gained by examining individual symbols, but rather from a combining process wherein symr bols are merged into fields to form patterns or regions (Jenks, 1973, p.27). The majority of psychophysical studies in cartography to date have examined the physical properties of individual symbols and the effects of individual symbols on map read- ing tasks, usually involving the transmission of tabular data. Very little research has been done to examine the perception of patterns on maps and the transmission of in- tegrative data. This research gap is a serious one since the primary use of thematic maps is to illustrate integra- tive or regional patterns and distributions to the map reader. One reason for this inequity in psychophysical carto- graphic research is suggested by Lavin (1979) in his exami- nation of region perception variability on choropleth maps. He states that, "...unlike the case of symbol properties, the cartographer frequently has no clear vision of the dis- tributional message he wishes to communicate" (Lavin, p.144). Without a precise definition of the intended map message, the relationship between the information extended, and that actually received by the viewer, cannot be exa- nined in total. 18 The presentation and perception of regional informa- tion on maps is a prime example of this problem. Until cartographers can identify precise definitions of the re- gions they wish to portray, studies concerning the region communication process must be restricted to an analysis of perceptions of the map user. Such an analysis might in- volve how the map user's perceptions relate to the stimulus (in this study, black and.white or color dot maps); and how his perceptions compare with those of other map users (re— gion perception variability) (Lavin, p.145). Based upon the recommendations of McCleary (1975), psychophysical experiments which are a part of region com- munication studies should be designed to approximate the region perception experience. Since... "it is assumed that the perception of regions involves the establishment of lines of demarcation between mapped areas which are somehow seen as being internally homogeneous, an appropriate experi- mental task is to request that the map user physically re- produce those boundary lines on maps presented to him” (Lavin, p.145). In the present study, test subjects were asked to draw boundary lines around specified areas of dis- tributional purity and mix within dot patterns. This test- ing technique assumed a direct link between the regions subjects form mentally, and their ability to reproduce these mental constructs. Region drawing has been used as an experimental task by a few cartographers. In an attempt to increase l9 cartographic understanding about different forms of map generalization, Jenks (1973) examined subject consistency in outlining areas of high, medium and low density on a dot map (Figure 4). Although the responses were highly varied, he found each to be a logical generalization of the test map. ‘McCleary (1975) also asked subjects to sep- arate differences in dot density in a regionalization experiment. Two styles of region drawing emerged in his test responses, and are referred to as the 'atomist' and the 'generalist'. The atomist is obsessed.with great de- tail,regardless of the overall pattern of density, while the generalist is concerned with portraying major regional trends. Region drawing was also employed by Lavin (1979) to determine the effect pattern complexity of a choropleth map has on regional perceptions. Results indicated that a direct relationship existed between perception variability and pattern complexity. The design and implementation of the color dot map experiment was fashioned after testing methodologies employed in these studies. Design of the Experimental Maps In order to make the evaluation of the color dot map technique directly applicable to common cartographic as- signments involving region portrayal, real world data were used to construct the test maps. Because religious distri- butions are representative of the complex patterns cartog- raphers must often portray, data from a recent survey of 20 «JJJ. I“ ,. IJJIJIJJJJJJJJJJJ ' I! I'J' 4%! J" J. . i i‘ . ii‘. V i‘ ‘ ' , ‘ , J i‘,l Figure 4. Examples of Region Drawing Responses. These ten very different generalizations of a dot map were created by students who were asked to subdivide the map into areas of high, medium and low density. (From Jenks, "Visual Integration in Thematic Mapping - Fact or Fiction", 1973) 21 church membership in the United States (Johnson, et a1. 1974) were chosen to produce the experimental test maps. The survey was administered by the Glenmary Research Center on a county level in 1971. Over 50 religious denominations were included in the study. The three-state area of Indiana, Ohio and Kentucky was selected as the geographic base for the test maps due to a number of factors. First, examination of the county meme bership statistics in these states showed that three domi- nant religious affiliations exist: the Catholic Church, the United Methodist Church, and the Southern Baptist Conven- tion. This was a practical number of distributions to represent on a multipattern color dot map given perceptual limitations and color production costs. In addition, it seemed reasonable to ask test subjects to mentally compare three separate black and white dot distributions. A second reason for selecting this geographic area was that the dominant religious distributions have characteristics of all three theoretical classes of point symbols: clustered, random and uniform, Finally, within Indiana, Ohio and Kentucky, the three distributions have areas of relative purity, and also areas which are highly mixed between two or three of the religions. Only the religious affiliations of the rural pOpula- tion in the three-state area.were mapped for practical purposes. The smaller range in data values among the rural population was more suited for representation on a dot map 22 than the dramatic value changes over space for the total population. Had the urban population been included, the resulting maps would either have had hundreds of overlap- ping symbols around the urban areas (use of a small dot value) or very few dots in sparsely settled areas (use of a large dot value). The numbers of rural members were cal- culated by multiplying the percent rural population (City and County Data Book, 1977) with the total number of ad- herants belonging to each religious group for every county. This data manipulation technique assumed that within the counties, the religious distributions were the same for both the urban and rural populations. Two sets of test maps were produced from the religious data for use in the region drawing experiment. The first set consisted of three black and.white dot maps, one map of each of the three dominant religions in Indiana, Ohio and Kentucky (Figures 5a, 5b and 5c). The second consisted of a single multipattern dot map portraying the same three religious distributions, each distinguished by a different color (Figure 6). The Catholics were mapped with blue dots, the United.Methodists with red dots, and the Southern Bap- tists with green dots. To ensure direct comparability bet- ween the black and white maps and the color dot map, con- sistency in scale, dot size, dot value, and exact dot place- ment was maintained. All maps were constructed within an 8%" x 11" page format, using dots of .05" diameter for each 1000 church members. In addition, no dots were allowed to 23 .mHmcHwHHo onu mo unmouom om um mums moonoouoou mum Anna Hoaoo ago no coauaooxo £ua3v mama umou HH< “ouoz .mmmz umoH ouwnz use xomam .mm muswwm u o o o o oooooouuooonoo o o oooo ooo o 0.. O O 0.... O O O OOOOO..