WM ~ 3 1 HM um I i N i k E “WWII USNG :‘ANCfiGR 335235233 30' NCRFASE do THE C 1.39. CH :A'XNEE i. C;A?AC§?‘:’ " 3 4:. - ' "‘ '2‘$S:5 "'3' .3"; 3232339 {2: in. $3“ :9 \} asp .- 0:17: L1 3:15? ant: ‘11- .'.~.-"§x.i -2:..A':'- * a, 2:35;;‘1 ’ 3.: (9‘. .3 . «33 '33? ”3‘5! '5) ‘5 555': ’4'"! '1": 3,4 I: 4 :52! ~‘.‘ 9“." (S I ' 1-46 3! G W b LIBRARY Michigan State University ABSTRACT USING ANCHOR POINTS TO INCREASE THE COLOR CHANNEL CAPACITY By'James'Wegryn In order to diSplay the use of color in coding con- tinuous series of more then eight elements, a scale of discrete colors was constructed by means of two experi- ments. A third eXperiment tested this scale. Necessary in this extension of the number of colors used to code was the use of anchor points along the scale and a pro- grammed method of learning the colors. In order to establish if certain colors were agreed upon by observers as anchors, and what these colors were, 25'Munsell colors were laid out in a circle in EXperi- ment 1 for 103 observers to Judge. There was consensus among the observers in picking five colors which they thought would serve as standard reference points in the scale of colors. In constructing the scale of colors with anchors which.would'be used as codes, it was necessary to find out how many colors could be learned in an.anchorless scale. This was done by having subjects learn number reSponses to a series of eight Nunsell colors between the anchors found in EXperiment 1. It was found, in terms of information theory, that 2.3 bits of informa- tion was transmitted in the anchorless scales of color. This means that five colors could'be learned.and correctly identified in an anchorless scale. ’\ v ... IHI..’ I «1,.‘31 . Jame s Wegryn A scale of 2S Munsell colors was then constructed from the five anchorless scales of five colors each found in Experiment 2 with the five anchors found in Experi- ment 1 located as each fifth color. The scale of colors was then paired with the reaponse numbers 0 through 2).; and taught to 12 subjects by a programmed method. It was found by information theory that LLJI bits of infor- mation was transmitted by this scale of colors, which is about 20 colors. This result suggests that, for example, in the industrial application of office files the 12 months of the year could easily be coded by color with little error in identification. It was concluded that anchors can extend the number of colors employed in a coding system and that they can be more effectively taught by a programmed method than by a random presentation method. ;0 LL5¢‘(' 2/25/ch /// //‘W USING ANCHOR POINTS TO INCREASE TE COLOR CHANNEL CAPACITY By James Hegryn A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Psychology 196M. ACKNOWLEDGMENTS There are many to whom I owe a debt of gratitude for their contributions to this thesis. Especial thanks are due to Professor Terrance Allen who has read through the many drafts of the manuscript and who has continuously offered encouragement as well as many helpful suggestions. Thanks are due also to Professor James Karslake and Dr. Richard Ball Who reviewed the thesis and.made many valuable criticisms. I also profitted from the suggestions of Professor Ray Denny. I thank the Mhnsell Color Company for their coOpera- tion. I thank also not only Philip Keenan who contributed to the pilot studies but also the many subjects who parti- cipated in the experiments. The typing burden was borne patiently and cheerfully by Linda Wegryn. ii AC MOI-EEDGMENTS There are many to whom.I owe a debt of gratitude for their contributions to this thesis. Especial thanks are due to Professor Terrance Allen who has read through the many drafts of the manuscript and who has continuously offered encouragement as well as many helpful suggestions. Thanks are due also to Professor James Karslake and Dr. Richard Ball who reviewed the thesis and made many valuable criticisms. I also profitted from.the suggestions of Professor Ray Denny. I thank the Munsell Color Company for their c00pera- tion. I thank also not only Philip Keenan who contributed to the pilot studies but also the many subjects who parti- cipated in the experiments. The typing burden was borne patiently and.cheerfully by Linda hegrmn. ii TABLE OF CONTENTS Page IIJTRODWTIONCOOOOOOOOOO0.000.0COOOOOOOOOOOOOO... 1 PROBLEMOOOOCOOOOOOOOOOOOOOOOOOOOOO00.000.000.00. 10 EXPERIMENT l MTHODOOOOOOO000......OOIOOOOOOOOOOOCCCCOOOCO. 11 FESULTS AND DISCUSSION.......“noun"...ooo 12 EliPERIPENT 2 I‘IETHODocoooooooooo000000000000000.000.0000.... 19 RESULTS AND DISCUSSION..........o............o 20 EXPERIMENT 3 I‘ETHODQQQOOooooooooooooooooooooco0000000000000 2% RESULTS AND DISCUSSIONOOOOOOOOOOCO0..0.0.0.... 2 CON'CLUSIONQQOOOOQQOO000000000000.00.00.00.000... 31 REFEIENCESoOQQa...to...coo00000000000000.0000... 35 APPELTDIXOOOCOOOOO0.000.000.00000.000.000.0000... 36 iii LIST OF TABLES Table Page I Colors chosen as a function of number of colors chosen.................. 1? II Amount of information, Ht, transmitted in 98.611 0010:? range....................oo 23 III Amount of information, Ht, transmitted for subjects learning 25 colors.......... 30 iv LIST OF FIGURES Figure Page 1 Frequencies of colors chosen as reference points or as colors easieSt to rememer.OOOCOOOOOOOOOO0...... 13 2 Number of subjects giving number of responses as anchor points............ 1h 3 median number of colors chosen by subjeCtS ChOOSing eaCh color............. 18 ha Summary frequency matrix for purple-red region-.0000...-ooooooooooooooo 22 hb_ Summary frequency matrix for red’yellow regionOOOOOOOOOOOOOOOOOOOOOOOO 22 ho Summary frequency matrix for yellow-green region...................... 22 Lid Summary frequency matrix for green-blue regionOOOo 0.000000000000000... 22 he Summary frequency matrix for blue-purple regionOOOOOOOOOOOOOOIOO00.... 22 hf Summary frequency matrix for combined region-3.00.00.00.00...oooocoo-o. 22 5 Summary frequency matrix for subjects learning 25 celorscooo00000000000000.0000 29 6 Average number of correct responses over five trials............... 