Chapter 3 Robustness and sensitivity to change
Status: manuscript in preparation, presented as conference poster on Perception Day 2018 (Van Geert & Wagemans, 2018e)
Wertheimer’s (1923, 2012, p. 319) description of a series of Gestalts in which one component is varied in systematic, physically equidistant steps but which results in unequal psychological steps, is very related to the idea that we need psychological scaling rather than physical scaling to assess perceived similarity between stimuli or differences in reactions to stimuli (Fechner, 1860; Shepard, 1987). In most literature, psychological scaling has been used as an explanatory variable, but it has rarely been considered which factors – besides physical (dis)similarities – influence the formation and dynamical adaptation of these psychological scales. The formation and development of Prägnanz steps may be one way to understand the emergence of non-physically equivalent psychological scales and thus categorization.
As mentioned in Chapter 2, prägnant Gestalts are said to be both robust and sensitive to change: although prägnant Gestalts serve as a reference point for a wide range of Gestalts, small deviations from the prägnant Gestalt will already be noticed. We can reconcile these findings in at least five, not mutually exclusive ways.
Whereas sensitivity to change is mostly present on the direct perceptual, ‘lower’ level (primary processes in perception, related to segmentation of the visual field), robustness involves more conscious, higher-order processes (secondary processes in perception, related to identification and categorization).
Unfavorable viewing conditions (e.g., limited exposure, reduced contrast) could lead to more robustness and less sensitivity to change, whereas the opposite may be true for favorable viewing conditions.
Whereas robustness is mainly present within the range of prägnant Gestalts, sensitivity to change could be present when comparing prägnant Gestalts to close-to-prägnant Gestalts.
Prägnant Gestalts could be robust when the underlying stimulus information stays the same, but be sensitive to change when the stimulus changes slightly.
In line with the Prägnanz tendency, the direction of the stimulus change can play a role. When going from a less to a more prägnant structure, robustness will be stronger, and it will be hard to go away from the prägnant Gestalt; when going from a more to a less prägnant structure, sensitivity may be more prominent.
Goldmeier’s (1937, 1982) hypothesis on the sensitivity to change in the near-prägnant zone and insensitivity in the non-prägnant zone relates very closely to the category boundary effect that is reported in the categorical perception literature. The discontinuities (i.e., the transitions between a prägnant and an intermediate step) described by Wertheimer (1923) relate to the increased discrimination performance found around the category boundary: keeping physical distance equal, differences between stimuli belonging to the same category are perceived as smaller than differences between stimuli belonging to different categories (i.e., stimulus pairs crossing the category boundary; see Figure 3.1; Harnad, 1987). In other words, if the stimuli are drawn towards different prägnant Gestalts, they will become more dissimilar than when they are drawn towards the same prägnant Gestalt.
Figure 3.1: Illustration of the category boundary effect.
Furthermore, the Prägnanz tendency is in line with the asymmetry effects found in the categorical perception literature: If there is a tendency to transform less prägnant figures into more prägnant ones, this will make stimulus pairs in which the more prägnant exemplar is in the referent position (e.g., how similar is 99 compared to 100) look more similar than when the more prägnant exemplar is in the subject position (e.g., how similar is 100 compared to 99).
The literature on Prägnanz thus leads us to posit the following hypotheses:
A category boundary effect will exist, because, when comparing physically equidistant pairs, a pair of stimuli that are drawn towards different prägnant Gestalts will look more dissimilar than a pair of stimuli that are drawn towards the same prägnant Gestalt.
Prägnant Gestalts will be categorized more consistently (and possibly more rapidly) than less prägnant Gestalts.
Less prägnant Gestalts will tend towards more prägnant ones, but not the other way around. Therefore, asymmetries in discrimination performance as well as perceived similarity will exist depending on whether the more or less prägnant Gestalt is used as the referent. Assuming the second stimulus in a pair will be used as the referent, we expect worse discrimination performance and higher perceived similarity between two different stimuli when the first stimulus is less prägnant than the second.
In the current study, we used both identifiable and non-identifiable morph series (see Figure 3.2) as an operationalization of Wertheimer’s series of Gestalts varying on one dimension only. The identifiable morph series were based on the ones used in Hartendorp et al. (2010) and Burnett & Jellema (2013). The non-identifiable morph series were based on stimuli from Op de Beeck et al. (2003b).
Figure 3.2: The three identifiable (i.e., car-tortoise, penguin-child, watch-seahorse) and three non-identifiable morph series used in the experiment.
