Effects of stimulus order on discrimination processes in comparative and equality judgements: Data and models

Abstract

In typical discrimination experiments, participants are presented with a constant standard and a variable comparison stimulus and their task is to judge which of these two stimuli is larger (comparative judgement). In these experiments, discrimination sensitivity depends on the temporal order of these stimuli (Type B effect) and is usually higher when the standard precedes rather than follows the comparison. Here, we outline how two models of stimulus discrimination can account for the Type B effect, namely the weighted difference model (or basic Sensation Weighting model) and the Internal Reference Model. For both models, the predicted psychometric functions for comparative judgements as well as for equality judgements, in which participants indicate whether they perceived the two stimuli to be equal or not equal, are derived and it is shown that the models also predict a Type B effect for equality judgements. In the empirical part, the models' predictions are evaluated. To this end, participants performed a duration discrimination task with comparative judgements and with equality judgements. In line with the models' predictions, a Type B effect was observed for both judgement types. In addition, a time-order error, as indicated by shifts of the psychometric functions, and differences in response times were observed only for the equality judgement. Since both models entail distinct additional predictions, it seems worthwhile for future research to unite the two models into one conceptual framework.

Keywords:

• Discrimination
• Stimulus order
• Equality judgement
• Time-order error
• Internal reference.

We thank Åke Hellström and an anonymous reviewer for helpful comments and Julia Dietrich for assistance in data collection. This research was supported by the DFG grant UL 116/13-1.

Notes

¹ DL is usually calculated as half the inter-quartile range, that is, half the distance between the magnitudes of c that correspond to 75% and 25% “c > s” responses, respectively.

² PSE is defined as the magnitude of c that corresponds to 50% “c > s” responses.

³ It should be noted that in the temporal generalization task, the standard stimulus s is presented only at the beginning of the experiment and, on each trial, participants indicate whether or not they perceive the comparison stimulus c to be the same as s.

⁴ A negative time-order error means underestimation of the first relative to the second stimulus. For stimulus order , underestimating the first stimulus (i.e., s) is equivalent to overestimating the second stimulus (i.e., c), that is, a smaller magnitude for c suffices in order to yield subjective equality to s, hence PSE < s. Conversely, for stimulus order , underestimating the first stimulus (i.e., c) results in PSE > s.

⁵ We thank Åke Hellström for suggesting this definition of the Type B effect and for relating the Type B effect to the “position effect” by Rammsayer and Wittkowski (1990).

⁶ This part of the instruction was included because in a pilot study without this instruction, some participants reported that they felt they should press the response keys associated with “tones equal” and “tones not equal” approximately equally often.

⁷ In separate analyses, we assessed effects of task order, that is, whether a participant performed the comparative judgement followed by the equality judgement or vice versa, on DL or SD of the psychometric function, PSE or mean M of the psychometric function, and RT. To this end, we conducted an ANOVA with the within-subject factor stimulus order ( vs. ) and the between-subjects factor task order (comparative-equality vs. equality-comparative) for each judgement type and each dependent variable separately. The two ANOVAs for DL or SD of the psychometric function yielded only significant main effects of stimulus order indicating Type B effects, , , , and , , for the comparative and the equality judgement, respectively (cf. Figure 4a). Thus, discrimination sensitivity overall, as well as the Type B effect did not differ significantly between the participants who performed the comparative judgement first and those who performed the equality judgement first. The ANOVA for PSE in the comparative judgement yielded only a marginally significant main effect of task order, , , and the PSE for comparative judgements was slightly smaller (499 ms) when participants started with the comparative judgement than when they started with the equality judgement (503 ms). In contrast, the ANOVA for the mean M of the psychometric function in the equality judgement yielded a significant main effect of stimulus order indicating a time-order error as indexed by shifts of the psychometric functions, , , (cf. Figure 4b). In addition, the interaction stimulus order × task order was significant, , , and the difference in the mean of the psychometric function was smaller when participants performed the comparative judgement first (20 ms) than when they performed the equality judgement first (31 ms). Finally, the ANOVA for RT in the comparative judgement yielded no significant effects whereas the ANOVA for RT in the equality judgement yielded a significant main effect of stimulus order, , , , indicating a longer RT for stimulus order than for stimulus order (cf. Figure 4c).

⁸ We thank Åke Hellström for pointing this out.

⁹ We thank Åke Hellström for bringing this line of argumentation to our attention.