City Research Online Perceptual Categorization 1 Comparison and Contrast in Perceptual Categorization

We report a series of five experiments in which people categorized pairs of perceptual stimuli varying in degree of category membership and in similarity to one another. Experiments 1-4 investigated color categorization. Experiment 1 required conjunctive or disjunctive category judgments, and Experiment 2 required simultaneous but separate categorization of each stimulus. In both experiments, categorization of one color was reliably contrasted from that of the other: As one color became more likely to be included in the category, the other color became more likely to be excluded. This similarity-based contrast effect occurred only when the context stimulus was relevant for the categorization of the target stimulus (Experiment 3). The effect was not simply owing to perceptual color contrast (Experiment 4), and it extended to pictures from common semantic categories as well (Experiment 5). Results were consistent with a sign-and-magnitude version of Stewart and Brown’s (2005) SD-GCM model, in which both similarity to a target category and difference from a contrasting category inform categorization choices. The data are also modeled in terms of the balancing mechanism of Criterion Setting Theory (Treisman & Williams, 1984), whereby the decision criterion is systematically shifted toward the mean of the current stimuli. Perceptual Categorization 3 The categorization of perceptual stimuli, such as colors and pictures, is one of the most basic functions of cognition. But how are such category decisions made? Traditional models of perceptual categorization posit that the target stimulus is initially compared to the category representations in long-term memory, and is subsequently judged to belong in the category to which it is most similar (for review see Murphy, 2002, Ch. 2). For example, Nosofsky’s (1986) Generalized Context Model (GCM) first computes the similarity of a target to some set of stored exemplars from each candidate category, and then applies Luce’s Choice Axiom to derive the probabilities that the target will be judged to belong in one category or another. Alternatively, in Ashby & Gott’s (1988) Decision Bound model, a stimulus is deterministically allocated to a category depending on its position in stimulus space relative to some fixed decision criterion separating the candidate categories (see also Gardenfors, 2000). The location of a target in stimulus space is essentially its similarity to the other exemplars. Thus, in one form or another, most traditional models share the common assumption that categorization is similarity-based. However, recent evidence suggests that these similarity-based models may be too simplistic. In particular, when a number of targets are categorized in turn, the similarity of successive targets may additionally influence categorization (DeCarlo, 2003; Petzold & Haubensak, 2001, 2004; Stewart & Brown, 2004; Stewart, Brown & Chater, 2002; Treisman & Williams, 1984). This inter-stimulus similarity can provide either a positive or a negative cue to categorization: If two instances are similar, they likely belong in the same category, and if two instances are dissimilar, they likely belong in different categories (Stewart & Brown, 2004). Long-term category representations with fixed decision criteria (e.g., the Decision Bound and GCM models) are unable to account for such effects of stimulus comparison, as described below. We report five experiments that investigate how the similarity or dissimilarity of two stimuli affects their categorization. The importance of such Perceptual Categorization 4 inter-stimulus effects lies in their implications for models of perceptual categorization. Similarity-based Models of Categorization In this section we consider the predictions of two well known similarity-based models of perceptual categorization (i.e., prototype and exemplar models), using color categorization as a paradigmatic example. According to prototype models, the color space is divided into (more or less) universal categories anchored around particular focal hues (Berlin & Kay, 1969; Kay & McDaniel, 1978; MacLaury, 1991; Rosch, 1975; Rosch Heider, 1972; but see Roberson, Davies & Davidoff, 2000). For example, there tends to be greater consensus about the best example of BLUE (i.e., focal blue) than about the boundary between BLUE and PURPLE. The categorization of any hue, then, is based on its similarity to the focal hues of the different color categories (Bornstein & Korda, 1984; Rosch, 1975; Rosch Heider, 1972). In order to decide if a given hue is BLUE or PURPLE, a decision criterion is defined on the color spectrum between those categories, and judgments are based on which side of this boundary the hue falls. According to exemplar models, a category is represented by storing exemplars as they are experienced, and categorization is a function of the similarity of the target instance to some set of those stored exemplars that are retrieved for comparison (W. K. Estes, 1994; Lamberts, 1995, 2000; Medin & Schaffer, 1978; Nosofsky, 1986; Nosofsky & Palmeri, 1997). So continuing our example, the target hue is compared to a