32 Using Anchor Points to_ Increase the Color’Channel Capacigy James Wegryn I NTRO DUC TIO N : Efficient color coding has been the focus of much research in the field of color discrimination and color memory. Investigators have sought to determine if color can be a useful dimension by which.information can be conveyed, and, if so, how much information can be con- veyed. All reported research seems to indicate that color is an efficient code. Smith (13), for example, has shown that color aids in visual search and counting tasks, that it may usefully be employed as a redundant code in a complex diaplay, and that color coding pro- duces fewer errors and faster reaponse times than shape coding. These results confirm those obtained by Green and Anderson (A) who employed a projected.matrix of color coded numbers as the target of a search.task. Hitt, Schutz, Christner, Ray and.Coffer (8) demonstrated that color codes are better than codes of shape, letter and configuration in tasks involving counting, comparing, locating and verifing. While these experimenters have shown that color can be used in information diaplay systems efficiently, others have sought to find the maximum.number of colors 1 r‘ I . . . . W . . ; . . ‘ o . ‘ v ‘- . ‘ - '. _ fi . f \ A " ‘ I V A . r I . 1 ' . I . ' . . | .1 ¢. _. ) ‘ | . l l ‘ r . h I ' m . . ') ' .- . ‘ . . ~ \ / ’ . ' ‘ 1 . . ’ ' ' . .‘ . -, , ‘ ’ ~ - . . \x ‘ I. " \I ‘ . I |4 1 . ‘ . ‘ O ‘ ‘ I ‘ .—. that can be utilized for coding. Such utilization de- pends upon absolute recognition of each color used in the system.without reference to or comparison with a standard. Thus, the problem of the latter researchers is linked with color memory. In terms of information theory, channel capacity of the color sense receptors is under investigation. We shall deal with the problem of the maximum num- ber of colors in information theory terms.*- Channel capacity is the amount of information that can be trans- mitted by a receiving system such as the color receptors. The transmission of information through a system is given in units of bits. One bit is the amount of information needed to make a decision between two equally-likely alternatives. One bit of information reduces the amount of uncertainty by a half. In a series of four alterna- tives two bits of information are needed to choose the correct alternative. The channel capacity, then, can be given in bits so that, for example, a channel capacity «It is realized that the information theory model of information transmission does not fit exactly in its application to determine the maximum.number of categories of a coding system. Information theory allows one to calculate an absolute number of categories which reduce uncertainty to zero, but in practical applications un- certainty can never be zero for a large population. However, since no other analysis provides a better estimate of the maximum.number of categories to be used in an information system, information theory shall be used. of 2.0 bits can be said to transmit correctly four al- ternatives or categories. In the search for the channel capacity of the color perceiving system investigators have used two methods of color presentation. One of these is with self-luminous, or light emitting, colors such as colored lights. Here the brightness can be held constant'by controlling the light source and all colors can be adjusted to a high stimulation level. Saturation can‘be held nearly con- stant since fine filtering of the light is possible. The second method of color presentation is in the use of surface colors which.depend upon pigments for bright- ness and saturation levels. Here brightness is dependent to some extent upon hue; for example, high brightness occurs in the yellow region of the spectrum. If high saturation of a color is desired, the brightness of that color is even.more restricted. Most researchers have used.the maximum.saturation levels for each.hue, thus fixing the dimension of brightness. Such.experiments have found about the same color channel capacities as those using colored light. One of the most thorough investigations using colored lights in a diSplay was done by Halsey and Chapanis (5). Using signal lights and only spectral hues, (i.e., not including the purples), they found eight colors which.were never confused with each.other L). by their observers. This would mean that they found a channel capacity of 3.0 bits. They plotted their results as confusion contours on the CIE diagram and picked the eight colors whose confusion contours never crossed. They hypothesized that ten hues could be obtained if a different combination of contours were used. In an earlier study Halsey and Chapanis (6) attempted to esti- mate the accuracy with which discrete color codes could be used to represent values on a continuous scale. Again using self-luminous colors they found ten colors with a 2% error rate in judgment. MacAdams (9) using the same method but with smaller fields obtained very similar results. Emile CIE coordinates are used to Specify colors of colored lights, the Munsell notation of colors is used as such a standard in most experiments with surface colors. In the Munsell system (11), the dimensions of hue, saturation and brightness are labelled hue, chroma and value. In choosing a set of colors for a code, chroma (saturation) is usually maximized for each hue, and this maximum chroma usually occurs at only one value (brightness); thus value is fixed when the maximum chroma of a hue is chosen. The channel capacity of the color receptors using surface colors has been found to be nearly the same as 5 with lights. The most thorough study was done by Con- over (1). Using Munsell colors of high chroma, Conover found a charmel capacity of 3.2 bits, which is equivalent to nine spectral hues which could be absolutely identified with little or no error. A channel capacity of about 3.5 bits is obtained when the purples were included or about 11 colors. I The conclusion that might be drawn from these studies is that the number of colors that can be utilized in cod- ing is around ten. The channel capacity for color seems to be about 3.3. Hanes and Rhoades (7), however, have come up with a less conservative number. They