i l THS A TEST OF STIMULUS GENERALIZMMN MQDELS ‘ Ttmis for fine Degree of M. A. Ml‘CHtGAN STATE URWERSITY WEE A HARRIS 1967’ ABSTRACT A TEST OF STIMULUS GENERALIZATION MODELS by Lance A. Harris Two predominant theories of stimulus generalization, the Spence S—R theory and the Zeiler Adaptation Level theory, have had only limited experimental application in varying situations. In order to relate the theories outside the transposition problem a design was utilized that employed light intensity as the discriminative stimulus dimension and extinction as a special experimental manipulation. After a brightness discrimination had been estab— lished in a conventional Skinner box, all gs were given 5 minutes of warm-up followed by extinction with the stimu— lus lights off (extinction 1). This was followed in turn by 10 non-reinforced test trials with alternately pre— sented training stimuli (extinction 2). t—tests of the warm—up data indicated that none of the differences observed in extinction l and extinction 2 could be attributed to differences present in training. In extinction 1 all D groups (training SD = dim light) responded significantly more than all B groups (training sD = bright light). Lance A. Harris In extinction 2 all B groups responded significantly more to the bright stimulus than all D groups. The results were as predicted by the Spence model of generalization gradient summation. The Zeiler theory also predicts the outcomes if the value of the mathematical constant y is varied from .01 to .1 or from .9 tn) .99 with the most accurate prediction made when y approximately equals .9. Further experimentation with both theories is indi- cated, but because of the greater generality of the Zeiler theory, it is probably a more potentially powerful formuli- zation than the Spence model. . ' f1 L! / . . Approved 2 U 1 fimu balk/v“ , :7 / .7 . w , , -, Date @L‘j” 0:1 (I y //L (1L 1/ J I A TEST OF STIMULUS GENERALIZATION MODELS by Lance A. Harris A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Psychology 1967 ACKNOWLEDGMENTS I would like to express my gratitude to the members of my committee: Dr. Mark Rilling; Dr. David Raskin; and Dr. M. Ray Denny. A very special debt is owed to Dr. Denny for the guidance and stimulation that may yet bear the fruit of a psychologist. It is with love that I dedicate this effort to my wife Mary who, uncomplaining, became a research widow during the time the data was collected, and who, in the few hours that she was not working at her job, attending to our home, or loving our demanding cats, acted as my secretary-at-arms. Special acknowledgment must be given to Maureen Hattle, Jenny Fidura, and Fred Fidura, without whose help in conducting the research, and more important, without whose comradeship, this thesis would likely have remained an idea. ii ACKNOWLEDGMENTS LIST OF TABLES. LIST OF FIGURES INTRODUCTION. . METHOD. . . . . RESULTS . . . . DISCUSSION. . . REFERENCES. . . TABLE OF CONTENTS iii Page ii iv 12 15 19 26 Table 1. 3A. 3B. 4A. 4B. LIST OF TABLES Designation of groups . . . . . . . . . . . Order of presentation of stimuli in warm-up Group mean response in warm-up. . . . . . . t-tests of warm-up responses. . . . . . . . Group mean responses in extinction l. . . . Analysis of variance of extinction 1 responses 0 O O O O O O O O O O O O O O 0 Analysis of variance of extinction 2 responses 0 o o o o o o o O o o o o o o 0 Adaptation levels and ratios. . . . . . . . iv Page l3 14 15 l6 l6 l6 17 22 Figure 5A. 5B. 6A. 68. LIST OF FIGURES Example of the Spence model. . . . . . . . . Spence model derived from an experiment. . . Perkins' use of the Spence model in stimulus intensity dynamism . . . . . . . . . . . . Spence model for the intermediate size problem. . . . . . . . . . . . . . . . . . Spence model for extinction l and 2, B groups 0 O O O O I O O O O I I O O O O O Spence model for extinction l and 2, D groups 0 O O I O O O O O O O O O 0 O O 0 Graph of SD responses in extinction 2. . . . Graph of SA responses in extinction 2. . . . 