~OO O O O O O O O 0 oo oooooooo oo oo o o ouo o o o o ooooooohuooooooo o oooooooH o o o o o o o ofiuoonoooooooonouooo oooo ooooH ouooouooo o o o oo o o o o o o o o o oooooooooooo o ooouo o ooooouooo o .oo o o o uoooooouoo o o ofloooo ooooo o o o o 23 .mecwwHHo one mo unmoumm em up who: moonuouoou mum Aamfi Hoaoo onu mo cowuaooxm nua3v mama umou HH< ”ouoz .mamz puma ouwnz pom xomam .mm oufiwwm 24 .mde umoh ouauz pom xomam .bm 3:me 25 Black and White Test Maps. Figure 5c. 26 27 overlap between the three distributions in order to main- tain distinct colors on the multipattern map. Map titles and legends identifying the three religious distributions were eliminated to avoid any bias in region perception responses on the part of the test subjects. Had the distributions been explained, it is possible that pre- viously formed concepts about the religions might have in- fluenced the test results. Instead, each distribution was identified by an upper case letter. On the black and white maps the letters were placed in the lower right-hand corner. The color dot map included a simple legend consisting of three boxes, each containing the same random pattern of dots in a different color. The blue dots representing the Catholics were identified by the letter 'A', the red dots showing the United Methodists by a 'B', and the green dots showing the Southern Baptists by a 'C'. The same letters were used to distinguish the distributions on the black and white maps. In order to avoid many of the registration problems encountered by Jenks on his color dot map of crop produc- tion, flat color printing was used to reproduce the color test maps rather than four-color process printing. Process printing uses four specific colors -- yellow, magenta, cyan and black -- to produce a full range of colors by overprinting. When printed, the four process colors appear as dots of solid color which combine in various sizes and patterns to duplicate the desired colors. The colors are 28 not created by physically mixing inks, but by the optical ‘mixing of the four process colors by the viewer's eyes (Craig, 1974). If perfect registration is not maintained in printing color dot maps, the process colors will not meet exactly around the dot edges leaving a halo effect. This problem can be avoided by using flat color printing wherein inks are mixed to match the map designer's color choices. However, a cost comparison should be considered. Because each color used in flat color printing requires a separate printing plate and a separate run on the press, the more colors used, the more expensive the job. As a result, since process printing requires a maximum of four press runs, it is best to print a color dot map of four colors or less (representation of two or three distribu- tions, and black) with flat color. If more than four colors are needed, the cartographer must compromise either quality or cost in choosing the printing method. Color selections for the multipattern dot map were based on suggestions made by Thomas (1955), and on cost limitations imposed by the flat color printing process. Three distinct hues, blue, red and green, were chosen from Thomas' recommendations, but his value and chroma guide- lines could not be followed exactly due to cost considera- tions. Printing costs were reduced by choosing commonly used ink tones which were in stock and did not have to be specially mixed. However, these tones did give the appear- ance of being equally vivid and equally distinct from.the 29 white background as Thomas advised. Exact color selections are listed in Table 2. Table 2 Color Choices for the Color Dot Test Map Distribution Religion Color A Catholics Pantone Blue #293U B United Methodists Pantone Red #185U C Southern Baptists Pantone Green #347U Testing Methodology Task Design Two test instruments were used in the psychophysical test design. The black and.white version consisted of a set of numbered, step-by-step instructions to complete the test task; three separate black and white dot maps of the religious distributions, Maps A, B, and C; and two black and.white maps of the combined dot distributions for re- cording purposes, Maps T and X (Figures 7a and 7b). The second test instrument, or color version, was similar. It consisted of a set of numbered instructions; a single multicolor dot map of the three religious distributions; and the same two black and white maps of the combined dot distributions, Maps T and X. The directions accompanying each test instrument were almost identical. The only dif- ference was in the identification of the test pieces. 30 .mcowuanauumfin won moawofioo mfiu mo mamz muwsz mam xomHm .mn whomwm o oooouoooo oooo o ouo ooooo oo ”ouo o o o o o ofiofinwooooooooounoooooouooo ooooo ”ouMHoooooo ooo oooooo o o o o oouoooo oo o ooo o o oooooooooooo o ooouo o ooo“ oo ooooo o oo o o o oo ooouoo oo oo ooo oo a3: . . 2.... .m........" . . . . ouooouuuoooo o o o 31 .mcoaus u no omen ooo emaagaoo we“ we mam: «page a so xowam .Bu shaman 32 There was no difference in the regions the subjects were asked to draw for either test version (Appendix A). The written instructions were very detailed to elimi- nate as many misinterpretations and incomplete responses by test subjects as possible. First, subjects were asked to look at, and compare the three distributions A, B and C. For those subjects taking the black and.white version of the test, this meant mentally superimposing the distribu- tions from separate maps. Next, using the black and.white maps, or the color dot distributions as general references, the subjects were asked to draw lines around areas they saw as predominantly homogeneous on a black and white map of the combined dot distributions (Map T). For example, first they were asked to outline and label areas which they per- ceived as predominantly distribution A, then distribution B, and finally distribution C (Figure 8). On the second map of the combined dot distributions (Map X), subjects were instructed to draw boundaries around areas which they per- ceived as predominantly mixed, for example, a combination of distributions AB, AC, BC or ABC (Figure 9). Upon com- pletion of the region drawing task, test subjects were pre- sented two multiple choice questions. The first rated the difficulty of identifying regions on the test maps. The second question asked.which type of region was easiest to see. Subjects were instructed to draw their regional boun- daries on the black and white maps of the combined dot .chfiwom mnoocowofiom oo>Hoonm mo omcoamom onEmm .m muswwm 33 ooooo o O O O. O O ooooooo ooouoo o o o o ooo o O O ...... 