The threshold task revealed sensitivity to be similarly low for auditory and tactile intervals, and higher for visual intervals. If there is a relationship between thresholds and estimation slopes, as Jones et al. (2009) suggested, we would expect slopes to follow the same modality pattern as thresholds. Therefore, we now replicated Jones et al.’s estimation task, and predicted that slopes would be steepest for auditory intervals and shallowest for visual intervals. In addition, there might be no significant difference between the slopes for auditory and tactile intervals. We will consider inter-individual differences following the same steps as in Experiment 1A.
The same participants completed this experiment who had taken part in Experiment 1A.
The first independent variable was the modality of the stimulus (auditory, tactile, or visual), and the second was its duration (77, 203, 348, 461, 582, 767, 834, 958, 1,065, or 1,183 ms).Footnote 12 This short range of durations was used to prevent “chronometric counting” (Hinton & Rao, 2004; Wearden, 1991), in which participants might verbally or mentally measure time with a “one–one thousand, two–one thousand” type heuristic, which would reduce or negate the effects of presenting the stimuli in different modalities. The dependent variable was participants’ estimates of stimulus duration in milliseconds, which they typed into the keypad.
Apparatus and materials
The same apparatus and materials were used as in Experiment 1A.
The task included three modality-specific blocks of 50 trials, presented in a random order, in which the ten stimulus durations were presented five times in each modality. Participants were told that the intervals were random durations between 50 and 1,250 ms and that they could only enter estimates within this range (inclusive). Trials were presented in a random order within each block. Each trial began with the presentation of a fixation cross for 500–1,000 ms, followed by the stimulus. Participants were prompted onscreen to type in their estimate in milliseconds and were reminded that 1 s = 1,000 ms. Five practice trials were presented at the start of each block, but advancement was not contingent on performance. The task was self-paced and took approximately 17 min to complete.
Participants who were unable to perform the task were excluded. This was defined as estimates being invariant as to stimulus duration, identified as linear functions not significantly different from the null when mean estimates for each duration were regressed against stimulus duration, separately for each participant. This led to the exclusion of one individual (P47),Footnote 13 leaving a sample of 51 participants. See Fig. 4 for the mean verbal estimates for each modality across stimulus durations.
Inspection of Fig. 4 suggests a general underestimation of all except the shortest durations (77 ms) for all modalities. Estimates were higher for auditory durations, whereas tactile and visual estimates appear to be lower and quite similar, the same pattern found in Jones et al. (2009).
These suggestions were examined using a factorial ANOVA with two repeated measures factors: stimulus duration and modality. We found a significant main effect of stimulus duration, F(2.60, 130.17) = 750.70, p < .001, ηp2 = .938. Post hoc analyses (Holm–Bonferroni corrected) revealed that each of the ten stimulus durations was estimated significantly differently from each of the others (p < .001 for all comparisons), which simply means that participants were sensitive to the presented duration.
There was also a significant main effect of modality, F(2, 100) = 7.50, p = .001, ηp2 = .131. Post hoc analyses (Holm–Bonferroni corrected) revealed that participants estimated auditory durations to be significantly longer than both visual (a = .017, p = .002) and tactile (a = .025, p = .004) durations. However, the estimates for visual and tactile durations did not differ significantly (a = .050, p = .303).
The was also a significant Stimulus Duration × Modality interaction, F(8.39, 419.32) = 4.91, p < .001, ηp2 = .089. This suggests that stimulus modality affected the slope of the function relating the mean estimates to stimulus duration, consistent with a multiplicative effect.
Slopes and intercepts
To investigate this interaction, we regressed each participant’s estimates against stimulus duration to extract slope and intercept values for each modality. See Table 2 for the resulting linear regression equations. The standard deviations of the auditory, tactile, and visual slope values were 0.18, 0.16, and 0.19, respectively, and the intercept values were 129.04, 91.84, and 118.21 ms.
Inspection of Table 2 suggests that the auditory and tactile functions have similar slopes but different intercepts—that is, they are approximately parallel. In contrast, the visual function appears to have a shallower slope than the others, but an intercept similar to that of the auditory function. The mean visual slope was 16% shallower than the mean auditory slope. See Fig. 5 for mean slopes and intercepts of these linear regressions.
Inspection of the upper panel of Fig. 5 suggests the slopes to be shallowest for visual estimates, and little difference between the slopes of auditory and tactile estimates. A repeated measures one-way ANOVA comparing the slopes across modalities revealed a significant difference between the three modalities, F(2, 100) = 12.76, p < .001, ηp2 = .203. Post hoc analyses (Holm–Bonferroni corrected) confirmed that visual slopes were significantly shallower than both auditory (a = .017), t(50) = 4.33, p < .001, BF–0 = 548.74, d = 0.61, and tactile (a = .025), t(50) = 3.96, p < .001, BF–0 = 193.12, d = 0.56, slopes. Auditory and tactile slopes did not differ significantly (a = .050), t(50) = 0.86, p = .392, BF0+ = 2.96, d = 0.12.