10 10 l8 18 I '19:. _.l-‘~‘i—_1r '— . _ L— INTRODUCTION A critical test of a stimulus generalization model as it pertains to a discrimination task has been the trans— position problem. In a typical transposition situation, gs are trained to respond differentially to two stimuli, and subsequently tested by presenting one or more new stimuli lying on the same physical dimension. As an example, if S has been trained to respond to an SD (positive stimulus) of 430 cm2 and not to respond to an SA (negative stimulus) of 220 cm2, then S is said to have transposed if a 240 cm2 stimulus is preferred to a 110 cm2 stimulus in test. In other words, transposition is defined behaviorally as the response to the relational properties (e.g. larger or brighter) of the stimuli. Kohler (1938) conducted a series of experiments where chickens were trained to discriminate between two shades of gray. The S3 responded to a light gray stimulus as SD and a dark gray as SA. In the test with the SA (dark gray) and a darker gray, the previous 5A was preferred. Kohler reasoned that "when an animal is trained, it may well be that . . . its choice is of one side of the pair which the colours together compose" (Kohler, 1938). Fur- thermore, since the gs did not respond to the absolute properties of the stimuli (i.e. X foot-candles = SD, 1/2 X foot-candles = SA), the data was taken as evidence that the absolute, or S-R theories of discrimination were inadequate. However, Spence (1937) points to several studies where transposition has failed to occur. As an explanation for the diverse findings Spence offers a S-R theory based on three postulates. These are: (a) learning is "a cumu- lative process of building up the strength of the excitatory tendency of the positive stimulus cue . . . by means of suc- cessive reinforcements of the response to it . . ."; (b) similarly,non-reinforced responses to the negative stimulus establish an inhibitory tendency for non response to it; (c) total response tendency to any particular stimulus can be predicted by subtracting the inhibitory gradient from the excitatory gradient at the value of the stimulus in question (Figure l) (Spence, 1937). 5D Total resp.ten- 1) dency @ stim. value 3 (SA) response tendency @ Excita- stim.value 4 (SD) tory resp.tendency @ + stim.value 5 resp.ten— @ stim. value 7 0Stimulllus vzalue3 “ 5 61///7 :3 Inhibi--~ tory SA V Figure 1. Example of the Spence model of total response tendency. In an attempt to support his theory, Spence (1937) trained chimpanzees to respond differentially to 160 cm2 (+) and 256 cm2 (-) white squares. After a criterion of 90% correct responses was met the SS were presented with two white squares of either 256 and 409 cm2 or 100 and 160 cm2, with responses reported as the percentage of transposition in the test trials, i.e. a preference for the smaller test stimulus of the pair. In the critical test, 100 and 160 cm2, percent transposition was only 53.3%. This confirmed the prediction made by the Spence model as illustrated in Figure 2. Since the SS did not prefer the smaller of the two stimuli as predicted by the relationist' position, the results demonstrate the superiority of the Spence theory in explaining the simple two choice trans- position test procedure. 103:9 (+) <—) Stimulus size Figure 2. Diagrammatic representation of relations be- tween the hypothetical generalization curves, positive and negative, after training on the stimulus combination 160 (+) and 256 (-). The numbers above the stimulus size numbers rep- resent total response tendency. (Spence, 1937) in _ ‘4‘- . 1’13““... Perkins (1953) noted that although studies using differential conditioning have consistently found the stimu- lus intensity dynamism effect postulated by Hull (1943), studies using a simple, or non-differential re5ponse tech- nique have often found that an increase in stimulus inten- sity often depresses response rate. Perkins postulated that stimulus intensity dynamism was an artifact of the differential conditioning technique that could be explained by the Spence model as illustrated in Figure 3. Perkins' interpretation of this model is "although generalization of the effects of positive training are the same, there is greater response strength to