used the entire Munsell Student Set and had one subject learn as many as she could. Learning covered a period of five months and at the end of this time 50 color chips were learned with their Munsell notation. This rather large difference in number of colors learned may be attributed, in part, to factors which were unique to this study. The subject had meaningful reSponses to associate with each stimulus by using the Munsell labels. Three dimen- sions were used by the subject in learning - chroma (satur- ation) and value (lightness) as well as hue. The experi- ments using lights, and those using surface hues utilized only the dimension of hue, holding the dimension of satur- ation at maximum. Also the five months of training was far more than the few experimental sessions employed by Conover and Halsey and Chapanis. Yet Conover feels that the improvement through extended learning cannot increase the number of hues much beyond 13 even though he found that some of his subjects showed significant learning effects over eight sessions. No certain conclusion can‘be drawn from these ex- perimental results except that color can be used as a code employing somewhere from eight to 50 categories. These equivocal results are due to at least three reasons. One of these reasons comes from the three entangled di- mensions of color. Another arises in the use or elimina- tion of anchor points. Another results from the learning procedures employed by each.experimenter. Let us see how each of these confounds agreement across researchers. Color consists of three dimensions - hue, chroma (saturation) and value (brightness). When one dimension such as hue is changed the other two dimensions compris- ing color are altered also. Hue represents wave length which in itself can transmit information through receptors as the pitch of sound can. However, in the pure colors which we perceive and recognize as the familiar primary and secondary colors, the continuum does not only change along hue. Lightness changes as yellow is approached, and saturation becomes greater in the red region and lesser in the green region. This interdependence of dimensions produces a problem when we wish.to study the transmission of information by color. The experimenters mentioned previously here have shoWn.that about 3.3 bits can'be transmitted through the color channel of the human sensory mechanism. Garner (3) gives evidence of a.maximum of 2.3 bits along all other sensory dimensions. He further cites work investigating combined.dimensions such as pitch.and.loudness, and.hue and lightness where more than 2.3 bits is transmitted. If the question “Should.we expect only 2.3 bits to be transmitted'by hue alone?“ has an affirmative answer we mdght suSpect that the 3.3 bits reported by the researchers is, disregarding possible occurrences of anchors, a re- sult of two or three dimensions transmitting information along the scale of color. Perhaps, then, 50 colors dif- fering along three dimensions, as reported by Hanes and Rhoades, can be learned. Another important variable affecting the learning of colors is the use of anchor points. It is held by current learning theory that anchor points aid.1earning. In serial learning tasks a significant item.is quickly learned with generalization occurring to neighboring items (3). In the scale of color unique colors seam to exist. Dimmick (2) tried to locate these colors on the Spectrum. Conover (1) also has found clusters of colors and suggests they are psychologically unique. \/ Such results indicate that colors such as red, yellow, green and blue are probably anchors. This may be due to either social factors since primary and secondary colors are taught at an early age, or to physiological factors such as the luminosity functions of certain re- ceptors. Which set of factors is reaponsible is not relevant here. But it is important to recognize the fact that anchors probably occur in the scale of colors and thus permit the transmission of potentially more information. The question of how much more information anchors can transmit can be answered in terms of information theory. Data indicate that anchorless scales of any kind can transmit only a limited amourt of information. Miller (10) summarizes data from many types of experi- ments on the human sensory capacity and concludes that the channel capacity of the senses can deal effectively with only about 2.6 bits of information or about 6.5 items. Garner (3] states more precisely that studies indicate a human channel capacity of 2.3 bits for most senses. If an anchor is interjected into the middle of a series, Garner holds that the bits transmitted is in- creased by one - exactly the amount of information given by the anchor - giving a total of 3.3 bits. With three anchors which divide the series into equal fourths, 2.0 bits are added for a total of [“3 bits. Halsey and Chapanis did not direct any attention to anchors. Thus, their obtained 3.0 bits may be the result of subjects using the psychologically unique colors as anchors. Conover tried to eliminate the anchors by using a circular scale of colors, but he apparently was not successful. The 3.3 bits of information demonstrated by'Conover may also be too high resulting from the occur- rence of anchors. In fact, Conover points out that the responses tend to group in about six.independent clusters. These clusters were found around the red, orange, yellow, green, blue and purple regions. Hanes and Rhoades let their subject learn with or without anchors as she chose. ‘We do not know if she actually used themw Since it appears that observers are using anchors it would be advantageous to use these subjective anchors effectively rather than to pretend they do not exist. In this way, information transmitted by the color scale would.be maximized. Examination of the learning procedure used'by'Conover and Halsey and Chapanis brings out another possible factor which.may have allowed fewer colors to be learned compared to the results of Hanes and Rhoades. The former experi- menters used a random.presentation of colors in the paired associated technique and discouraged any use of anchor points in the circular continuum.of hues. Such a learn- ing procedure certainly does not appear to be an efficient I. .4. 