set of blue exemplars and a set of purple exemplars, and the target is included in the category to which its summed similarity is greatest. Thus, prototype and exemplar models both posit that categorization is a function of the similarity between the target instance and the category representation. Ordinarily it is clear to which category a target instance is most similar, and hence categorization is simple and unambiguous. However, because category boundaries are not explicitly represented in either prototype or exemplar models, different individuals may well Perceptual Categorization 5 set the decision criterion at different points on the dimension, and even a single individual may vary the placement of the criterion across occasions. Thus, due to the continuous nature of many perceptual categories, vagueness arises in borderline regions between those categories. For example, the color spectrum gives rise to borderline stimuli when a target hue is equally similar to the BLUE and PURPLE categories. In such cases, judgments of the hue should be randomly divided between the two color categories (see Bornstein & Korda, 1984; Rosch, 1975; Rosch Heider, 1972). Our experiments investigate the hypothesis that the categorization of borderline stimuli is not wholly based on similarity to stored category representations. Rather, some evidence indicates that participants tend to adopt a strategy of inter-stimulus comparison: When categorizing a borderline stimulus, the indecision produced by its equal similarity to the competing categories is resolved via comparison to other recent stimuli (Stewart et al., 2002). This inter-stimulus comparison results in systematic deviations in borderline categorization. Notice that, because prototype and exemplar models were developed to explain the categorization of individual stimuli, neither model specifies any mechanism by which interstimulus comparison would affect category decisions. However, these similarity-based models can be adapted to accommodate the effects of recent stimuli. If the prototype is a running average of previously categorized stimuli, then one can assume that the category representation will be biased toward weighting recent stimulus values more heavily. And likewise in an exemplar model, recent exemplars may be more likely to be retrieved as representative of the category, or may be more heavily weighted in the computation of similarity (Nosofsky & Palmeri, 1997). The result of this overweighting of recent stimuli is that presentation of any non-focal hue will cause the category representation to shift in the direction of that hue. For example, presentation of a hue midway between focal blue and the Perceptual Categorization 6 blue-purple boundary (call it stimulus S1) will draw the center of the BLUE category slightly toward the PURPLE category, since S1 has been given greater weight than other stimuli. In fact, the magnitude of this category shift will depend on the extremity of the stimulus, with more distant stimuli causing greater shifts in the category representation. To consider the effect of inter-stimulus comparison, suppose that a hue on the category borderline between BLUE and PURPLE (stimulus S2) is judged in the context of S1. Because S1 has drawn the BLUE category toward PURPLE, S2 will now appear more similar to the BLUE category than it would have otherwise, and the categorization probability for S2 therefore tips in favor of BLUE. Thus, in this case, similarity-based models would predict an assimilation effect, such that the target hue is more likely to be included in the category of the context hue. 1 Furthermore, given that the magnitude of the category shift is an increasing function of stimulus extremity, it follows that the likelihood of assimilating a borderline stimulus S2 should increase as the context stimulus S1 approaches that category boundary (providing of course that S1 is itself still categorized in the target category). That is, if S1 is a focal blue, it will not shift the category representation, and hence there should be no assimilation of S2. But as S1 approaches the BLUE-PURPLE boundary, the magnitude of the category shift increases, and therefore the likelihood of assimilating the borderline hue S2 will also increase. To summarize, then, this adapted version of similarity-based models predicts an assimilation effect that increases as the context stimulus approaches the borderline stimulus. The Similarity-Dissimilarity Model An alternative account of inter-stimulus comparison has been proposed by Stewart and Brown (2005). Before describing their model, we first describe the category contrast effect that it was devised to explain. The basic finding is that the categorization of an atypical stimulus close to the category borderline is more accurate following a stimulus from the Perceptual Categorization 7 opposite category than following a stimulus from its own category. To demonstrate the phenomenon, Stewart et al. (2002) presented ten tones of varying pitch, with each tone perceptually equidistant from its neighbors, and they taught participants to categorize the five lowest (i.e., tones 1 to 5) into one category and the five highest (i.e., tones 6 to 10) into another. They