stimulus G [a stimulus of greater intensity than SD] than to stimulus L [a stimulus of less intensity than SD]. This difference is the result of greater generalization of extinction [non-reinforcement] effects to L than to G"(Perkins, 1953). A subsequent test with rats in a simple versus a differential response train- ing model supported this interpretation. \ 'L M G Stimulus intensity Figure 3. Diagrammatic representation of the hypothetical generalization curves, present in all differen- tial conditioning situations according to the Spence model of discrimination. (Perkins, 1953) In a critical review of transposition by Hebert and Krantz (1965), the authors point to various inadequacies inherent in the Spence formulation. One very important weakness is that the shape of the gradients has a profound effect on the predictions made by the model. It is unlikely that enough research on specific gradient shapes will be done in the near future to enable the exact selection of the appropriate gradient. In addition, the Spence model is incapable of ex- plaining the results of the intermediate size problem. In this situation §s are trained to differentially respond to one SD (the intermediate sized stimulus) and two SA stimuli, with three stimuli instead of two presented in the test set. In an experiment by Gentry gt_§l. (1959), monkeys trained to respond to an intermediate sized box preferred an intermediate sized box in subsequent transposition tests even when the intermediate member of the test set was not the original SD. The Spence model should predict that re- gardless of its new relational position, the training SD would be preferred (Figure 4). 34 ‘ 62 100 160 256 409 655 (—) (+) (') Figure 4. The Spence model for the intermediate size prob- lem. The solid line below the positive gradient represents a summation of the two negative gra- dients. (Spence, 1942) A recent formulation of the process of discrimina- tion by Zeiler (1963) utilizes certain basic postulates of the AL theory first proposed by Helson (1947). The Zeiler AL theory has been found to be capable of explaining the results of the intermediate size problem where theory has failed, and because Zeiler's theory volve generalization gradients, the difficulty the shape of the gradients is not encountered. In the Zeiler theory discrimination is process of learning to respond to the ratio of (SD) stimulus to the AL instead of learning to the Spence does not in- in specifying seen as a the positive respond to a particular absolute stimulus value. The Specific postu- lates of the Zeiler theory (Zeiler, 1963) are: l. The AL is the weighted log mean of the disciminative stimuli and residual AL (previous AL). Let Xi rep- resent the discriminative stimuli, R the residual AL., y the constant applied to the log mean of the discriminative stimuli, x the constant applied to the residual AL, y + x = 1.00, and n the number of discriminative stimuli. The AL is: 2 . Log AL = y { 1:9 X1) + x log R (a) The S enters training with a residual AL which exerts an extra-experimental effect on the AL. With each successive trial, R becomes increas- ingly a function of the series stimuli since R is primarily dependent upon immediate past stimulation. The effect of irrelevant prior stimulation in negligible by the completion of training so that: Log Training AL = E—£%E—§£ (b) The AL on the first test trial immediately after the completion of training is eXpressed by the formula: Z ' . . Log Test AL = y ——£%3—§£ + x log Training AL 2. Each stimulus in the series is defined as the ratio of the stimulus area to the AL. 3. The S learns in training to respond to the ratio of the positive stimulus to the AL. 4. (a) Probability of response on the first test trial is a function of the degree of similarity be- tween the individual test stimulus ratios and the positive training ratio whenever all of the test stimulus ratios are not either larger or smaller than the positive training ratio. (b) When all of the test stimulus ratios are either larger or smaller than the positive training ratio, response will be divided randomly among the test stimuli. Since the