34 .mcowwom moxwz_om>aoouom mo omcoomom mamfimm .m whowam 35 distributions, rather than on the test maps, so responses from.the two test instruments would be directly comparable. The reason for this decision was that subjects viewing the black and.white maps had to mentally superimpose the sepa- rate dot distributions to compare them. Had the boundary lines been reproduced directly on one of the black and white test maps, error derived from mentally relocating the other distributions onto that map, and drawing regions based on those mental relocations, would have biased the comparison of the conventional and color dot mapping tech- niques. Error caused by mental relocation of distributions would not have occurred had lines been drawn directly on the color dot map because the distributions were all lo- cated and distinguished on the one map. By drawing all regions on the maps of the combined dot distributions, error due to the relocation of distributions and perceived regions, and that caused by subject ability to draw these regions, was similar for both test instruments. Therefore, it was assumed that response variation between the test instruments would be due to differences in the effective- ness of the two mapping techniques as regional communica- tion devices, and not caused by the experimental test design. A small preliminary test with eight subjects was con- ducted to determine whether the region drawing experiment was reasonable in terms of difficulty and the average time required to complete the test task. The pre-test was also 36 used to determine if the types of responses which would result would be appropriate for evaluation of the proposed research questions. It was found that subjects had little difficulty understanding the instructions, and in most cases were able to complete the experiment within 10 to 15 minutes. Examination of a number of responses indicated that the interior state boundaries might have influenced region drawing. However, pre—test subjects advised that the boundaries be included because they served as necessary reference lines during mental comparisons of the dot dis- tributions. Test Administration Each test instrument was administered to a separate group of 43 graduate and undergraduate students enrolled in geography laboratory courses at Michigan State University. None of the subjects dealt with both the black and white dot maps and the color dot map. The tests were conducted under normal viewing conditions in small laboratory classes where subjects had room to spread the maps out for visual comparison. No previous map reading experience was re- quired of the subjects. A brief oral introduction was given to each group of subjects before distributing the test instruments. The introduction included a short description of dots maps and their uses, and an explanation of the purpose of the ex- periment. The importance of reading the instructions care- fully, and following the numbered instructions step-by-step 37 was stressed to the subjects, as well as the fact they could make changes in their boundaries if they wished. Subjects were also advised that they were working under no time constraints. It was felt that a time limit repre- sented an unrealistic map reading situation. Finally, colorblind subjects were asked to identify themselves as the tests were being distributed so they could be given the black and white test version. Upon completion of the region drawing experiment, tests with incomplete responses, and those in which the instructions were not followed, were discarded. Five tests ‘were eliminated from the black and white group leaving a total of 38 responses, while three were discarded from.the color group resulting in 40 responses. CHAPTER III DATA ANALYSIS Introduction The general problem in this research was to determine which technique of dot mapping, single distribution black and white maps or multipattern color dot maps, was more effective in communicating regional information to the average map user. Two quantitative measures of regions drawn by test subjects were employed to compare the com- munication effectiveness of the mapping techniques. The first was the consistency with which regions were located within the map. The second was the accuracy of dot composition within the regions. These measures are exa- mined in detail in this chapter. Consistency within the Map I Data were collected from.the response maps as frequen- cies in the following manner. First, a quarter-inch grid ‘was placed over all test responses. This size format was chosen so the grid cells would be smaller than the smallest regions identified by test subjects. The grid was regis- tered in the same position over all responses. Next, a frequency count was compiled for each grid cell within the 38 39 map (444 total cells) indicating the number of subjects who placed the cell in a particular region. A cell was considered as part of a region if more than half of its area fell inside the boundary line. These frequencies were referred to as consensual response maps (Lavin, 1979, p.161). Fourteen separate consensual response maps were compiled, one for each of the seven classes of regions drawn by subjects ( A, B, G, AB, AC, BC and ABC) for both the black and.white, and color test maps. Figure 10 illus- trates the consensual response map of region A compiled from.responses of 40 subjects viewing the color dot map. On this map, large frequency values near 40 indicate that nearly all subjects included the cells within an 'A' region. Cell values near zero show that subjects agreed that the cells were not part of an 'A' region. Disagreement in re- gional perception is indicated by frequency values in the mid-range near 20. In these cases, approximately half of the subjects saw the cell as part of an 'A' region, while the others did not. Measures of the consistency of region location within the map were determined by individually calculating the statistical variance of the frequencies compiled on consen- sual response maps for each region type. Normally, vari- ance is considered as an indicator of variability. However, in this study, it is important to understand that variance has an unusual relationship to region drawing. High vari- ance indicates low region perception variability and, 40 . no: u on HoHoo .