found that tone 5 was categorized more accurately after tone 10 than after tone 1. And conversely, the categorization of tone 6 was more accurate following tone 1 than tone 10. In a second experiment they produced a similar result with visually-based categories of geometric stimuli. Thus, the categorization of a borderline stimulus was reliably contrasted from the category of the preceding stimulus. This is the opposite of what similarity-based models would predict. Using a different perceptual domain, Friedenberg, Kanievsky and Kwasniak (2002) created ambiguous borderline face stimuli by morphing a male face and a female face, such that the morphed stimulus was a 50:50 male:female composite. Participants judged the apparent sex of those morphed faces, with judgment of each morphed face preceded immediately by either its original male face or its original female face. Friedenberg et al. also obtained a category contrast effect, such that the same morphed face was more likely to be judged FEMALE after presentation of its male face, and was more likely to be judged MALE after presentation of its female face. To account for this category contrast effect, Stewart and Brown (2005) proposed an extension to the GCM – the Similarity-Dissimilarity GCM (SD-GCM). The novel aspect of the SD-GCM is its claim that the categorization of a stimulus is based not only on its similarity to the exemplars in category A, but also on its dissimilarity to the exemplars of category B. Effectively, when the target item is very similar to a category A exemplar, the similarity component will carry most weight, and one would expect assimilation (as in the similarity-based models). So if a context stimulus S1 is very similar to the BLUE-PURPLE Perceptual Categorization 8 borderline stimulus S2, and if S1 is categorized as BLUE, then S2 will also be called BLUE. However, if S1 is quite different from S2, then the dissimilarity component assumes more weight, and S2 is more likely to be called PURPLE. Thus, the SD-GCM predicts assimilation when the stimuli are similar, and contrast when they are dissimilar. In intuitive terms, people may wish not to differentiate between very similar stimuli, and therefore will be biased to categorize them together. But when faced with a pair of stimuli that are quite different, people will be biased to place them into different categories. In comparative judgments of this sort, the direction of difference (i.e., the sign) between S1 and S2 may constrain the response to S2. To illustrate the concept of sign, consider three stimuli S1, S2 and S3 that vary in order from least to most blue. In the context of S1, S2 has a positive sign, as S2 is more blue than S1. But in the context of S3, S2 has a negative sign, because S2 is less blue than S3. In certain cases, this sign information produces a monotonicity constraint: If S1 is included in the target category, and if the sign of S2 is positive, then S2 should also be included in that category. For example, if S1 is called BLUE, and S2 is more blue than S1, then by deduction S2 must also be BLUE. In addition to this monotonicity constraint, Stewart et al. (2002) made further use of sign information. In fact, sign allows the SD-GCM to explain the contrast effect: If tone 1 belongs in category A, and tone 5 has a negative sign (i.e., is of higher pitch), then tone 5 is less likely to belong in category A. Stewart and Brown (2004) evaluated two alternative versions of the SD-GCM. Both models use sign to predict category judgments. However, the models differ in their use of this sign information. In the sign-and-magnitude model, both the direction and the size of the difference between S1 and S2 affect the judgment of S2. In Stewart et al.’s (2002) study, the borderline tone 5 has a negative sign in the context of both tones 1 and 3, but the magnitude of this difference is greater for tone 1 than for tone 3. Thus, by the sign-and-magnitude Perceptual Categorization 9 model, the judgment of tone 5 should exhibit a larger contrast effect when preceded by tone 1 than by tone 3. As an alternative, Stewart and Brown (2004; see also Laming, 1997) also tested a sign-only model, which incorporates the direction of difference between S1 and S2 but not the size of that difference. By the sign-only model, the judgment of tone 5 should exhibit a contrast effect of equivalent magnitude following tones 1 and 3, since it solely uses ordinal information to predict categorization. The evidence for differentiating between the sign-and-magnitude and sign-only models is limited. Both Stewart et al. (2002) and Friedenberg et al. (2002) showed strong contrast effects between borderline stimuli and extreme category exemplars, but neither study manipulated the similarity of the context stimulus (S1) to the borderline stimulus (S2). For instance, Stewart and colleagues examined the judgment of tone 5 in the context of tone 1, but not in the context of tones 2, 3, or 4. As a result, neither study is capable of discriminating between the sign-and-magnitude and sign-only models. Stewart and Brown (2004) conducted a further experiment in which the borderline tone 5 was judged in the context of each of the other tones, and the category contrast