weighting constants x and y must sum to a total of 1.00, as the value of one constant increases the other must decrease. Thus the formula for the test AL indicates that as the impact of the discriminative stimuli becomes greater on the establishment of the new Al, the im- portance of the residual AL in the determination of the new AL must decrease and vice versa. Zeiler (1963) has noticed that as the distance separa- ting the values of the test stimuli becomes larger, the value of y increases, and to date this is the extent of the informa- tion available on the determining factors of the weighting constants. It should be noted that the Zeiler theory makes no men- tion of the negative or non-reinforced stimulus. In constrast to Spence, Zeiler assumes that transfer is primarily of the positive stimulus and that "While learning of the negative stimulus may and undoubtedly does occur, the re-analysis of the data in the literature and the results of the author's experi- ments do not require consideration of the negative ratios in order to deduce the test response" (Zeiler, 1963). Besides predicting the results of various interme- diate size problem experiments by Spence (1942), Gonzales EE_El' (1959), Gentry EE_El° (1959), and Stevenson and Bit- termann (1955), Zeiler has conducted a series of experiments using 4 and 5 year old children in the intermediate size problem. He was able to find six basic phenomena that, at this point, only the Adaptation Level theory is able to integrate under a single unified explanation. "They are: (a) relational choice (tranposition); (b) systematic ab- solute response; (c) systematic choice of neither an absolute nor relational stimulus; (d) equal preference for two of the three [test set] stimuli; (e) random response; and (f) the points of transition between each of these modes of response" (Zeiler, 1963). All of the previous research and predictions with the Zeiler Adaptation Level theory has involved size dis- criminations. In the same vein the Spence theory has not been experimentally verified much outside the transposition problem. The present design will introduce intensity as the discriminative stimulus dimension and extinction as a spe- cial experimental manipulation. Specifically, after the brightness discrimination has been established, all Ss will be extinguished with the stimulus light off and .125 foot- candles of ambient light present (extinction 1). Following this, non-reinforced responses will be recorded with the original discriminative stimuli presented (extinction 2). Given this situation the Spence model is constructed as in Figures 5A (groups with a bright light SD in training) and 5B (groups with a dim light SD in training). In ex- tinction 1 it can be seen that the total response tendency with the stimulus lights off is much greater for the D groups than for the B groups. Therefore the D groups should respond more to the stimulus lights off than the B groups (prediction 1). In extinction l, a second inhibi- tory gradient is being established. The subtraction of both inhibitory gradients gives the total response tend— ency to SD in extinction 2. Thus the response tendency 10 to SD should be much greater in the B groups than in the D groups (prediction 2). 3D + R.A e s p Resp. tend. ReSp. tend. after ext. 1 0 before ext. 1 n s e t Resp. tend. @ 25 fc : ' 7. foot—candles F d - : Gradient from ext. to off lights / c ,r’ SA (ext. 1) Y Figure 5A. Summation of gradients for all B groups. D S + R1) Resp. tend. before ext. 1 e s P o Resp. tendency after ext. 1 n s e Resp. tend. @ .125 fc. t \ e \ g r ‘ . n 5.0 16.8 , , ” / foot-candles——‘+ d z" . _ e ,,/ TJ/' Gradient from ext. to off n lights (ext. 1) c ,” y ”' SA Figure 5B. Summation of gradients for all D groups. 