10 one. Hanes and Rhoades, on the other hand, left the learning method entirely up to their subject, which.pro- bably aided greatly in learning. The subject could.main— tain high motivation by learning small groups of colors or by concentrating on favorite colors, and she could regulate the Speed of learning ‘as well as amount of rest. So it would seem that a number of alterations in the learning procedure could reduce learning time and perhaps improve the performance in color identification. It seems that a programmed presentation, including in- struction of the subject in the utilization of cues and concentration on unlearned colors, is more likely to increase correct reSponses. PROBLEM: The three problems stated above - the use of anchors, interdependence of dimensions and learning procedures - will be investigated here. In this way some practical estimate may be gained as to the number of colors that can be utilized in color coding. Three experiments were necessary to find the number of colors which can be utilized in a coding system. First of all, it was necessary to find out what colors serve as anchors and to what extent there was consensus among individuals. This was done by asking subjects to choose their own anchor points. Secondly, it was necessary I \ n I u .\ . r - 2 ‘_ ‘ I . . . , . ,‘ 11 to determine the amount of information transmitted be- tween two anchors. If the information transmitted by any scale without anchors is constant we would expect to find 2.3 bits transmitted in this short range. Thirdly, by combining these results of anchors and bits of information between anchors, we determined how many colors in the complete range could be learned. Such a scale was then constructed and tested using a.more effi- cient learning procedure than was employed in previous studies. EXPERIMENT I METHOD: The stimuli consisted of 25 Munsell hues, 5P through 10 PB. These hues were chosen from.a ho hue series on the basis of equal ease of discrimination. Each hue was of maximum.saturation at the chosen value, and the hues varied in value, becoming lighter toward yellow with 7.5YZas the highest value, 9. Each.matte surface, 5/8" x 7/8", was placed on gray 5“‘x 8“ background. The hues were lettered.A through Y in serial order. Illumination was by indirect sunlight. subjects were taken from psy- chology and home economics courses. Color weakness was controlled by using only females, in whom.such.deficiencies are rare, and.males who had been previously tested.and found normal. The colors were laid out in serial order in a circle 12 to eliminate end points. Subjects gathered around the colors and were given these instructions: "Choose the colors from this circle which you think you could learn easiest if you had to learn all the colors. Or to put it another way, which colors would you choose as standard reference points for comparing the other colors to." Subjects wrote the identifying letter of the colors they chose on index cards. Results were tabulated. RESULTS AND DISCUSSION: Figure 1 shows the obtained frequency distribution for each of the 25 colors presented to 103 subjects. It can be seen that there are definite peaks which in- dicate agreement between subjects as to which colors would serve as reference points along the entire scale. Six peaks can be seen in Figure 1. However, we find that the average number of anchors chosen by a sub- ject is L)..96 or about five. This should lead us to think that five anchors, not six, is the number that can be best utilized in a scale. If we examine the distribu- tion of how many responses were given in Figure 2 we can see a slight bimodal distribution at four, five, and six with five falling slightly below the peaks at four and six. This means that subjects tended to choose four and six colors as anchors more often than they chose five. This might be the result of cultural training Frequency 13 ‘_ N=lO3 So LL0— 30—— 20*— 10—— __J|llL||l||llLlll|l|IIJLIL ABCDEFGHIJKLEMNOPQRSTUVWX (purple) (red) (yellow) (green) (blue) Fig. l. Frequencies of colors chosen as reference points or as colors easiest to remember. whereby these subjects learned either four primary colors, or three primary colors and three secondary colors making a total of six. Besides this slight bimodal distribution, however, a substantial number of subjects gave five anchor Number of subjects 11+ 10-—' — _— J I l J I l I 1 1 2 3L; 5 67 8910 Number of responses given Fig. 2. NUmber of subjects giving number of reaponses as anchor points. points. If five anchors should be used in the entire scale, one of the colors that is seen to peak in Figure 1 must be excluded from the list of anchors. The peak occurring at H (commonly called orange) indicates that 15 this color may not be as effective an anchor point as A, F, L, P and U even though H was chosen as often as P and.more often than U. The low frequencies of G and I indicate that little generalization occurred from H to its neighboring colors as occurred at each of the other anchors. Hence, H alone represents the anchor in this region. On the other hand, N and 0 show rela- tively high frequencies probably representing some general agreement on the part of the subjects in pick- ing a green as one of the anchor points. The same is true of T, U, V and'W in the blue region. Therefore, it can be said that the sum» of the frequencies in the flat distributions of the green and.blue regions is much greater than that in the orange region. IYet we still cannot be sure that the relatively small cluster about H is not due to the Spacing of the colors. Perhaps some of the distribution about H is lost in its nearness to F (red) in which case we might conclude that H was as much an anchor point as A, F, L, P and U. Another approach.may better justify the exclu- sion of H from the list of chosen anchors. We might suppose that the colors chosen as the first five anchors by a typical subject should be the anchors used in Experiment 3. The typical subject might be re- presented by the entire