effect was replicated. That is, the sign of the difference between stimuli affected the categorization of the borderline stimulus. However, Stewart and Brown found no evidence that the magnitude of the difference affected judgment—tones 1, 2, 3, and 4 produced equivalent contrast effects on the judgment of tone 5. Thus, the sign-only model received support. Despite this result, though, Stewart and Brown (2005) subsequently advanced the sign-and-magnitude model rather than the sign-only model. So it appears that before rejecting either model, further investigation is necessary. The Present Research We conducted a series of experiments that assessed the judgment of a borderline stimulus in the context of another stimulus of varying similarity either within or across the category boundary. The purpose of the experiments was to provide a more stringent and Perceptual Categorization 10 thorough test of the models of categorization described above. Our experiments differed in three important respects from the experiments of Stewart and Brown (2004; Stewart et al., 2002): We used familiar categories, without corrective feedback, and with simultaneous presentation of stimuli. These differences are discussed in turn below. First, whereas Stewart and Brown (2004; Stewart et al., 2002) used arbitrary categories (i.e., tones and geometric shapes), we used familiar semantic categories (i.e., colors and animals). We suggest that the use of arbitrary categories makes inter-stimulus comparison more likely. Because participants have no prior experience with an arbitrary category, they are unable to resolve the category decisions by reference to representations in long-term memory, and hence they likely will be more reliant on comparison to other experimental stimuli. In the case of well learned semantic categories, though, long-term category representations may be used to resolve the category decision. For example, when judging whether a given hue is BLUE, the participant can easily access a stable, long-term representation of the category, and therefore need not compare that hue to other contextual stimuli. But when judging whether a particular tone belongs in category A, there is no longterm category representation, and hence a context stimulus is likely to be used as a cue to categorization. Thus, inter-stimulus comparison would seem less likely with familiar semantic categories than with arbitrary categories. In order to provide a more stringent test of inter-stimulus comparison effects, then, we used perceptual stimuli from common semantic categories. Second, whereas Stewart and Brown (2004; Stewart et al., 2002) provided corrective feedback throughout the categorization task, our procedure did not include feedback. It seems likely that when the feedback for S1 immediately precedes the presentation of S2, that feedback will remain highly salient during the judgment of S2. Thus, much like the use of arbitrary categories, the use of corrective feedback could also encourage inter-stimulus Perceptual Categorization 11 comparison. So again, we sought to generalize inter-stimulus effects by using a categorization task without feedback. Third and perhaps most importantly, we used a method of simultaneous presentation, whereas Stewart and Brown (2004; Stewart et al., 2002; see also Friedenberg et al., 2002) used sequential presentation. This methodological difference is theoretically critical, as several investigations have shown that contrast is more likely to occur with sequential presentation than with simultaneous presentation of stimuli (Geiselman, Haight & Kimata, 1984; Wedell, Parducci & Geiselman, 1987; but see Wedell, 1995). For example, Wedell et al. (1987) found that a given face (S2) was judged reliably more attractive when presented after an unattractive face (S1). But when S1 and S2 were presented simultaneously, S2 was then judged less attractive. Thus, Wedell et al. found successive contrast and simultaneous assimilation. To extrapolate, then, the category contrast effect obtained with sequential presentation could potentially be reversed with simultaneous presentation. Such a result would suggest an important modification of the SD-GCM. We therefore used simultaneous presentation in our experiments. In summary, sequential presentation of stimuli from arbitrary perceptual categories with corrective feedback may be the optimal methodology for obtaining a contrast effect. This methodology was ideal for Stewart and Brown (2004; Stewart et al., 2002), as their intention was to demonstrate a novel phenomenon that cannot be explained by purely similarity-based models of categorization. The purpose of our experiments, though, was to provide a more challenging test of the SD-GCM in general, and also to discriminate between the sign-and-magnitude and the sign-only versions of that model. We therefore used simultaneous presentation of stimuli from familiar semantic categories without corrective feedback. If the contrast effect were to obtain under these drastically different experimental conditions, that would provide even stronger support for the use of dissimilarity in perceptual Perceptual Categorization 12 categorization. Friedenberg et al. (2002) also used common