11 Because the values of the weighting constants x and y cannot be determined before the data is collected, no predictions can be derived from the Zeiler theory. In- stead the Zeiler theory will be applied to the results and in this way it is hOped that information can be gathered concerning limitations and indications for further research. In addition, if the Zeiler theory.is able to handle the ob- tained data, some further information on the parameters de- termining the values of x and y may be found. In the application of both models, it is assumed that the S is responding to the total amount of light in the box which is a direct reflection of the intensity of the stimulus lights. Thus, with the discriminative stimuli off it is assumed that the rat is responding to the .125 foot-candles of ambient light rather than that reflected by the stimulus patch. METHOD Subjects: The SS were 32 male Sprague-Dawley rats, 90-120 days old. Apparatus: The apparatus consisted of a typical one-bar Skin- ner box provided with a grid floor. A l x l-l/2 inches white painted lucite stimulus patch was located midway between the bar and dipper 4 inches from the floor of the box. The patch was illuminated by a 28 volt light bulb located outside the training chamber. The discriminative stimuli, lights of 5.0 and 16.8 foot-candles, were presented in a random sequence programmed on a 64 pole stepper switch which was advanced D or SA stimulus was present every 30 seconds. Either the S at all times during training. With the stimulus lights off .125 foot-candles of ambient light was present inside the training chamber, provided by a 7-1/2 watt house light lo- cated outside the chamber. A white noise of 79 decibles served a masking function. Procedure in original learning: Discrimination training was given 45 minutes per day, typically 5 days per week, until criterion was met. The only water available on running days was that obtained in the experiment, while on days the Ss were not run 45 minutes of water was made available at the home cage. Food was given on an ad libitum basis. The Ss were randomly assigned to 8 sub groups (Ta- ble 1), and by the method of successive approximations 12 13 were trained to bar press in the constant presence of the SD. After the bar press response was established, one additional session was given with all responses reinforced and with SD stimulus present during the entire session. Table l. Designation of groups. . . . . . D . D Training Stimuli Bright S Dim S Extinction criterion in off lights (Ext. . . . . 1), consecutive min— 10 min. 5 min. 10 min. 5 min. utes with no response Type of stimulus pre- D A D A D A D A sented in Ext. 2 S S S S S S S S Group name abbreVia- B10D B10A B5D B5A D10D D10A D5 D5A tion Number of subjects 4 4 4 4 4 4 4 4 L l j\ I J B Groups D Groups The conditions were then programmed for discrimi- nation, and Ss were allowed to learn the discrimination to a criterion of 2 out of 3 consecutive days at 85% cor- rect responses or better. to 20 days of discrimination training. PrOcedure on test day: performance all Ss were given 5 minutes of warm-up con- On the day following criterion All Ss reached criterion in 4 sisting of 5 presentations each of the SD and SA in a pre-determined order (Table 2). This was followed by l4 extinction to criterion (refer to Table l) with the stimu— lus lights off (extinction 1), followed in turn by 10 non- reinforced test trials with the training SD and S pre- sented alternately for 30 seconds each (extinction 2). Table 2. Order of presentation of stimuli in warm-up. Minute B Groups D Groups 1 SD SD sA SD 2 SA SA SD SD A SA 3 D S S 4 sA sA A S D D 5 S S U) U) RESULTS The mean responses in warm-up for all groups to SD and SA are given in Table 3A. t-tests of the data (Table BB) indicate that there are no significant differences between the various groups that would tend to produce the results obtained in extinction l and extinction 2. Table 3A. Group mean response to SD and SA in warm-up trials. Mean Responses Group SD SA 810D 39.5 13.0 810A 46.3 10.5 BSD 41.3 8.8 85A 37.5 11.5 010D 38.0 5.8 010A 41.0 6.3 05D 40.3 6.0 05A 35.8 9.0 In extinction l the group mean responses, given in Table 4A, were greater for the B groups than for the D groups. An analysis of variance (Table 4B) showed the dif- ference to be significant (P<.001). No other effects were significant. 