population and the color chosen 16 by a subject picking only one anchor would be that color which our typical subject would pick first. Likewise, the subjects picking two anchors would choose the two colors which our typical subject would choose first and second. We can extend this reasoning to the case where the subject choosing one, two, three, four or five anchors will represent fairly well the first five colors chosen by the typical subject. Table I groups the data so that we can see which colors would be chosen first by the typical subject. The typical subject, as characterized by the popu- lation in Table I tends to choose K first as an anchor point. We can see that H would be chosen as an anchor on about the sixth reaponse. If we calculate the median case for each color we can see which colors would tend to be chosen soonest. Figure 3 shows for each color the median number of colors chosen with it when it was chosen as an anchor. We see five definite valleys where colors in these re- gions tended to be picked relatively more by subjects picking five or less anchors. Color H is the only one of all the six anchors determined by the frequencies in \D L) J- 17 TABLE I Colors Chosen as a Function of Number of Colors Chosen. Number of Colors Chosen Colors 1 2 3 h 5 6 7 8 9 10 Total A A 11 9 11 u A 1 #5 B 2 3 7 5 S 1 l 21L c 3 1 2 1 1 2 1 11 D L; A E 1 2 2 1 F 9 11 7 12 6 3 2 1 51 G 1 L1 3 3 2 2 15 H 2 k 5 10 7 2 1 31 I 1 3 5 1 1 11 J l 1 l l l 5 K 1 2 3 8 t 9 3 3 1 37 L 1 u 10 1o 11; 7 2 1 1.9 Mb 1 2 1 l 2 l 8 M1 1 2 l 2 1 g N 1 2 6 2 3 2 1 o 1 L; 11 5 2 2 1 25 P 2 9 7 7 3 2 l 1 32 Q 1 1 5 3 10 R l 2 l 2 l 2 l 1 11 s 1 2 3 1 L; 1 12 T 3 g 2 3 2 1 1 15 U 1 1;; 7 L; 3 1 1 26 V 1L 5 LL 9 l l 2 w 1 2 3 2 2 3 3 1 1 1 x 2 l 3 2 A 3 15 Re. of Resp. 1 8 151011 95126 63 no 18 10 510 No. of Subj. l h 15 26 19 21 9 5 2 l 103 Figure l which is not found in.the low parts of the curve in Figure 3. The five low points in Figure 3 suggest, as Figure 2, the use of only five anchors. 18 Median number of colors chosen . / filllllllllllllllllllHill? XABCDEFGHIJILMCMNOPQRSTUVWX Colors Fig. 3. Median number of colors chosen by subjects choosing each color. Thus we have the five anchors of A, F, L, P and U which.are used in EXperiment 3. EXperiment 2 attempted to find how many colors could be correctly identified between any two anchor points using the anchors found here. l9 EXPERIMENT 2 METHOD: The stimuli consisted of a set of nine colors in- cluding two of the anchor points found in.Experiment 1. Subjects were many of the same used in Experiment 1. The colors were presented one at a time in a.neutral gray device eXposing only the center of each.stimulus, a retangular area 1/2" x.3/ ". The stimuli were viewed at a 60° angle at a distance of 2' from the observer, illuminated'by indirect sunlight. Each.subject was told that the experiment consisted of learning nine colors which.would'be fairly close to- gether but which could be discriminated. She was told not to guess when she was unsure of a color since it would cause her to make the same mistake again, and.to try to use lightness differences between colors as well as hue in learning them. The reaponses to the nine colors were the numbers zero through eight. Familiarization with.the colors began by giving the subject a chance to make the correct responses to all of the colors. They were presented first in forward serial order then in backward order and finally in alternating forward and backward serial order, the subject being aware of the method of presentation. The subject was then asked if there were any colors which were confusing and which 20 she would like to see together. After these confusions were clarified the subject was told that the colors would be given in a random order and that She should give the reaponse without guessing. If she didn't know or gave a wrong reSponse, correction was given. The series was presented four times with knowledge of results. Again confused colors were closely examined. After a serial presentation of the colors was given to establiSh the series again, four more random.trials were run.with.know- ledge of results and necessary correction. This was continued.until the subject reaponded correctly to the entire series. Three final trials were run without know- ledge of results or correction. These were the test trials. Results were tabulated for all subjects and analyzed to find.the amount of information transmitted between.anchors. Each interval was tested.in the same way. The time nec- essary to learn these short series of color varied from 20 to h52minutes. RESULTS AND DISCUSSION: In analyzing the results of EXperiment 2 information theory was employed. Following the method used by Con- over (1) the information transmitted Ht was computed.by summing the response uncertainty, Hr, and the stimulus uncertainity, HS, and subtracting the combined.uncer- tainty, H The data were placed into matrix form as rs‘ 21 shown in Figure A with each cell containing the fre- quency of a given reaponse to a stimulus. The computa- tional formula which was used on this matrix to find the amount of information transmitted, where the limiting factor is the response information, is as follows: Ht = log2NS + EgNrslog2Nrs _ ger°g2Nr Nt N1; where N8 is the number of stimuli, Nrs is the frequency of cell 33, Nr is the number of reSponses of color 2, and Nt is the total number of stimulus presentations. The results of EXperiment 2 are shown in.Figure h and Table II. It is seenn that the amount of informa- tion transmitted'by the short anchorless color scales agrees with.other data found concerning human sense channel capacity (3, 10). The number of bits is very close to the hypothesized 2.3 lbmit with the highest occurring between red and yellow with 2.392 and the low- est between green and blue with 2.189. The average amount is 2.297. If all the intervals are combined, disregarding color, the short interval of nine colors between two anchor points transmits 2.2h5‘bits. The antilog of 2.2h5 gives n.7h or about five as the number of colors that can be correctly identified in the anchorless color scale. Yet we might have aXpected.more information trans- mission in this scale since color varies along the three dimensions of hue, saturation, and lightness. However, Response category 0 1 2 3 4 5 6“? 