< aowwom .. no: mmcommom Hmnmcmmcoo m Smum¢¢ — N m 0— o 2 .OH muswam 41 subjects generally agree on their placement of regional boundaries. They are consistent in locating regions within the map. The reverse is true of low variance. Low vari- ance indicates high variability in which subjects disagree on the location of boundaries and are inconsistent in their regional perceptions (Lavin, 1979, p.166-7). The reason for this relationship lies in the distributional character- istics of the consensual frequency maps. Figure 11 com- pares hypothetical examples of two consensual response maps. Map A represents complete agreement, or consistency, in the regional perceptions of ten subjects. A high degree of disagreement, or inconsistency, is reflected on Map B. Variance, a measure of the dispersion of a numerical dis- tribution, is calculated for each map using a standard variance formula with bias correction: $2 _— £(xi - X)2 n - 1 where: Xi = frequency response to a cell X = mean frequency of response n = total number of cells Zeros indicate no response to the cell, but they are in- cluded in the calculation of 32. Since the frequency responses on Map A (consistency) are more dispersed than the responses on Map B (inconsistency), the variance of 42 IOIOOO 543I IOIOIOO 67I3 IOIOIOO 3356 0000 7442 MAP A CONSENSUAL MAP B RESPONSE Consistency MAPS Inconsistency 2 2 S = 26.67 OBSERVED S = 3.60 VARIANCE Figure 11. Relationship between Region Drawing and Variance. Map A is greater. In other words, a more uniform distri— bution of response frequencies leads to a lower computa- tional variance. The relationship between variance and region percep- tion variability can be visualized by representing dif- ferences between the frequency responses of grid cells as three-dimensional frequency surfaces (Figure 12). A sur- face which is comprised of very high and very low prisms has high variance, indicating a high level of consistency in the subjects' regional perceptions. A surface whose cells have fairly uniform frequencies results in low come putational variance and indicates inconsistency in regional perceptions. Variations in frequency values compiled on the 43 4O 4O 36 30 2 2] 2O 25 27 22 40 40 37 32 I 20 28 3O 25 22 36 38 8 I O 20 2O 22 2O 20 2 4 2 I 0 IS 18 2O 20 16 I O 3 3 0 5 I7 I7 14 I3 Figure 12. Frequency Surfaces Conshtent lnconsmtent Region Perception Variability Visualized as Three—Dimensional Frequency Surfaces. 44 consensual response map presented in Figure 10 can be vi- sualized as a three-dimensional surface in Figure 13. The highest and lowest prisms illustrate areas in which subjects were most consistent in locating 'A' regions. Variance Standardization Lavin (1979) suggests that observed variance of raw frequency scores may not be the best measure of region per- ception variability. One disadvantage is that variability as measured from.subject responses by variance has no clear numerical limits. As a result, a computed variance for one consensual response map may not be directly comparable to a variance derived for another. Additionally, variance only has meaning in a relative sense; one cannot directly extra- polate meaning from variance to region perception variabil- ity (Lavin, p.172). A simple example may prove helpful in explaining why observed variance of consensual response maps cannot be directly compared. Figure 14 shows two example frequency response maps. Assuming a total of ten subjects performed the region drawing task, within each map frequency values indicate that subjects were in total agreement in the place- ment of regional boundaries. However, results of the re- sponse variance calculations differ, even though the subject responses show no variability within either map. Conse- quently, the variances are not directly comparable. The cause of the variance difference is a function of the total 45 .OH ouawwh a“ mouoomoum no: uncommom anamcomcoo osu mo oommufiw mocoaoonm .mH musmam 46 IO IO 0 O 0 O O 0 IO IO IO 0 O 0 O 0 IO IO IO 0 O O 0 IO 0 O O O O 0 IO IO MAP A CONSENSUAL MAP B RESPONSE MAPS TOTAL RESPONSE 8O FREQUENCY 30 s2 = <1/n-1) <~:x2 - ((2x>2/n>) MAP A MAP B x 80 30 n 16 16 sxz 800 300 (i X)2 6400 900 32 26.67 16.25 X = frequency of response to a cell n = total number of cells S: = .0667 (800 - (6400/16)) = 26.67 8% = .0667 (300 - ( 900/16)) = 16.25 Figure 14. Total Subject Consensus in Regional Boundary Placement. 47 response frequency (sum of the times each grid cell was included in the region) and the total number of zero cells (Lavin, p.196-7). In order to achieve both comparability and meaningful descriptions of differences in region drawing performance, Lavin developed a standardized expression of region per- ception variability called the variance ratio. The variance ratio, referred to as the Vratio, accounts for differences in total response frequency between consensual response maps making direct comparisons possible. A simplified ex- planation of the variance ratio is presented in this chap— ter. For a more complete discussion, Lavin's dissertation should be consulted (1979, p.198-203). The equation for the variance ratio is given below: Vratio = observed variance (Vobserved) maximum possible variance (Vmii) Observed variance is the actual response variance of the consensual frequency maps. Maximum.possible variance (Vmax) occurs when all subjects are in perfect agreement in the placement of regional boundaries. Vmax can be calculated if the total response frequency and total number of subjects are known. The formula for Vmax is: 48 n - l where: X frequency of response to a cell total number of cells n N = number of subjects EX n = mean response per cell a): N = expected number of cells The use of the variance ratio in this study has two advantages. First, the values derived from the Vratio equation range from zero (theoretically) to 1.0, with higher values indicating more consistency in subject location of regions within the map. The Vratio standardizes observed variance, allowing direct comparisons between the consensual frequency maps derived from the black and white test re- sponses and the color dot responses. Second, Vratio values are directly related to region perception variability. For example, a value of .78 can be interpreted as meaning 78 percent of the maximum possible agreement among subjects was achieved (Lavin, p.203). No such interpretation can be given observed variance. Lavin suggests several reservations concerning the use of the variance ratio. First, the measure is not a general solution because the computation of the Vratio is dependent 49 upon the sample size and the total response frequency. The variance ratio is experiment dependent. A new Vmax and Vratio would have to be calculated if any change in sample size was