15 16 Table 3B. 2—tailed t—Tests of SD and SA responses in warm-up. Test ; Response t- Signifi- Groups Type Value d'f' cance # 810 vs 85 SD .838 14 N.S. D10 vs D5 sD .371 14 N.S. 810 vs B5 sA .619 14 N.S. D10 vs 85 sA 1.034 14 N.S. pooled 810,85 vs 810,85 SD .852 30 N.S. pooled BlO,DlO vs 85,85 sD .110 30 N.S. pooled 810,85 vs 810,85 sA 2.68 30 P<.02 pooled 810,810 vs B5,D5 sA .528 30 N.S. Table 4A. Group mean responses in extinction 1. Group " Mean R's J ' 810 *-_* 47.5 B5 50.2 D10 78.1 D5 72.7 Table 4B. Summary table of the analysis of variance of extinction 1. Source SS df MS f Sig Extinction criterion 38.28 38.28 .111 N.S. Bright or dim SD 7110.28 1 7110.28 20.59 INHOOI Interaction 457.53 1 457.53 1.33 N.S. Error 9669.63 28 345.34 Totals 17275.72 31 17 A graph of the cumulative responses to SD in ex- tinction 2 is given in Figure 6A, and it can be seen that the B groups responded significantly more than the D groups. An analysis of variance (Table 5) indicated the difference was significant (P<.05). No other effects, including SA responses (as cumulatively graphed in Figure 6B) were sig- nificant. Table 5. Summary table of the analysis of variance of extinction 2. Source SS df MS .f Sig Between Bright or dim train- ing SD (A) 558.13 1 558.13 8.14 P<.01 SD or SA first in ext. 2 (B) 3.51 l 3.51 .051 N.S. Extinction l cri- terion (C) 2.63 l 2.63 .038 N.S. A X B 3.52 l 3.52 .051 N.S. A X C 21.40 1 21.40 .312 N.S. B X C 1.27 l 1.27 .019 N.S. A X,B X C 5.64 1 5.64 .082 N.S. Error 1646.23 24 68.59 Total 2242.13 31 Within 313 or sA response (D) 456.88 1 456.88 8.63 P<.Ol A X D 228.78 1 228.78 4.32 P<.05 B X D 1.90 l 1.90 .036 N.S. C X D .78 1 .78 .015 N.S. A X B X D 1.88 1 1.88 .036 N.S. A X C X D 9.78 l 9.78 .185 N.S. B X C X D .38 l .38 .007 N.S. A X B X C X D 3.53 l 3.53 .067 N.S. Error 1220.50 24 52.94 Total 1974.41 32 m pg 131' 12” Figure 6B. 41"!"" Key 71 ' l8 B D J 10 Q J 6., 81049 0 L! - /. BSA G “a 3‘ c II--I’--I---I--‘I—’:El:"la 010D. ‘‘‘‘ ‘ 2- / D—--D---D’ 2r" 810A ------ J , xCo-uo—"t’ 0- 0 1 DSD .‘-T-'—--. . 85A ------- 0 1 2 3 4 5 6 7 8 9 10 E] :1 Minutes of extinction 2 >: Figure 6A. Number of cumulative responses to SD, extinction 2. Key Group /\6- B101). 4 5” BlOAcr e—<3 uJ B5D I) _4| 3.1 I ‘___ _ BSA G— _B A 7' - - __ __ ______.~—— D 2T 4.7 «"810 .-—--_.. 1'1 — ”&---M-. ._ .I..._. —"../-6 DloAO- - _ a O -0 01 -- -- - ' ~- ’--—-‘-—’--DSD .- -———_' 1 3 A 5 6 7 8 9 1085Al:J—-----El —"—"" Minutes of extinction 2 > Number of cumulative reSponses to SA, extinction 2. DISCUSSION The first prediction derived from the Spence model was that all D groups would respond more than the B groups in extinction 1. This prediction was supported by the analy- sis of the data. The second prediction; that the B groups would respond more in extinction 2 than the D groups was also confirmed by the data. It should be noted that in the t-test analysis of the warm-up data, the significant t-ratio obtained between the pooled B10, B5 versus D10, D5 groups (SA responses) was produced by a greater response level to SA in the B groups. This would tend to work against the predicted results and therefore poses no problem to the interpretation of the data obtained in extinction 1 and extinction 2. For a detailed mathematical analysis of the data by the Zeiler theory, the values of the constants x and y must be determined. Since the method of obtaining these values is basically an after the fact computation followed by a re-test, x and y cannot be precisely employed in this de- sign. However, the various adaptation levels and stimulus to adaption level ratios have been computed with y varied from .01 to .99 and are presented in Table 6. For the B groups it can be seen that at a value of y of .85 to .9, the B groups would definitely be responding to the ratio 19 20 hm. om.H mm. em. mw.a mm.w oma. Hm.m mm. om. mo.m mo. em. mm.a mm.o mma. Hm.¢ om. em. mH.m mm. em. mm.a mm.m mmm. Hm.m mm. vm.a om.v mm. vm. ~m.a mw.m eme. HN.m on. mm.H mm.m ma. em. mm.a va.m mo.H Hm.m om. mo.a Ho.m Nmo. em. mm.a mm.v om.m Hm.m om. No.H vv.m mmo. em. Nm.H mm.v nm.v H~.m ma. om. mm.