283 first-year psychology students from KU Leuven participated in the study. Each participant completed each main task of the study (categorization, discrimination, and similarity judgment task) for a different identifiable and non-identifiable morph series. The assignment of morph series to tasks was counterbalanced between participants. The order of the three tasks and the order of identifiable versus non-identifiable series was randomized across participants. More information on the procedure can be found in Appendix C.
We replicated the category boundary effect (CBE) in both the discrimination and the similarity judgment task (Figure 3.3): keeping physical distance between the stimuli equal, stimuli belonging to the same category were perceived as more similar and were harder to discriminate than stimuli belonging to different categories.
Figure 3.3: (a) Discrimination accuracy for within- and between-category trials, for each step size (~difficulty of the trial), morph series, and trial type separately (averaged across participants). (b) Standardized similarity judgments for the different trials, for each step size, morph series, and trial type separately (averaged across participants). Note. In the interactive version of this document, hover over the bars to see the exact value of each bar as well the number of trials related to each bar.
Although we found indications for a CBE in both types of morph series, the CBE appeared stronger in the identifiable morph series. As the categories (i.e., Prägnanzstufen) in the identifiable morph series probably already existed in participants before starting the tasks, these prägnant Gestalts functioned as stronger attractors than the ones in the non-identifiable morph series. Additional evidence for this explanation is the stronger categorization for identifiable compared to non-identifiable morph series (see Figure 3.4a).
Figure 3.4: (a) Proportion of times each stimulus was labeled as category B (averaged across participants), with a 95% confidence interval. Lines indicate predictions based on a frequentist binary logistic regression. (b) Categorization response times for each stimulus and morph series separately (averaged across participants). Note. In the interactive version of this document, hover over the data points to see the related stimuli as well as the exact value and the number of trials related to each data point.
The main focus of the study was investigating whether we can locate the reference points or prägnant steps on the dimension that are responsible for the CBE by looking at the ease of categorization, directional asymmetries in discrimination performance, and directional asymmetries in perceived similarity. Differences in ease of categorization were present for both categorization response and response time. Rather than one morph level being the most prägnant, a range of almost equally-well categorized good Gestalts was present (Figure 3.4a). Furthermore, in comparison to the morph levels in the near-prägnant and non-prägnant zone, not only the best Gestalts yielded shorter response times but also a range of good Gestalts around them (see Figure 3.4b).
Unexpectedly, there were no clear directional asymmetries in the discrimination and similarity judgment data (see Figure 3.5). If slightly present, then the asymmetries were in the opposite direction from what we expected: when the more prägnant Gestalt was shown second, discrimination performance was better and perceived similarity lower than when the more prägnant Gestalt was shown first.
At least three factors add to the difficulty to interpret these results. One limiting factor here is the ambiguity concerning which Gestalt will serve as the reference point: in language examples it is often the second (e.g., 99 is similar to 100), but in perceptual examples with sequential presentation, what comes first may be the reference point (although it is not traditionally viewed that way; e.g., Op de Beeck et al., 2003b). Secondly, the interpretation of the data may depend heavily on where one assumes the boundaries between the prägnant, close-to-prägnant, and non-prägnant zones to be located. Thirdly, the results can be analyzed in a multitude of ways, and it is unclear which analysis would be the most appropriate one.
Figure 3.5: (a) Discrimination accuracy for the within-category trials, for each morph level, morph series, and direction separately (averaged across participants). (b) Standardized similarity judgments for the within-category different trials, for each morph level, morph series, and direction separately (averaged across participants). Note. In the interactive version of this document, hover over the data points to see the related stimuli as well as the exact value and the number of trials related to each data point.
Exploration of the data yielded an additional interesting finding. Besides the known CBE, we found evidence for a within-category CBE: keeping the physical difference between stimuli equal, a pair of ‘good’ exemplars of a category (i.e., both belonging to the prägnant zone) was perceived as more similar and was more difficult to discriminate than other types of within-category pairs (i.e., good exemplar first, good exemplar second, both worse category exemplars; see Figure C.1). Does this mean that the Prägnanz tendency is stronger within the prägnant zone, and will lead to complete assimilation within the prägnant zone, but will be slightly less strong in the near-prägnant zone?
What happens with our perception when no clear prägnant steps are available on a dimension, such as for the non-identifiable morph series in this study? A reanalysis of the data from this study suggests that the lack of prägnant steps may be compensated by a more extensive use of immediate context information, more specifically in the form of an attractive influence of the previous percept and a repulsive influence of the previous stimulus on the current percept (see Chapter 4).