8 T O 17 1 18 1 1 15 2 2 3 1h 1 3 2 1# 1 1 8 3 13 2 5 8 13 1 6 1 18 3 7 2 15 1 8 . 18 T 18 19 18 18 18 17 17 18 19 162 Fig. #8. Summary frequency matrix for purple-red region. Response category 0 1 2 3 8 5 6 7 8 T 0 17 1 18 1 15 2 1 2 2 13 3 3 3 14 1 8 1 13 3 1 5 an 2 6 3 13 2 7 2 15 1 8 2 16 T 17 17 19 19 18 18 18 19 i7 162 Fig. he. Summary frequency matrix for yellowagreen region. Response category 0 1 2 3 # 5 6 7 8 T 0 17 1 18 1 1 15 1 1 2 2 13 3 3 # 13 1 4 2 12 h 5 3 18 1 6 1 1 13 3 7 1 15 2 8 1 1 16 T 18 18 18 19 17 19 16 19 18 1 2 Fig. he. Summary frequency matrix for bluenpurple region. 22 Stimulus category Stimulus category Stimulus category Response category 0 1 2 3 4 5 6 7 8 T l7 1 18 2 16 U 3 1 tekelo HEHH HgNH 3 D 2 H Hm? 5.1 1 N1 ! Hm'QQM-F'UNHO 19 17 18 17 17 18 18 20 18 162 Fig. 8b. Summary frequency matrix for redqyellow’region. Response category 0 1 2 3 h 5 6 7 8 T 16 1 1 18 1 3 13 h 3 14 1 1 rakn~a 16 17 18 18 18 18 20 19 162 Fig. 46.. Summary frequency matrix for greenpblue region. Response category 3 h 5 6 7 8 T 90 o 12 m #2 8% 8 9 68 D 8856 1 9 e m 1 2 10 66 16 10 7k 6 6 84 88 88 91 91 88 90 88 96 9O ugdw F-JCDNIChUX-PUNHO 810 Fig. 8f. Summary frequency matrix for combined regions. |- A f‘J' (J I I "IS: 59152 C :‘II "JII I Eff. ."VI 1’." I I‘I',-" IYI '1' ‘3'»: 0.1 ' - - ' .(. . 0'"; ' 7‘-" ~. ' 'r‘ “ "O t“ ‘ ‘ ' ‘ r P ' I c I I \u I ."I I'If‘.‘ I I I IYI I -' a. " I u- . .rr". 7 "I 'r—‘ ‘I '~" ."" 2".) o :o 2 rI P: r - \f rr If . C. 'r' 0 . fy ," I. I . ('l’—/)£1H -/J 'L L. (‘4 '.:-/') ' 3.1—: " - u h I f}: A_'f‘J‘:f‘) r ') )l)'fi J 23 TABLE II Amount of Information, Ht, Transmitted in.Each.Color Range Color Range Ht Purple-Red 2.383 RedAYellow 2.397 Yellow-Green 2.266 Green-Blue 2.189 Blue-Purple 2.2h9 Combined 2.2h5 Average 2.297 the data.indicate that the scale of color transmits an amount of information characteristic of a single dimen- sion. It is not likely that this result of 2.3 bits is an.artifact since all subjects said they could discri- minate between.all colors. In fact, it was found.that neighboring colors which differed in both.dimensions were confused 11.1%nof the time while neighboring colors differing only in hue were confused ll.8% ‘ a a c a c o ' o o e . I o . . * I ‘ I ' c o I ' t .0 I o o 'J a O O O o O I v 'I u 0 fi 0 O 21L It should be noticed that the greatest amount of information transmission occurs in the red-yellow region where orange can be found. Yet if orange had served as an anchor we would have obtained a result nearer to 3.3 bits. Therefore, it is probably true that orange did not serve as an anchor. The least amount of transmitted information occurs in the greenéblue region which is as expected since all researchers in the field of color have found this region to cause the most difficulty in their studies. Here the difficulty lies in the apparent closeness of these two anchors, bounding the information transmission by discrimination limits rather than channel capacity. With the results of the first two experiments we have found that there are five anchor points in the scale of colors and that we can expect five colors to be learned between any two anchor points. Thus, we hypothesized that 25 colors could be haarned in the complete color scale. EXperiment 3 was designed to test this scale. EXPERIMENT 3 METHOD: The stimuli were the Nunsell colors chosen as an- chors in Experiment 1 with four colors between each.an- chor:making a total of 25 colors. The presentation of the stimuli was in the same device as in Experiment 2. The subjects were from.the same population but did.not . _ ' _ . o b I O . - u _ O l ‘ ‘ C . ‘ .- . ' I D 1 3 I . . ‘8 . \ - : a . - - O O . I . . — - ' . v “ n I a . ) o l a ' u I _. ' n . I _ ' '3 ' ' ‘ l . O. . ' ' ’ , c - 0 . . .. . . u . . I a - .. ' . \ . . ‘0 ‘ ' | ‘ ' . . s - . . . o I. l . ' . . t 1 ‘ ' . O . . D- o , o a n 0 ' .' ' I . . \l ' ' . ' ' - . . I . | I \4 o ‘. . o e \ o . ‘ o - o . ' , . . u o ' ‘ ' ' n ‘ \ . . ' _ . -. . I . . U . , . n . . I I ’ I ' ' l 5 o o I 0- I . ' . l ‘ o . g I o '0‘ t . - ' ' \ . . . , . . .- I . .. a. _ . 7‘ r . . . ' c O . O . . 3 . . - - 1 . a i . ' . . . l . ‘ ' . . ' .. \ . I o u ‘ . I a I ‘ I I . u . - . n C . - ' c ‘ ' ' -. I n l . ‘ . ~ _ ' . . t. , ' . a l I ‘ D t ' o. . 9 ' ' ‘ u . o - . n l " " ‘ . i - n . , I ' _' O I ' a ' ' . . I . . - ' . .. o - - ' ‘ " o . . . . , \ " . . o - ' " I ' O - . ' . . t . - ' l _ I o 6 25 include any subject used in Experiment 2. Instructions to the subject were as follows: "This is an eXperiment in color memory. The task is to see how many colors you can learn. It is generally believed that only about ten colors can be learned in the complete color range. How- ever, we believe this number is too small and is a result of poor training as well as averaging over large differ- ences between individuals. Some people can learn only five colors while one subject was reported to have learned 50. Here we are asking you to learn 25 colors in the complete range. (The subject is shown a color wheel to gain an idea of the series.) As you can see, the colors gradually vary as we go from.purple to blue. The colors have an order. we are labeling 25 colors in this con- tinuous series by the numbers 0 through 2h starting with this color as 0 (subject is shown 0) and ending with this one as 2h (subject is shown 2h). Ybu might imagine this color series being applied to a scale going from very hot - represented by purple - to very cold - represented by bluish-purple. 0r very dangerous to safe. Our scale will be the numbers 0 through 24. After color 2h comes color 9 again which.makes the series a circle. In order to make learning easier let me point out that you Should not only try to remember the color but also the lightness. ‘When two colors seem.to be nearly the same compare their lightness or darkness. When you are not very sure of 26 the color, don't guess. If you do, you are apt to make the same confusion at some other time. First, it is extremely helpful to learn thoroughly some reference points. These are the colors which you will see the most. I will now show you Which colors will be the best reference points.