~ No. em. mm.H mm.m oo.m Hm.m oa. Hm. Hm.a wao. em. mm.a mm.m mm.m Hm.m Ho. ~mq< mmmw\\. AWMM\\\ fimw\ wmw\\. Ammqev N Aamqsv H Lease sea usmflum 10mmma.vmmo sec unmeum ooHuosHuxm ooHuosHuxm maesfloue Ad‘ I. -3- - - ii. . _\MMMMEflum moflumm mam>mq soflumummod wsam> m .mm. on AC. Eoum pmfinm> M Spas mam>ma soflpmummpm ou Hasfiflpm mo moflumu pom mam>wa coaumummwm muoflum> .m magma 21 of the original training SA in extinction 1. For the re- maining y values it is questionable whether the ratios in extinction l are close enough to the original SA ratio to warrant the assumption that further extinction to SA is taking place. However, since it is certain that there is no effect of extinction 1 on extinction to the SD train- ing ratio, the response of the B groups in extinction 2 can be predicted by finding the ratio of the bright and dim stimulus values to ALE2 that most closely correspond to the training SD ratio. Thus, if the ratio of the bright light to AL is more similar to the training SD ratio than E2 the training SA ratio, response to the bright light in ex- tinction 2 would be predicted. If, however, the ratio of the dim light to AL is closer to the training SD ratio, E2 response to the dim light would be predicted in extinction 2. It can be seen from the table that if y were equal to .01 to .l and .9 to .99 the predicted response for the B groups would be to the bright stimulus. Values of y from .15 to .85 would result in a prediction of reSponse to the dim light. For the D groups response in extinction 1 can be predicted by noting that all ratios computed in extinction 1 are nearer to the training SD ratio than the training SA ratio. However it is difficult to specify how close is close enough to warrant the assumption that the Ss are responding to the original training SD ratio, but y values of .85 and .9 result in extinction 1 ratios that 22 are very close to the training SD ratio. In this case the D groups should respond a great deal in extinction 1. Prediction of response of the D groups in extinc- tion 2 must take into account whether extinction 1 actually produced extinction to the training SD ratio. Thus, if a S has been extinguished in extinction l to the training SD ratio, and if the ratio of SD to AL is similar to the E2 original training SD ratio, no response would be predicted to the dim light. This is certainly the case where y = .85 to .9. If, however, the value of y is varied from .01 to .7 it is questionable whether extinction 1 would produce extinction to the original training ratio, and if it did not, response to the dim light would be predicted. By pooling all of the preceding considerations it can be seen that values of y from .15 to .85 will result in erroneous predictions. If y is varied from .01 to .1 the predictions resulting are weak but largely correct, while y values of .9 to .99 are very accurate. In summary, with y = .9 extinction 1 will result in extinction to a ratio very similar to that of the dim stimulus in training. This results in the prediction of more response in the D groups than in the B groups in extinction l (prediction 1). In extinction 2, the B groups will respond to the training SD stimulus because extinction 1 has only served the pur- pose of further extinguishing responses to SA. However the D groups will have been extinguished to their train- ing SD ratio in extinction 1 resulting in little response 23 to the dim light in extinction 2. In addition there should be little response to the bright stimulus because a ratio of 1.82 had not been reinforced in original training. This results in more response to the bright stimulus in the B groups than the D groups in extinction 2, with little or no response to the dim light in either group (prediction 2). Both predictions were supported by the data. The uncommonly large value of y (.9) necessary to account for the results seems to indicate that since the two extinction situations are so drastically different from the situation immediately preceding it the residual AL has little bearing on the establishment of the new AL. This conclusion seems logical in that it might be expected that the radical change in the stimulus conditions from warm—up to extinction l, and extinction l to extinction 2 would tend to make the new AL more dependent on the pres— ent stimulation than the residual AL. In addition, as previously mentioned Zeiler (1963) found that as the sep- aration of the values of the test stimuli becomes larger, the value of y increases, and this type of distance inter— action could reasonably be true across stimulus sets as well as within. While the Spence theory is able to predict the results of the present experiment, it is limited not only by its non applicability to the intermediate size problem, but also by the extent to which the shape of the generali- zation gradients can be specified. 