Inspection of the lower panel of Fig. 5 suggests intercepts to be lowest for tactile estimates, followed by auditory estimates, and highest for visual estimates. A repeated measures one-way ANOVA was conducted to compare the intercepts of the estimation functions across modalities, and it revealed a significant difference between them, F(1.76, 87.75) = 6.86, p = .003, ηp2 = .121.Footnote 14 Post hoc analyses (Holm–Bonferroni corrected) confirmed that the intercepts for tactile durations were significantly lower than the intercepts for both visual (a = .017), t(50) = 3.40, p = .001, BF–0 = 43.96, BF01 = 0.05, d = 0.48, and auditory (a = .025), t(50) = 3.04, p = .011, BF–0 = 17.36, BF01 = 0.12, d = 0.43, durations. The intercepts for auditory and visual durations did not differ significantly (a = .050), t(50) = 1.11, p = .142, BF01 = 3.66, d = 0.16.
Research Aim 2: Exploration of inter-individual differences in auditory, tactile, and visual slopes
The upper panel of Fig. 6 presents the percentages of the 51 participantsFootnote 15 whose steepest, intermediate, and shallowest slopes fell within each of the modality categories. No participants achieved the same slope value in two or more modalities.
The most frequent steepest slope was for not for auditory intervals, but for tactile intervals (47%). The most frequent intermediate slope was for auditory intervals (51%), and the most frequent shallowest slope was for visual intervals (69%). The lower panel of Fig. 6 displays the percentages of participants whose modality orders corresponded to each of the six possible patterns. The most frequent modality pattern was a steeper tactile slope, followed by an intermediate auditory slope and a shallower visual slope (37%). The next most frequent pattern was auditory, then tactile and visual slopes (31%). The least frequent patterns were auditory, then visual and tactile slopes (4%) and visual, then tactile and auditory slopes (4%), with two participants apiece. A total of 73% of the participants had steeper auditory than visual slopes, whereas the remaining 27% had steeper visual than auditory slopes.
As had been found in previous research, durations in all three modalities were generally underestimated (Jones et al., 2009; Wearden et al., 1998). The initial factorial ANOVA showed durations to be estimated as relatively longer (i.e., underestimated less) when presented as auditory intervals than when presented as tactile or visual intervals of the same physical duration. Estimates for tactile and visual durations were found not to differ significantly. In terms of our slope analyses, the slopes for visual estimates were significantly shallower than those for auditory and tactile estimates, indicating an apparent difference in pacemaker rate. However, auditory slopes were not significantly higher than tactile slopes.
Although the significant difference between auditory and visual slopes found in our data is well-reported (Jones et al., 2009; Wearden et al., 1998, Wearden et al., 2006), Jones and colleagues found that tactile slopes did not differ from visual slopes. Therefore, although the evidence suggesting a difference in pacemaker rates for auditory and visual intervals is robust, it is not clear whether pacemaker rates for tactile intervals are as distinct.
Although we were able to compare the standard deviations of our thresholds to those of Jones and colleagues, these authors did not provide the standard deviations of their slope values. In the absence of this direct comparison, comparison of our standard errors to those presented in their Fig. 3 (upper panel) suggests that we replicated the effect of the smallest standard error for tactile intervals (0.022, in our case). However, we found the highest standard error for visual slopes (0.026), and an intermediate standard error for auditory slopes (0.025), whereas Jones et al. (2009) found the opposite pattern (though our difference was marginal).
In addition to slope differences, there were also some significant differences in intercepts. Intercepts were significantly lower for tactile estimates than for auditory and visual estimates. Scalar timing theory interprets intercept differences as differences in switch latency (Jones et al., 2009; Wearden et al., 1998). Therefore, this suggests that the switch has a reduced latency when timing tactile intervals than in the other two modalities. This contrasts with Jones et al.’s finding of no significant differences in intercepts.
The exploration of inter-individual differences for Research Aim 2 showed that steeper tactile slopes were more common than steeper auditory slopes. This might seem at odds with the mean auditory slope being higher in value than the mean tactile slope, but the ranking of slopes does not take magnitude differences into account. It may have been the case that one group of participants had slightly steeper tactile than auditory slopes, whereas another group had much steeper auditory than tactile slopes. More than two-thirds of participants had their shallowest slope for visual intervals. When looking at the overall pattern of slopes, the most frequent one (37%) was for participants to have steeper tactile, intermediate auditory, and shallower visual slopes. This was closely followed by participants who had steeper auditory, intermediate tactile, and shallower visual slopes (31%). Therefore, though the auditory–tactile–visual pattern manifested in the mean data, this pattern was not the most common at the individual level. Regardless of the placement of tactile intervals, around three-quarters of participants had steeper auditory than visual slopes (73%). This suggests that the pacemaker may run faster for auditory than for visual intervals for most people, but the opposite may be true for around a quarter of people. We do, however, acknowledge the role of measurement error, which may have obscured the pattern of participants’ true pacemaker rates, and we will take this into consideration in later discussions. Finally, the pacemaker rate resulting from tactile intervals is not as clear.