made. In addition, Vmax is derived empirically. Lavin contends that its computation provides maximum possi- ble variance, however this has not yet been mathematically established (Lavin, p.212). Variance Ratio Comparisons Variance ratios calculated from region drawing re- sponses can be compared to determine which mapping tech- nique, the black and white dot maps or the multipattern color dot map, resulted in more consistent regional per- ceptions. Table 3 lists the Vratios for all homogeneous and mixed region types identified by subjects for both test instruments. Table 3 Comparison of Variance Ratios Black and White Dot Maps Color Dot Map A = .453 A = .533 B = .192 B = .263 C = .556 C = .664 AB = .295 AB = .341 AC = .299 AC = .265 BC = .325 BC = .386 ABC = .089 ABC = .170 50 With the exception of region AC, there was less region per- ception variability in responses on the part of subjects viewing the color dot map. Only in locating region AC, was perception variability slightly lower for subjects viewing the black and white dot maps. Overall, color test subjects had an average of six percent higher agreement in their placement of regional boundaries than black and.white sub- jects. The results indicate that color dot maps may be more effective in communicating regional information to map users, however the difference in variance ratios is fairly small. Simple statistical tests cannot be applied to determine whether the Vratios are significantly different because in- dividual responses cannot be sorted within the frequency data. Variance ratios in Table 3 can also be examined to come pare region perception variability among region types. As expected, the Vratios of homogeneous regions are generally higher than those of mixed region types. Subjects viewing both the black and white, and color dot maps were more con- sistent in identifying regions of predominantly Single dis- tributions. Of the homogeneous region types, regions A and C were seen with much more consistency than region B. In fact, region A on the color dot map and region C on both test instruments were the only region types in which greater than 50 percent of the maximum possible agreement in boun- dary placement was achieved. In comparison to the percep- tion of region B, a substantial average of 32 percent more 51 agreement occurred in the boundary lines drawn around re- gions A and C. This difference is related to the varying characteristics of the dot distributions. Distribution A was clustered to a large degree, while distribution C was localized in the southern portion of the map; both charac- teristics making these regions fairly easy to see. Distri- bution B, however, was spread almost uniformly throughout the map causing the perception of any predominantly pure regions to be much more variable (Figure 6). Among mixed region types, the highest region perception variability occurred in the identification of region ABC. While between 25 and 40 percent boundary agreement was achieved for mixed regions of two distributions, only 17 percent agreement on the color dot map and 8 percent agree— ment on the black and.white maps resulted for the region of complete mix. Accuracy within Regions The second portion of the data analysis compares the accuracy of distributional composition within regions iden- tified from the black and.white maps with that of regions drawn from the color dot map. Data for this analysis were collected in the following manner. First, for every region identified by test subjects, the number of dots belonging to each of the three religious distributions were counted. The composition of the regions were determined from these values by calculating the percentage of each region's total 52 dots that represented distributions A, B and C. Next, the total error in each region's distributional composition from what would be the 'ideal' composition of its particular region type was figured. For example, the ideal composition for a mixed region labeled 'AB' would be comprised of 50 percent A dots, 50 percent B dots, and no C dots. If an AB region drawn by a subject was found to consist of 55 percent A dots, 35 percent B dots, and 10 percent C dots, its total error index, or deviation from perfect composition would equal 30. This value is figured by adding the absolute values of the difference between ideal and actual dot com- position percentages for each distribution. In the case of the AB region, the percentage of A dots was 5 percent great- er than the ideal mix, the percentage of B dots 15 percent less, and the percentage of C dots 10 percent greater; add- ing up to a total error index of 30. The error in distributional composition within regions can be visualized by plotting the mix of dot distribution percentages on a triangular graph similar to the commonly used soils texture graph. In the case of this analysis, the percentage of total dots belonging to each of the three re- ligious distributions are scaled along the three sides of the triangular graph (Figure 15). The error from.complete accuracy in regional composition for each area drawn by sub- jects is proportional to the length of the vector from the plotted point representing its actual dot mix to the point of ideal mix for the particular region type. Therefore, 53 100 Ideal C 0 Ideal ABC O 0 Ideal AB '9 '2 3‘ ‘o 00 0 Percent A Dots (Blue) Figure 15. Triangular Graph Used in the Accuracy Analysis. 54 the farther away a response is plotted from its ideal dot mix, the less accurate the subject's regional perception. The error vector for the AB region described in the previous paragraph is illustrated at point B on the triangular graph in Figure 15. The dot mix of all region types drawn by test subjects were plotted on triangular graphs. Figure 16 illustrates one set of test responses; the compositional mix of A re- gions perceived by subjects viewing the color dot map. It appears that the majority of A regions identified are clus- tered near the ideal 'A' dot mix location and consist of greater than 70 percent A dots, less than 30 percent B dots, and very few C dots. However, the overall group error in perceptual accuracy is increased by regions with a lower percentage of A dots, located further from the ideal mix. A visual comparison of triangular graphs such as Figure 16 between the two test groups indicated that no substantial differences existed in their response accuracy. Simple statistical techniques were employed to deter- mine if, in fact, no significant differences existed in the accuracy of regional perceptions between the two test groups. The indices of compositional error for each region were used to calculate the mean error of individual subjects' perceptions for each region type. The individual subjects' ueans were determined in order to avoid the perceptions of subjects who identified a comparatively large number of regions from weighting the results of the comparison between 55 OABC A . ., ..' v ' ' v ~B AB Percent A Dots (Blue) Figure 16. Sample Triangular Graph - Region A, Color Group. 