Separating the contributions of primary and unwanted cues in psychophysical studies

Abstract

A fundamental issue in the design and the interpretation of experimental studies of perception relates to the question of whether the participants in these experiments could perform the perceptual task assigned to them using another feature, or cue, than that intended by the experimenter. An approach frequently used by auditory- and visual-perception researchers to guard against this possibility involves applying random variations to the stimuli across presentations or trials so as to make the "unwanted" cue unreliable for the participants. However, the theoretical basis of this widespread practice is not well developed. In this article, we describe a 2-channel model based on general principles of psychophysical signal detection theory, which can be used to assess the respective contributions of the unwanted cue and of the primary cue to performance or thresholds measured in perceptual discrimination experiments involving stimulus randomization. Example applications of the model to the analysis of results obtained in representative studies from the auditory- and visual-perception literature are provided. In several cases, the results of the model-based analyses indicate that the effectiveness of the randomization procedure was less than originally assumed by the authors of these studies. These findings underscore the importance of quantifying the potential influence of unwanted cues on the results of psychophysical experiments, even when stimulus randomization is used.

Figure 1

Schematic representation of the stimulus-conditional probability density functions (PDFs) of the stimulus variable corresponding to the unwanted cue, X_u, to which uniform roving is applied. The solid line labeled f_{Xu |A}(X_u |A) shows the conditional PDF of X_u given that stimulus A was presented. The dashed line labeled f_{Xu |B}(X_u |B) shows the conditional PDF of X_u given that stimulus B was presented. The two PDFs have the same range, D, and only differ by a horizontal shift, equal to the size of the unwanted cue, Δ_u .

Figure 2

Predicted relationship between PC_p and PC_c for different relative unwanted-cue sizes (Δ_u/D), in the presence of (uniform) roving. Knowing the size of the unwanted cue (Δ_u) and the roving range (D), researchers can use this figure to determine the value of PC_p as a function of PC_c. (See text for details.)

Figure 3

Schematic illustration of the stimuli used in the profile-analysis study by Mason et al. (1984) and in the intensity-discrimination study by Dai & Green (1992). a. In Mason et al.’s study, listeners had to discriminate a “standard” complex tone with a “flat” spectrum, i.e., equal-amplitude frequency components, from a “signal + standard” complex tone in which one of the components (here, the center component) was added a tone of the same frequency (the “signal”), resulting in an increased amplitude for that component. To limit listeners’ ability to perform the task based on changes in the absolute level of the center component, the overall level of the complexes was roved on each stimulus presentation. As a result, the “signal + standard” stimulus could have a lower overall level than the “standard” stimulus, as illustrated here. b. In Dai & Green’s (1992) experiment, listeners were presented on each trial with two successive pairs of tones that had the same or different frequencies (here, 200 and 1000 Hz), and they had to indicate the pair in which the first tone had a higher level. To limit listeners’ ability to perform the task reliably based on level differences between the two pairs, level was roved across pairs, so that both tones in the pair containing the louder tone (the second pair shown) could actually have a lower level than the tones in the other pair (the first pair shown).

Figure 4

Re-analysis of Mason et al.’s (1984) data on spectral-shape discrimination as a function of roving range. The thresholds measured by Mason et al. are shown as triangles. As is customary in the auditory “spectral-profile analysis” literature, these thresholds are expressed as signal-to-standard ratios, in dB (see the main text for details). The error bars show one standard deviation of the mean across listeners. The thresholds that could theoretically be achieved by relying solely on the unwanted cue (overall level differences) are shown as squares. The “corrected” thresholds for the spectral-shape discrimination, after eliminating the possible contribution of the unwanted cue, are shown as circles.

Figure 5

Re-analysis of Dai & Green’s (1992) data on auditory intensity discrimination. In that study the listeners compared the level of a 1000 Hz tone with the level of a second tone. The stimuli that were used in this experiment are illustrated schematically in Figure 3b. The thresholds that were measured originally by Dai & Green are plotted as a function of the frequency of the second tone, and are shown as triangles. The horizontal dashed line shows the threshold that could theoretically be achieved by relying solely on the unwanted cue. The filled circles show the thresholds that could theoretically be achieved by relying solely on the primary cue; these thresholds were computed as described in the main text. The grey upward-pointing arrows near the top of the plot indicate that the estimated thresholds were too large to be displayed on the plot. The dark upward-pointing arrows indicate conditions in which the predicted thresholds based on the primary cue alone could not be computed, because performance could be accounted for using solely the unwanted cue. All of the thresholds shown in this figure are expressed as signal-to-standard ratios in dB.

Figure 6

Re-analysis the data of Moore & Glasberg (, panel 6a) and Dai et al. (, panel 6b) on auditory frequency discrimination. These plots show frequency-discrimination thresholds for pure tones as a function of the frequency of the standard. The thresholds that were reported in the original studies are shown as triangles. The circles show the thresholds that were predicted, using the analysis described in the text, assuming that the observers used only the primary cue.

Figure 6

Re-analysis the data of Moore & Glasberg (, panel 6a) and Dai et al. (, panel 6b) on auditory frequency discrimination. These plots show frequency-discrimination thresholds for pure tones as a function of the frequency of the standard. The thresholds that were reported in the original studies are shown as triangles. The circles show the thresholds that were predicted, using the analysis described in the text, assuming that the observers used only the primary cue.