“ Preliminary learning began with the learning of the anchor points followed by learning of small ranges between anchors. Colors 0, 5, 10, 15, 20 and 0 again were shown to the subject successively with the eXperi- menter announcing the numbers and the subject repeating them. They were then shown randomly with the subject making the reSponses alone. This was repeated until all responses were correct without prompting. After this the subject was told that she would be shown the first six colors of the series (those between the first two anchor points) plus all the anchor points. Learning of each set of colors between two anchor points proceeded in exactly the same way as the first set to be described. Every time the subject saw a new color she was told the associated number and responded. Every time the sub- ject was presented a color that she had seen before she was asked to reSpond.by herself. For example, anchor point 0 was presented first which the subject had seen earlier and she responded. Then color 1 was presented with the experimenter giving the reSponse followed by 27 the subject responding. After 0 and 1 had been presented, 5 and h were given in the same way. The anchors followed the presentation of newly introduced colors. The series then was expanded by giving 0 and 1 followed by the in- troduction of 2. Then from the other direction 5, h and 3 were given similarly. Following colors 0, l, 2 and 3 were 5, h, 3 and 2. This eXpanding continued until the subject was reaponding to all six colors forwards and backwards. The colors were then given randomly until she was reSponding without error. The next set of colors, 5 through 10, was then presented and learned in the same manner. When all sets of colors in the series had been learned in this way the entire series was given once in serial order and then randomly with knowledge and cor- rections, and all confusions were noted. The experimenter displayed the confused colors with neighboring colors successively giving the correct reSponse and.having the subject reSpond. A minute rest was given at this point. The learning resumed with familiarization of the entire series to be learned with a serial presentation of all the colors. The subject was told that the colors would be presented 0 through.2h and that she was to re- Spond to each hue as a review. Then a trial was given in which confused colors again were noted and corrected. Trials to correct confused colors were given four times. Due to a_time limitation no greater learning could be 28 achieved than that gained to this point. Finally, the series was presented randomly twice in succession with no knowledge or correction given and the responses noted for each stimulus. These were the test trials. The entire process took from 1 hour to lé-hours. RESULTS AND DISCUSSION: The results of EXperiment 3 were treated in the same way as those of Experiment 2 using information theory. The matrix of responses of the 12 subjects is shown in.Figure 5. It can be seen that only two subjects made wrong responses across more than one category. All other errors occurred at categories adjacent to the correct one. Figure 5 also shows that anchor points 0, 5, 10 and 20 were correctly identified every time. Anchor point 15 (green) had one wrong response. From.the summary frequency matrix the amount of information transmitted was computed. Table III lists the calculated Ht for each subject and the corresponding antilog which represents the number of colors that could be correctly identified. The mean Ht is h.392. Con- over's 25 color series yielded a mean Ht of 3.h86. This difference is significant. This study indicates that at least 20 colors can be correctly identified by a cola? normal population. Conover's best subject obtained an Ht of h.035 while the poorest subject here obtained an Ht of h.073. According to these data, greater information 29 .muoaoo mm wadsnsoa oveofinso non Kansas hccosceum huesssm .n .mah con fifififififififififlfiflfiflflflfiflfififlfifififi HA H H HM rco\oa ri:1rl r4:1r+ sN mm mm HN on ma mH he ma nH 3H nH NH dd ed a m m o m s n N A o H 0 NM flfimfimmfi 2 flxofieqeo snInmmqg 33 3 mnemopdo uncommon M tn '; 9‘1 ‘ ‘V j - > ‘ I 'r—-—‘. v H y—c L.1 F: L“. H H F1 tr. - l '7‘} +1 1'1 {W J).— t—a 30 TABLE III Amount of Information, Ht! Transmitted for subjects Learning 25 Colors Sub j. Correct Ht Antilog 1 25 8.61111 25 2 25 11. 61m 25 3 211 11.5211 23 ’4- 211 11.5211 23 5 23 11.11511 22 6 23 11.11311 21 7 23 11.11311 21 8 22 11.3511 20 9 22 1.313 19 10 20 11.1511 17 11 20 8.152 17 12.: 19 LL.o73 15 Mean 22.6 11-. 392 20.7 transmission has been shown possible. The number of colors that was eXpected to be identi- fied was 25. The obtained results fall short of this by five. This may indicate that perhaps not quite one bit is added with the addition of an anchor. Yet the results of Experiment 3 prObably fall short of 25 for another reason. In using information theory a smaller number of categories than one started with must always result since any error in responding causes a reduction in the 1 q‘ ._, — 31 number of categories that can be utilized in absolute identifications. For example, we can.see in Table III that a ceiling of 25 colors does not allow us to find 25 colors by information theory since no subject can do better than 25'but some subjects can do worse causing a drop in the mean Ht’ Conover also found a similar dr0p in the number of colors that could be identified'by his validation group. This suggests that information theory has a limited appli- cation in this type of prdblem. It might be contended that the identification of only 20 colors may be attributed to the learning proce- dure. Perhaps more learning trials would have produced a greater number of colors. Figure 6 indicates that this is not necessarily the case since no increase in learning is found.between the third and fourth trials. A large drop occurs on the test trial which is probably due to the lack of knowledge of results and correction. This drOp might be reduced with greater over-learning. Such learning over several sessions might yield a test trial result equivalent to that obtained in trials three and four here. Limitations on time prohibited the investi- gation of this possibility. CONCLUSION: The results of other experimenters would.make it seem undesirable to go beyond a scale of more than ten colors to code a series. Conover (1) has shown that L 32 211?