56 the two mapping techniques. Next, the mean 'group' error and standard deviation of distributional mix were calculated for each of the seven region types from individual subjects' mean errors, for both the black and white, and color test instruments. The values are listed in Table 4. It should be noted that in the calculation of mean error and standard deviation for each region type, the number of subjects de- creased by one for every person who did not identify any regions of the type in question. An inverse relationship exists between mean error and the effectiveness of a mapping technique in portraying re- gional information. The smaller the mean error, the more accurate the distributional composition within regions. The mapping technique which results in a higher level of accuracy in perception responses is assumed to be more ef- fective in communicating regional information to the aver- age map user. Additionally, standard deviation measures the consistency with which subjects perceive regions at the accuracy level indicated by the group mean error. The smaller the standard deviation, the more consistent the sub- jects' regional perceptions are as a group. A general comparison of the two mapping techniques through the data in Table 4 shows that for all homogeneous region types, color subjects as a group were more accurate in their regional perceptions. For mixed region types, with the exception of region ABC, the mean errors for each test group are very close to one another indicating there was 57 Table 4 Comparison of Mean Error and Standard Deviation Black and White Dot Maps: Region Mean Error Standard Deviation Number Subjects (38 Total) A 64.82 16.71 38 70.11 18.66 32 C 48.71 6.42 38 AB 22.94 11.44 37 AC 34.12 10.15 33 BC 51.46 15.20 35 ABC 38.43 14.66 23 Color Dot Map: Region Mean Error Standard Deviation Number subjects (40 Total) A 57.45 16.09 40 B 63.99 17.45 37 C 45.58 8.28 40 AB 19.70 9.48 40 AC 33.56 11.36 35 BC 51.67 9.74 35 ABC 45.12 14.58 35 58 little difference in the accuracy of their perceptions. In the identification of region ABC, the region of total mix between the three distributions, black and white sub- jects were more accurate as a group. However, it should be noted that subjects viewing the black and white maps were able to see far fewer ABC regions (29) than those viewing the color dot map (81 ABC regions drawn). Finally, no identifiable pattern is apparent in Table 4 between the standard deviation values of the two test grOUps among dif- ferent region types. Overall, it appears that the color mapping technique resulted in slightly more consistent regional responses. The F test for analysis of variance was performed to determine if the variability in response for any one region type was significantly different between the black and.white, and color test groups. In theory, if a significant differ- ence did exist in the variances, the mapping technique with the smaller variance would be assumed to portray more con- sistent regionalizations to viewers. The following F ratio formula was used to test the equality of variances: Ill 312 (n1 - 1) F = n2 822 (n2 - 1) where: s = standard deviation n = number of subjects 59 Results of the F test show that at a .05 significance level, no significant difference in variances existed bet- ween the black and white, and color test groups for any re- gion types except regions C and BC (Table 5). In the per- ception of region C, the variance for the black and white group was significantly smaller than the variance of the color group, but its mean group error was slightly larger. In other words, subjects viewing the black and white maps were more consistent in their perceptions of region 0, but at a less accurate level. The mean error for both groups identifying region BC was approximately equal. However, the color group was significantly more consistent in their regional perceptions in terms of distributional composition at this accuracy level. Color subjects drew regions with fewer extremes in error from.the ideal 'BC' dot mix. When all region types are considered though, the F test results confirm the null hypothesis that neither mapping technique resulted in more consistent viewer responses. A second statistical test was employed to determine whether any differences between the mean errors of each test group for the seven region types were significant. The comparison of the means was accomplished by subjecting the mean group errors to the student‘s t test using the following formulas: 60 Table 5 Analysis of Variances F Test a = .05 HO: Sb/W2 = sc2 Region Degrees of Critical F Freedom A 37,39 1.53 F = 1.08 Accept Ho 31,36 1.59 F = 1.15 Accept Ho C 37,39 1.53 F = 1.66 331223 Ho AB 36,39 1.53 F = 1.46 Accept Ho AC 32,34 1.59 F = 1.25 Accept HO BC 34,34 1.57 F = 2.44 32132; HO ABC 22,34 1.84 F = 1.03 Accept Ho For those region types in which no significant differ- ence in sample variance was found between responses of the two test groups (A, B, AB, AC and ABC), the pooled variance estimate was used: t= Xl'iz n1 $21 + n2 322 n1 + n2 * nli+ n2 - 2 n1 * n2 For those region types in which a significant differ- ence in sample variance was found between responses of the two test groups (C and BC), the separate t estimate was used: 61 n1 - 1 n2 - 1 where for both equations: §'= mean group error 5 = standard deviation n = number of subjects df=nl+n2-2 Results of the student's t test indicate that at a .05 level of significance there was no significant difference in the mean group errors between the black and white, and color test instruments for any of the seven region types (Table 6). Although it was mentioned earlier that the mean errors for homogeneous regions perceived by color test subjects were smaller than the mean errors of the black and white group, the t test indicates that the differences were not statistically significant. As a result, one cannot say that subjects viewing the color dot map perceived regions which were more accurate in dot distribution composition than those viewing the three separate black and white dot maps. 62 Table 6 Student's t Comparison of Means a = .05/2 tailed Critical t = 2.00 Ho: ub/W = 11C Region: A (pooled est.) t = 1.99 Accept Ho B (pooled est.) t = 1.36 Accept Ho C (separate est.) t = 1.85 Accept Ho AB (pooled est.) t = 1.37 Accept Ho AC (pooled est.) t = 0.21 Accept Ho BC (separate est.) t = 0.07 Accept Ho ABC (pooled est.) t = 1.70 Accept Ho Additional Data Analysis In addition to the two measures of region communication effectiveness already employed in this study, consistency within the map and accuracy within the regions, a number of other statistical comparisons can be made with the