semantic categories (i.e., MALE and FEMALE), however they used the same sequential presentation paradigm as Stewart and Brown (2004). Moreover, because Friedenberg and colleagues did not manipulate the similarity between S1 and S2, their data cannot discriminate between the sign-and-magnitude and the sign-only versions of the SD-GCM. Experiments 1 through 3 shared a common methodology, with only minor modifications. A calibration phase was followed by an experimental phase. In the calibration phase, hue patches were presented individually, and participants provided binary color judgments of the presented patch (e.g. “Is this square blue?”). Using data from the initial phase, the experimental phase was calibrated so as to center on each participant’s borderline hue. This calibration resulted in a set of hues ranging from clearly blue to clearly purple for that individual. The experimental phase consisted of simultaneous presentation of two hue patches, with participants again providing color judgments. All possible pairwise combinations of hues were presented several times each in the experimental phase. We initially elicited disjunctive or conjunctive judgments of the hues. For instance, we asked participants whether either stimulus was blue (Experiment 1a), or whether both stimuli were purple (Experiment 1b). We then allowed independent assessment of the two hues by broadening the range of response options in Experiment 2: Participants were asked whether the left stimulus only, the right stimulus only, both stimuli, or neither stimulus was blue. Next, by introducing an expanded range of hues (BLUE-PURPLE-RED), Experiment 3 tested whether the inter-stimulus effect depends on the context item's degree of membership in the category, or on its similarity to the borderline stimulus. In Experiment 4 we tested whether there could have been a low-level perceptual color contrast effect operating in Experiments 1-3. Finally, Experiment 5 extended our results to other familiar semantic categories (i.e., CATS and DOGS). Perceptual Categorization 13 Experiments 1a and 1b Pairs of hues ranging from clearly blue to clearly purple were presented simultaneously, and participants judged whether either of the hues was BLUE (Experiment 1a), or whether both of the hues were PURPLE (Experiment 1b). Categorization of the borderline hue was the critical measure, with probability of a positive response serving as the dependent variable. Experiment 1b was a conceptual replication of Experiment 1a; judging whether either stimulus is blue is logically complementary to judging whether both stimuli are purple. Thus, the results of Experiment 1b should mirror those of Experiment 1a. In the shorthand notation used to denote the various hues, we have centered on the borderline hue, designated b. The other six experimental hues radiate outward from the borderline, such that hues from the blue end of the spectrum are negative in denotation (relative to the borderline hue) and hues from the purple end of the spectrum are positive in denotation. Thus, the hue just inside the blue region of the borderline is designated hue b-1, while the hue just outside the blue region is designated hue b+1. And similarly, the bluest of the three blue hues is b-3, whereas the purplest hue is b+3. So the hues ranged from clearly blue (b-3) through the borderline (b) to clearly purple (b+3), with hue labels indicating distance and direction from the boundary between the BLUE and PURPLE categories. If color categories are represented as prototypes (e.g., Rosch, 1975) or as collections of exemplars (e.g., Nosofsky, 1986), then judgment of a borderline hue should be assimilated to the category of a context hue (cf. Nosofsky & Palmeri, 1997), and this assimilation effect should increase as the context hue approaches the borderline hue. Alternatively, the SD-GCM (Stewart & Brown, 2005) predicts a contrast effect when the context hue is relatively dissimilar from the borderline hue. More specifically, the sign-and-magnitude model predicts greater contrast as the context and borderline hues become more dissimilar, whereas the signonly model predicts a contrast effect that is impervious to the similarity of the context and Perceptual Categorization 14 borderline hues. Method Participants. All participants in each of the experiments reported below had normal color vision. Seventeen students of City University London participated in Experiment 1a, and 16 participated in Experiment 1b. All were paid £3 for participation. Materials. Stimuli consisted of nine hues that systematically varied from clearly blue to clearly purple, as determined by the probability of categorization as BLUE in pilot testing (N = 32). The hue range was centered on the modal borderline hue from the pilot test. The Red-Green-Blue (henceforth “RGB”) values for the hues, from blue to purple, were 15-5-55, 17-5-53, 19-5-51, 21-5-49, 23-5-47, 25-5-45, 27-5-43, 29-5-41, and 31-5-39 in Microsoft QuickBasic 4 programmed under DOS on an IBM-compatible PC with VGA graphics, where values for each scale range from 0 to 63. The stimuli were presented on a standard 8.5” x 11” color monitor with 640 x 480 pixels. 