— U) a) (D c S. 33 a *6 23— o a $4 8 g N=l2 i3 22 n ”— 5 c 0 hi) £6 a G) p 4 21.. % I l l I I l 2 3 A Test Trial Fig. 6. Average number of correct' responses over five trials. nine colors can be used by the color normal population. Halsey and Chapanis (5) found ten colors which.could.be identified with little error. The three experiments, described here have demonstrated that a scale of more than ten colors can be used for coding. The use of an- chor points can extend the length of such a scale to at 33 least 20. This fact makes possible more versatility in the use of colors for coding. A series such as the 12 months of the year can easily be coded by color with theoretically no error in identification. Less familiar reSponses to the series of colors, 1.8., not as common to the observer as the 12 months of the year, as might arise in industrial applications might hamper the learn- ing of the stimuli. Also, poor lighting conditions and the accomodation of color weak Observers would prObably diminish the number of colors used as codes. Even with these unfavorable factors entering into the application of color as a code it seems that the results of Sloan and Habel (12) of a.maximum of three colors used with color weak subjects may be loW. Even individual dif- ferences as might be found in a large population can easily be tolerated in series of less than 20 colors. Further research should be performed to confirm this possibility. The sensorial mode of color has been shown to be unique in the sense that it has definite anchor points - colors which are said to be psychologically unique. This means that the scale of colors can naturally extend the amount of information transmitted in a coding system. All other sensorial modes have been shown to transmit about 2.3 bits. There is no need to throw color into this list. It has been shown here that because of the anchors, potentially h.3 bits can be transmitted by colors. 3L1 It might be argued that color is consistently'bound by the dimension of lightness and, therefore, does not by itself transmit all the information attributed to it. It is highly doubtful that the dimension of lightness transmitted any information since confusions existed equally often between colors differing in lightness and hue as between colors differing only in hue. A word can be said about the learning procedure employed in Experiments 2 and 3. In EXperiment 2 all subjects reach a criterion of one perfect trial in less than three-quarters of a hour. In EXperiment 3 only four learning trials were given before the test trial. Figure 6 shows that nearly perfect reaponding is achieved by the end of the fourth trial. others such.as Conover and Halsey and Chapanis have used.many trials over several sessions to attain.maximum learning. This study differs from.other studies in the programmed pro-training periods used here. Random presentation of colors paired with arbitrary reSponses was not given, resulting in relatively short learning periods in.Experiments 2 and 3. Thus, the efficient learning procedure demonstrated here increases the practicality of using color in the industrial situa- tion. -\.a I n 1 . I o o .I 0 g c \ o. 'I one»- -\ - .' a. . O I ‘. .f . d '- I e' c\/. ,. .' . I o I _ l o ' k: l. 2. 3. u. S. 9. 10. ll. 12. 13. REFERENCES Conover, D.w. The amount of information in the absolute udgment of Nunsell hues. USAF WADC tech. note 58-2 2, 1959. ‘ Dimmick, F.L. a Hubbard, M.R. The Spectral location of psychologically unique yellow, green & blue. Ameri- can Journal_g£_Psychology. 1939, vol. 52, pp.2h2-2E9. Garner,‘H. R. Uncertainty and Structure a§_Ps cho- logical Concepts. 0 1 ey and Sons, Inc., New YOI’E, N.Y., I;62. Green, B.F. & Anderson, L.K. Color coding in a visual search task. §;_Exp. Psychol,, 1956, vol. 51, pp.19-2h. Halsey, R.M. 8c Chapanis, A. On the number of ab- solutely identifiable Spectral hues. g;_0pt. Soc. Amer., 1951, vol. hl, pp. 1057-1063. Halsey, R.M. & Chapanis, A. Chromaticity-confusion contours in a complex viewing situation. g;_02t. §9c0 Emern) 1958. V01. NE: PPO MAE-MEA- Hanes, R.M. & Rhoades, M.V. Color identification as a function of extended practice. g;_Opt. Soc. Amer., 1959, vol. E9, pp. 1060-106h. Hitt,‘H.D., Shuts, H.G., Christner, C.A., Ray, H.H. & Coffey, J.L. Development of design criteria for intelligence diSplay formats. USAF RADC Tech. Rep. 60-201, 1960. MacAdams, D.L. Small field chromaticity discrimination. §;_Opt. Soc. Amegl, 1959, vol. E9, pp. llh3-llh6. Miller, G.A. The magical number seven, plus or minus two; some limits on our capacity for processing in- formation. Psychol. Review, 1956, vol. 63, pp. 81-97. Munsell Color Company. flpnsell Book g£_Color. Baltimore, Md., 1929. Sloan, L.S. & Habel, A. Color signal system.for R—G color blind - Experimental test of 3 color signal system proposed by Judd. J. O t. Soc. Amer,, August, 1955. V01. #5. ppo—39 - 5. Smith, S.L. Color-coded diSplays for data processing systems. Electro-Technology) April, 1963, vol. 71, pp. 63‘670 35 ’ Q C. _ a . . 9 w x Q 41 1" ['3 APPENDIX 36 Colors Colors Colors Munsell used in used in used in _‘ Notation Exper.l Exper.2 Exper.3 7.5 R 5/12 1 10.0 R 6/10 2 6 2.5 YR 6/1h 3 5.0 YR 7/10 1 L; 7.5 YR 7/10 5 10.0 YR 7/10 6 2.5 Y 8/12 7 9 5.0 Y 6/111 L 8-0 10 7.5 Y 9/10 1 10.0 Y 8/8 Me 2 11 2.5 GY 8/10 3 5.0 CY 8/8 M A 12 7.5 GY 7/10 5 13 10.0 GY 7/10 6 2.5 G 7/8 0 7 11+ 5.0 G 7/6 0-8 15 7.5 G 7/6 Q 1 16 10.0 G 6/6 2 2.5 BG 6/6 R 3 17 5.0 B6 6/6 h 7.5 BG 6/6 s 5 18 10.0 BG 6/6 6 2.5 B 6/6 T 7 19 APPENDIX (Con't.) 5/ 6 5/6 5/ 8 5/10 5/10 5/12 11/10 11/10 3/10 11/8 11/10 11/10 11/12 11/10 5/10 5/10 5/12 37 8-0 «low-F'me 2O 21 22 23 211 0' \ "O I '1 II 1’ III 'I. l I III WIHWIW