24 On the other hand, the Zeiler theory appears to be more general than the Spence theory as shown by its ability to apply to the results of the intermediate size problem as well as the results of the present experiment. The major limitation of the Zeiler theory is that until sufficient information can be gathered on the parameters of x and y to allow their a.prionicomputation, its predictive value is limited to a test re-test design. Zeiler (1963) feels that in the future a specific probability statement may possibly be derived concerning t response on the first test trial, and this combined with an a priori computation of x and y would make the Zeiler theory a precise instrument for prediction. Because of the apparently greater generality of application and the potential precision of prediction, the Zeiler theory would seem to be more preferable than the Spence theory at this time. In applying Zeiler's mathematical model it was no- ticed that a simple extension of the present design should provide a difficult, if not impossible situation for the application of the Zeiler theory. If extinction l were done in total darkness, the log 2 Xi (the discriminative stimuli) in extinction 1 would equal minus infinity. This value would enter into the computation of AL as residual E2 AL thus making the mathematical manipulations at best dif- ficult. It is impossible to predict how the Zeiler theory 25 might handle this problem, and the results of such an ex- periment could prove to be valuable. Because the large value of the y constant can be defended by previous data some consistency of the distance effects is indicated. This could be easily checked in two ways: varying the intensity difference between the dis- criminative stimuli; and varing the difference between the training situation and extinction 1, between training and extinction 2, and between extinction l and extinction 2. If the value of y does not vary with a fair degree of cor- respondence as the separation vaires, the weighting con- stants would be suspect. REFERENCES Gentry, G. V., Overall, J. E., and Brown, W. L. Transpo- sition Responses of Rhesus Monkeys to Stimulus Objects of Intermediate Size, American Journal of psychology, 1959, 13, 453-455. ‘ Gonzales, R. C., and Ross, S. The Basis of Solution by Preverbal Children of the Intermediate Size Prob- lem, American Journal of Psychology, 1958, 71, 742-746. ‘— Helson, H. Adaptation Level as a Frame of Reference for Prediction of Psychophysical Data, American 5 Journal of Psychology, 1947, SS, 1-29. Herbert, A., and Krantz, D. L. Transposition: A re- evaluation, Psychological Bulletin, 1965, SS (4), 244-257. Kohler, W. Simple Structural Functions in the Chimpan- zees and in the Chicken, A Source Book of Gestalt Psychology. Edited by W. D. Ellis. New York: Harcourt and Brace, 1938. Perkins, C. C., Jr. The Relation Between Conditioned Stimulus Intensity and Response Strength, Jour- nal of Experimental Psychology, 1953, SS, 225- 231. Spence, K. W. The Differential Response in Animals to Stimuli Varying Within a Simple Dimension, Psy- chological Review, 1937, 13, 430-444. Spence, K. W. The Basis of Solution by Chimpanzees of the Intermediate Size Problem, Journal of Ex- perimental Psychology, 1942, SS, 257-271. Stevenson, H. W., and Bitterman, M. E. The Distance Ef- fect in the Transposition of Intermediate Size by Children, American Journal of Psychology, 1955, SS, 274-279. Zeiler, M. D. The Ratio Theory of Intermediate Size Discrimination, Psychological Review, 1963, 19, 516-533. 26 MICHIGAN STQTEl II III 3IIII I UNIV. LIBRARIES |IIII||IIII| IIII IEIDQOSI 19