2 Procedure. Because pilot testing revealed considerable variability across participants in the location of the blue-purple borderline, we used a two-stage procedure. In an initial calibration phase, participants were presented individual 4.45 cm (100 pixel) square patches of hue. Each hue patch appeared in either a left or a right location just above the vertical midpoint on the computer screen, alternating left and right locations on each successive trial. The left and right squares were separated by a gap of 8.9 cm (200 pixels). Viewing distance was not strictly controlled, but was approximately 50-60 cm, giving a horizontal visual angle of about 5 degrees for each square patch and 10 degrees for the gap between them. The background was dark gray (RGB = 10-10-10), and the target question (e.g., “Is the square BLUE?”) appeared in white letters (RGB = 63-63-63) in the lower half of the screen. The target question was “Is the square BLUE?” for Experiment 1a and “Is the square PURPLE?” for Experiment 1b. The inter-trial interval consisted of a blank gray screen for a 1 sec. duration, Perceptual Categorization 15 and there was a further 1.5 sec. delay between stimulus onset and presentation of the target question. Responses were not accepted prior to onset of the target question, which required pressing the plus (+) key for “Yes” or the minus (-) key for “No”, followed by the return/enter key. The color patch and question remained on the screen until a valid response was made. Each of the nine hues was singly and randomly presented eight times in the calibration phase, for a total of 72 calibration trials. The sequence was constrained so that the same hue was never presented on consecutive trials. At the end of this phase, the program used a regression algorithm to determine, for that participant, the hue for which probability of positive categorization was nearest to .50. In other words, the program estimated each participant’s borderline hue, or closest approximation to a borderline within the range of presented hues. This calibration procedure allowed us to focus on the judgment of each participant’s individuated borderline hue. Seven of the nine hues from the calibration phase were automatically retained for use in a subsequent experimental phase, while two were excluded. The seven stimuli retained for each participant were that participant’s borderline hue, the three hues from the blue range closest to the borderline, and the three hues from the purple range closest to the borderline. 3 Once a participant’s range of seven experimental hues was determined, the experimental phase began. In this phase two hue patches were presented simultaneously on each trial. The hues occupied both the left and the right locations used in the calibration phase. The only difference between Experiments 1a and 1b in the second phase was that in Experiment 1a participants were required to press the plus (+) key if either square was blue, or the minus (-) key if neither was blue, whereas in Experiment 1b participants were required to press the plus (+) key if both squares were purple, or the minus (-) key if either was not purple. After the (+) or (-) choice was accepted by pressing the return key, the next trial Perceptual Categorization 16 began. There were four blocks of trials, each consisting of two trials of each possible pairwise combination of hues, such that in each block each possible pair of hues appeared once with one of the hue patches in the left location and once with that hue patch in the right location. Trials on which both patches were the same hue were also presented twice per block. Thus, each of the four blocks contained 56 trials, for a total of 224 experimental trials. Trials within each block appeared in random order, subject to the constraint that the same hue never appeared in two successive trials. The task lasted 20 to 30 minutes, with a self-paced break halfway through the experimental phase. Results and Discussion Full results of Experiments 1a and 1b are presented in Tables 1 and 2, respectively. In the tables, the target is the hue for which data are presented, and the context is the other hue that was present during the trial. So for instance, when hue b was presented alongside hue b+3, the proportion of trials on which either hue was judged BLUE is listed in Table 1 at the intersection of target b and context b+3. If context had no effect, then the choice proportions in each column would be randomly distributed around the same value. This pattern was not found, however. For the column headed b – the borderline target hue – in Table 1, the probabilities increased as context hues became increasingly purple, and those probabilities decreased in the corresponding column of Table 2. In interpreting these probabilities, we assumed monotonicity of judgments. That is, we assumed that a positive response in Experiment 1a (is either blue?) always indicated that (at least) the bluer of the two hues was blue, and correspondingly that a negative response in Experiment 1b (are both purple?) implied that (at least) the bluer of the two hues was not purple. To explain with the example from above, hue b is bluer than hue b+3. Therefore, a positive response in Experiment 1a (“Is either blue”) is informative of hue b (hence the term “target”), but nothing can be inferred Perceptual Categorization 17 about the judgment of hue b+3 (hence the term “context”). For this reason the upper right half of each table is incomplete. (This assumption of monotonicity was supported in Experiments 2 and 3, where it could be tested directly.) The results of interest are presented in Figure 1, which shows the proportions of positive categorization responses for the borderline hue in Experiments 1a and 1b. Three findings are apparent in the Figure. Notice first that the data from Experiment 1b mirrored those of Experiment 1a, indicating that results of 1b successfully replicated those of 1a. Second, note that both lines have a nonzero slope between context hues b+1 and b+3. Thus, the presence of a context hue reliably affected categorization of the borderline hue. For context hues more than one step away from the borderline target, there was an increasing contrast effect, such that the more purple the context hue became, the more likely was the borderline hue to be categorized as blue (Experiment 1a) or as not purple (Experiment 1b). This contrast effect held regardless of the joint judgment (i.e., either, both) and regardless of the color category (i.e., BLUE, PURPLE). Finally, the b+1 context hue had a slight tendency to assimilate the borderline target towards the purple category, so that the lines are not straight from b through b+3. The positive categorization proportions for the borderline hue in Experiments 1a and 1b were initially submitted to two separate one-way repeated measures ANOVAs, each with four levels of Context Hue (i.e., b, b+1, b+2, b+3). Both analyses showed a significant main effect of Context Hue [F (3, 48) = 11.78, p < .001 in Experiment 1a, and F (3, 45) = 3.96, p = .01 in Experiment 1b]. Subsequently, the data from Experiments 1a and 1b were analyzed together. The data from Experiment 1b were reverse coded to determine their fit with the data from Experiment 1a. A 2 (Experiment: 1a, 1b) x 4 (Context Hue: b, b+1, b+2, b+3) repeated measures ANOVA, with Experiment as a between-participants factor, revealed that neither the main effect of Experiment nor the Experiment x Context Hue interaction was significant Perceptual Categorization 18 (both F < .5). Only the main effect of Context Hue was reliable, F (3, 93) = 13.69, p < .001. The data of Experiment 1a therefore essentially mirrored those of Experiment 1b. The main effect of Context Hue indicates that the presence of a context hue reliably affected the judgment of the borderline hue. A polynomial set of contrasts revealed significant linearity, F (1, 31) = 20.30, p < .001. The quadratic and cubic trends were also reliable, F(1, 31) = 6.35, and F(1,31) = 6.46, both p < .05, reflecting the changes in slope from b through b+3, as evident in Figure 1. One further question of interest is whether assimilation occurred when the borderline was presented in the context of the b+1 hue, relative to b paired with itself. Recall that the SD-GCM model predicts assimilation for very similar pairs. Figure 1 suggests that this might have been the case. The difference between [b|b] and [b|b+1] did not reach significance in either experiment alone (both paired samples t < 1.10), nor when the data from Experiments 1a and 1b were pooled (t (32) = 1.46). However examination of Table 1 shows that in fact for targets other than b, there was also a systematic tendency for assimilation when the context hue was just one step away. A t-test comparing the sum of positive responses to all target stimuli, either in the context of an identical hue, or in the context of a hue that was one step more purple, gave a significant assimilation effect for Experiment 1a (t(16) = 2.33, p = .03), but not for Experiment 1b (t < .5), nor when they were pooled. To summarize, inter-stimulus comparison was manifest as a contrast effect: The probability of positive categorization of the borderline hue varied systematically as a function of its similarity to the context hue. The more purple the context hue, the more likely was the borderline to be judged BLUE (Experiment 1a), and the less likely was the borderline to be judged PURPLE (Experiment 1b). The size of this effect was quite substantial, as the probabilities of positive categorization ranged across different context conditions from .28 to .54 in Experiment 1a and from .30 to .51 in Experiment 1b. This effect suggests that people Perceptual Categorization 19 are influenced by the difference between the hues when categorizing colors (Stewart & Brown, 2005). Moreover, the magnitude of this difference also appears to affect judgment, with greater contrast as the dissimilarity between the context and borderline hues increased. Thus, unlike the experiment by Stewart and Brown (2004), the present experiment supported the sign-and-magnitude version of the SD-GCM. Experiment 2 Experiment 1 demonstrated that the dissimilarity between two hues affects their categorization in a continuous (i.e., sign-and-magnitude) manner. However, because that experiment elicited joint judgments of the two hues (i.e., Is either square blue? Are both squares purple?), monotonicity of responses had to be assumed. In order to corroborate