region drawing data to increase our understanding of the effective- ness of the two dot mapping techniques. Table 7 compares the average number of regions outlined per subject on each test instrument. The most apparent message in this table is the fact that both the color and black and white test groups perceived a far greater number of A regions than any other region type. This difference in the average number of A 63 Table 7 Average Number of Regions Outlined per Subject Black and White Dot Maps Color Dot Map A = 5.21 A = 6.60 = 2.08 B = 3.15 C = 2.61 C = 1.78 AB = 2.79 AB = 2.65 AC = 1.42 AC = 1.55 BC = 1.26 BC = 1.53 ABC = 0.76 ABC = 2.03 regions is highly dependent on the nature of the A dot dis- tribution. The distribution contains small areas of rela- tively pure clusters of dots which lend themselves to well- defined regionalizations. It was also discovered that the group viewing the color dot map perceived at least an aver- age of one more region per subject than the group viewing the black and.white maps, for region types A, B and ABC. There was less variation between the average number of re- gions outlined by each test group for the remaining region types. It was apparent in the data collection process that the larger number of A and B regions perceived by color subjects was inversely related to the size of the regions outlined. Because all three distributions were mapped together in the . 64 same space on the color map, subjects viewing it were able to clearly see larger numbers of smaller, more defined A and B regions which were characterized by clustering in the up- per portion of the test maps. The fact that the group view- ing the black and white maps saw fewer ABC regions than the color group was likely the result of many subjects being unable to successfully perform the difficult task of men- tally superimposing three separate dot distributions. Sub- jects viewing the color dot map were able to see regions of complete mix.more easily because the dots were mapped to- gether in the same space. Table 8 presents the results of the multiple Choice questions answered by test subjects after completion of the region drawing task. Both test groups tended to rate the difficulty of identifying regions within the mid—range of the ranking scale. Only a few subjects considered the test task either 'very easy' or 'very difficult'. Overall, the subjects viewing the color dot maps considered the region drawing experiment to be easier than those viewing the black and white dot maps. Both test groups indicated that region A was the easiest type of region to identify, probably be- cause of the distribution's clustering characteristics. The ease of perceiving region C was also rated very close to that of region A by the black and white subjects. As ex- pected, more color subjects ranked regions of mix as easiest to identify than subjects viewing the separate black and White dot distributions. 65 Table 8 Responses to Multiple Choice Questions Difficulty: Very Very Easy Easy Difficult Difficult COLOR (40) 2 25 13 0 B/W (38) 2 18 17 1 Easiest Region to Identify: A B C Mixed COLOR (40) 22 1 10 7 B/W (38) 19 0 18 1 CHAPTER IV SUMMARY AND CONCLUSIONS Summary of the Research Geographers commonly use maps as a means of visually representing regions. The successful communication of regions with transitional boundaries often requires the map reader to areally compare two or more spatial distributions of related phenomena. In these cases, cartographers often illustrate each distribution separately with conventional black and.white dot maps. As a result, map readers must mentally superimpose distributions from separate maps to judge the degree of association between the phenomena. Although map readers may be partially successful, it appears thetask is difficult and many of the more subtle relation- ships between distributions go unnoticed. Previous literature suggests that map readers are likely to perceive regional information more consistently and accurately, if related geographic phenemena are mapped together in the same space. Representing several distribu- tions on one map enables map readers to directly compare spatial associations. It is possible to portray several distributions on one dot map if differences in color, size, shape or tone are used to distinguish the various dot 66 67 patterns. The ability of map readers to perceive regional infor- mation on multipattern dot maps which employ color to dif- ferentiate distributions, was examined in this study. The goal was to determine if the mapping technique offers an effective solution to the cartographic problem of portraying regions with transitional boundaries. More specifically, in a psychophysical experiment, the color dot mapping technique was compared to the conventional method of single distribu- tion black and white dot maps, evaluating their effective- ness to communicate regional information to the average map user. Two general research questions were posed: (1) Are there differences in the consistency or accuracy in which test subjects perceive regions of homo- geneity, or purity, between single distribution black and white dot maps and multipattern color dot maps? (2) Are there differences in the consistency or accuracy in which test subjects perceive regions of mix, or transition, between single distribution black and white dot maps and multipattern color dot maps? The effectiveness of each mapping technique was as- sessed by conducting an experiment in which subjects were asked to draw regional boundaries around perceived areas of homogeneity and mix. Two quantitative measures were 68 employed to compare the responses drawn on the black and white, and color test maps; (1) the consistency with which subjects located regions within the map, and (2) the accu- racy of dot composition within perceived regions. Conclusions Results of the region drawing experiment indicate that the color dot map was slightly more effective in communi- cating consistent perceptions of both homogeneous and mixed regions. However, the small differences in responses leave Open the question of recommending the use of color dot maps over single distribution black and white dot maps. As expected, the consistency measure also shows that subjects viewing both map types were less consistent in locating complex regions of mixed distributions, than in drawing predominantly pure regions of single distributions. It appears that as the complexity of the region increased (combination of a larger number of dot distributions), sub— jects found it more difficult to make spatial association judgements. As a result, their regional perceptions as a group became more variable. Regions comprised of dot dis- tributions with a high degree of clustering, or localiza- tion in one portion of the map, were easier for subjects to see. These findings suggest