the support for the sign-and-magnitude model, while also directly testing for monotonicity, in the present experiment we asked participants to indicate whether the left square only, the right square only, both squares, or neither square was blue. Thus, each judgment was informative of both hues per trial, and monotonicity could be observed rather than assumed. Notice also that, although the two judgments must be combined to provide a single response, context and target hues not need be judged together in this procedure. Hence the finding of a dissimilarity-based contrast effect here would provide stronger evidence for the SD-GCM. Method Sixteen students of City University London were paid £3 for participation. Materials were identical to those of Experiment 1. The procedure (calibration phase followed by experimental phase) was also identical to Experiment 1, with the exception that in the experimental phase participants were required to press the left arrow ( ) key if only the left square was blue, the right arrow ( ) key if only the right square was blue, the up arrow ( ) key if both squares were blue, or the down arrow ( ) key if neither square was blue. These four response options were displayed schematically on the screen as follows: Perceptual Categorization 20 BOTH LEFT RIGHT NEITHER Pressing one of the four arrow keys highlighted its corresponding response on the screen (i.e., Left, Right, Both, Neither). After the highlighted choice was accepted by pressing the return key, the next trial began. All other procedures were identical to Experiment 1. Results and Discussion Each response was analyzed to provide independent categorization responses for the left and right stimulus respectively. For example, the stimulus displayed on the left was scored as “blue” if either the LEFT or the BOTH response option was chosen, and as “not blue” otherwise. Categorization of each stimulus was then scored as a function of the other stimulus with which it was presented. This allowed examination of the monotonicity constraint. Of the 2,688 trials in the experiment (across participants), only four responses violated the monotonicity constraint. That is, only very rarely did participants judge the bluer of two hues as PURPLE and the purpler hue as BLUE. Clearly participants were extremely adept at using monotonicity to provide consistent responses on each trial of the experiment. In fact, the overwhelming monotonicity of responses suggests that inter-stimulus comparison again occurred in this categorization task. This finding also supports our assumption that responses in Experiment 1 were largely monotonic as well. 4 Figure 2 plots the observed probability of the borderline hue being categorized as BLUE in the context of the other hues. As in Experiment 1a, the probability of categorizing the borderline hue as BLUE increased as the context hue varied from blue to purple. Thus, the contrast effect was not limited to conjunctive or disjunctive response combinations, and the sign-and-magnitude model was once again supported. Full results are presented in Table 3. In the table, the target is the hue for which data Perceptual Categorization 21 are presented, and the context is the other hue that was present during the trial. For example, when hue b+3 was presented with hue b, the probability that hue b was judged BLUE is listed in Table 3 at the intersection of target b and context b+3, while the probability that hue b+3 was judged BLUE is listed at the intersection of target b+3 and context b. A one-way repeated measures ANOVA was performed on the probabilities of positive judgment of the borderline hue. There were seven levels in the analysis, one level for each of the seven possible context hues with which the borderline was presented (including itself). A reliable effect was detected, F (6, 90) = 10.63, p < .001. The effect was captured by a significant linear trend in a subsequent polynomial contrast, F (1, 15) = 16.77, p < .001. There was also a significant 5 th order trend, F (1, 15) = 5.72, p < .05, reflecting the four points of inflection in the curve, at hues b-2, b-1, b+1 and b+2. This significant fit to a 5 order polynomial function neatly captures the boundary conditions of the contrast effect (see Figure 2). It suggests that the contrast effect asymptoted from b-3 to b-2 and from b+2 to b+3, and that, as in Experiment 1, hues b-1 and b+1 produced only minimal changes in categorization of the borderline hue. In corroboration of Experiment 1, the results of Experiment 2 support the sign-andmagnitude SD-GCM (Stewart & Brown, 2005), which predicts increasing contrast as the context and target stimuli become more dissimilar. No assimilation effect was apparent, although the slope of the context effect did appear to flatten when the stimuli were only one step apart. The observation of an asymptote for the contrast effect at the two ends of the scale also makes good sense in terms of the SD-GCM. In the model, dissimilarity is just (1similarity), where similarity decreases exponentially with distance. Hence once would expect dissimilarity to asymptote after a certain point, and further increases in distance between context and target should have little further effect.