that the perceptual limit to the number of distributions map readers can areally compare depends strongly on the characteristics of the individual dot patterns, their complexity and degree of mixing, and the 69 viewer's ability to differentiate dot patterns by color, size or shape on a multipattern map. Comparison of distributional composition within regions indicates that there was no statistically significant dif- ference between the accuracy of responses gathered from.the black and white test version and the color version, for either homogeneous or mixed regions. However, the color :‘v- ILL 33 mapping technique resulted in more consistent viewer re- sponses in terms of internal regional accuracy. While these differences were small, the color dot technique can be recommended as being at least as effective in terms of in- ternal accuracy. The results of this study indicate that the innovative color dot map is at least as effective as the commonly used technique of single distribution black and white dot maps. As a result, cartographers should not overlook the color dot map technique when choosing a method to represent regions characterized by transitional boundaries between related geographic distributions. Despite the increased production costs of reproducing color, color dot maps may prove a use- ful alternative to conventional black and white dot maps for two potential reasons. Not only do color dot maps require less space than individually mapped distributions, but view- ers may find the uncommon cartographic product to be more interesting and attractive. Prior to this study, very little research had been con— ducted to assess the potential of displaying multiple 70 distributions on one map using color to differentiate dot patterns. Additional examination of a number of research questions must be completed before the full potential of the color dot mapping technique can be fully understood. Among these research tOpics is the need to investigate in detail, how dot density and other pattern characteristics of dot distributions affect the consistency and accuracy in which map readers see regions. In assessing the percep- tual limitations of the color dot map technique, it would also be useful to have a more accurate understanding of the relationship between complexity of distributional dot mix and region perception variability. Finally, extensive research in a map context must be completed to discover the color combinations which are best suited for use on multi- pattern dot maps, and to develop guidelines for determining the perceptual limits to the number of color dot patterns a map reader can distinguish. APPENDIX A 65 en JI 00 I} g. 71 APPENDIX A Test Instructions (Black and White Version). Follow the numbered instructions in order. Complete each step before going to the next step. Maps A, B, and C represent three different distributions in an area. Look at, and compare distributions A, B, and C. Map T is a map where all three distributions, A, B, and C, have been combined. Using Maps A, B, and C as general references, on Ma T, draw lines around any areas that you see as predominantly distribution A. Label each of these areas with the letter A. In the same way, on Map T, draw lines around any areas that you see as predominantly distribution B. Label each of these areas with the letter B. In the same way, on Ma T, draw lines around any areas that you see as predominantly distribution C. Label each of these areas with the letter C. Place Map T aside. Look at Map X. It is the same map as Map T. Using Maps A, B, and C as general references, on Map X, draw lines around any areas that you see as predominantly a mix of distributions A and B. Label these areas AB. In the same way, on Map X, draw lines around any areas that you see as predominantly a mix of distributions A and C. Label these areas AC. In the same way, on Ma X, draw lines around any areas that you see as predominantly a mix of distributions B and C. Label these areas BC. In the same way, on Map X, draw lines around any areas that you see as predominant y a mix of distributions A, B, and C. Label these areas ABC. Rate the difficulty of identifying the regions on these maps. Circle the appropriate description. Very Easy Easy Difficult Very Difficult Which was the easiest type of region to see? A B C Mixed Areas BIBLIOGRAPHY 73 BIBLIOGRAPHY Broek, Jan 0. M. and John W. Webb. A Geography of Mankind. Second Edition. New York: McGraw-Hill Book Company, 1973. Chorley, R. J. and Peter Haggett. Models in Geography. London: Methuen and Co., Ltd., 1967. Craig, James. Production for the Graphic Designer. New York: Watson-Guptill Publications, 1974. Dahlberg, Richard E. "Towards Improvement of the Dot Map," International Yearbook of Cartography, Vol. 7 (1967), pp. 157-67. Haggett, Peter, Andrew D. Cliff and Alan Frey. Locational Methods in Human Geography. Second Edition. New York: John Wiley & Sons, 1977. Jenks, George F. "Pointillism as a Cartographic Technique," The Professional Geographer, Vol. 5 (September,l953), pp. 4-6. . "Visual Integration in Thematic Mapping: Fact or Fiction," International Yearbook of Cartog- raphy, Vol. 13 (1973). PP. 27-38T Johnson, Douglas W., Paul R. Picard and Bernard Quinn. Churches and Church Membership in the United States. Washington, D.C.: Glenmary ResearCh Center, 1974. Lavin, Stephen. ”Region Perception Variability on Choro- pleth Maps: Pattern Complexity Effects," unpublished Ph.D. dissertation, Dept. of Geography, University of Kansas, 1979. MacKay, J. Ross. "Dotting the Dot Map," Surveying and Mapping, Vol. 9 (January, 1949), pp. 3310. McCarty, Harold H. and Neil E. Salisbury. Visual Compari- son of Isopleth Mgps as a Means of Determining Correlations between Spatially Distributed’Phenomena. Discussion Paper No. 3, Department of Geography, State University of Iowa, 1961. 74 McCleary, George F. "In Pursuit of the Map User," Proceedings, Auto-Carto II, (1975), pp. 238-50. Murphey, Rhoads. An Introduction to Geography. Third Edition. Chicago: Rand McNaIIy & Company, 1971. Robinson, Arthur H., Randall Sale and Joel Morrison. Elements of Carto ra h . Fourth Edition. New York: John WiIey & Sons, 187%. Taylor, P. J. Qpantitative Methods in Geography. London: Houghton Mifflin Co., 1977. Thomas, Edwin N. "Balanced Colors for Use on the Multicolor Dot Map," The Professional Geographer, Vol. 7 (November, 1955) pp. 8-10. Turner, Eugene J. "The Use of Shape as a Nominal Variable on Multipattern Dot Maps," unpublished Ph.D disserta- tion, Dept. of Geography, University of Washington, 1977. U.S. Bureau of the Census. "Livestock and Livestock Pro- ducts Sold in the United States: 1959," ed. of 1962; "Crop Patterns in the United States: 1959," ed. of 1961. Map Scale l:5,000,000. Designed and drawn by George F. Jenks. MICHIGAN STATE UNIV. 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