Mean errors (distance between response and centroid, measured in pixels) for full-set and target-only trials are displayed in
Table 3. Participants performed significantly better in target-only trials than in full-set trials for all four tasks. For homogeneous targets, the increase in error was over 20%; for heterogeneous targets, the increase was 34% with homogeneous distractors and 58% with heterogeneous distractors. From this, we can conclude that there was substantial room for performance improvement in the full-set trials for any of the four tasks. We also found that there was a cost of having heterogeneous instead of homogeneous targets. Even without distractors present, the error in the target-only trials with heterogeneous targets was greater than the error in the same trials with homogeneous tasks, Δ = 17.2 − 15.9 = 1.3,
t(7) = 5.379,
p = 0.001, Bayes factor (BF) = 40.199.
1
From the response-error data, we estimated the relative amount that each of the items in the display influenced the participant's centroid judgment; these values are referred to as
influence functions.
Figure 3 shows the influence functions averaged across all eight subjects, each panel displaying data for one of the four tasks. Each function reflects the attention filters for the six hues, shown on the x-axis of the plots. Each line in one of the panels in the figure connects the attention-filter estimates for one of the conditions for the task displayed in that panel. The points on each line represent the hues that were presented in the condition. Note that the lines serve only to identify the estimates from a condition; they should not be seen as interpolating the data between the data points. The y-axes represent the weight of each hue in the task. Influence functions are defined only up to an arbitrary multiplicative constant. As a matter of convention, we normalize the weights in any given influence function to sum to 1. Thus, in an ideal filter the weight of each target hue in the T3D3 and T3D1 conditions should be 1/3, whereas the ideal weight of the single target hue in the T1D3 and T1D1 conditions should be 1. In all tasks, the ideal weight of distractors was 0. Error bars on each point represent the 95% confidence intervals consistent with a repeated-measures analysis, with the main effect of participants removed (Morey,
2008; Franz & Loftus,
2012). These were calculated separately for the targets and the distractors, as the number of the number of target and distractor types varied between tasks.
The influence functions in
Figure 3 suggest that participants generally were able to base their centroid responses on the target items and ignore the distractors. At the same time, there are clearly systematic differences across tasks that can best be summarized using the selectivity measure, which we will do in the following. Here we note that in the T3D3 and T3D1 tasks, the purple target (rightmost on the horizontal axis in each panel of
Figure 3) exerts slightly less weight than the red and orange targets, which suggests that the purple hue was harder to categorize as a red than the orange hue: for the T3D3 task,
t(7) = −3.57,
p = 0.009, BF = 7.03; for the T3D1 task,
t(7) = −2.87,
p = 0.024, BF = 3.31. However, this asymmetry is not found in tasks T1D3 or T1D1, in which the targets were homogeneous. Also interesting is that, in all tasks, the distance in hue space between the distractor and target in the different conditions did not have a systematic effect on performance. We might have expected worse performance for conditions in which the target was closer to the distractor around the circle of hues, namely when Colors 3 (yellow-green) and 4 (orange) were paired or when Colors 1 (blue-green) and 6 (purple) were paired. Likewise, we would have expected the best performance to emerge when Colors 3 (green) and 7 (red) were paired, but none of these conditions was significantly different from one another. This noneffect of hue pairs confirms that performance in the centroid task is driven not by the saliency of the hues of the target dots but rather by whether or not attention is allotted to the hue. The evidence indicates that none of the hues used in the experiment was more salient than any other.
As noted before, the important differences between tasks are best captured using log10 selectivity and efficiency. These measures, averaged across participants in each task, are summarized in
Tables 4 and
5.
Looking at both measures, we observe effects of target homogeneity versus heterogeneity—for selectivity, t(7) = 4.39, p = 0.003, BF = 16.14; for efficiency, t(7) = 5.799, p = 0.0003, BF = 57.54—and distractor homogeneity versus heterogeneity—for selectivity, t(7) = 3.674, p = 0.008, BF = 7.84; for efficiency, t(7) = 2.381, p = 0.049, BF = 1.93—with significantly larger effects of target heterogeneity than distractor heterogeneity: for selectivity, t(7) = 6.969, p = 0.00011, BF = 143.96; for efficiency, t(7) = 2.451, p = 0.044, BF = 2.09. There was also little evidence for an interaction between target and distractor homogeneity versus heterogeneity: for selectivity, t(7) = −0.676, p = 0.521, BF = 0.406; for efficiency, t(7) = −1.274, p = 0.243, BF = 0.63.
Looking at the effects of skill level, there were significant differences in selectivity between experts and novices in the T3D1, T1D3, and T1D1 tasks. Experts' log10 selectivity ratios, on average, were greater than novices' by 0.6 (four times larger) in the T3D1 task, t(7) = 3.025, p = 0.023, BF = 3.92; by 0.7 in the T1D1 task, t(7) = 3.880, p = 0.008, BF = 9.70; and by 1.0 in the T1D1 task, t(7) = 3.881, p = 0.008, BF =7.14. There was no significant difference in performance between the expert group and novice group on the T3D3 task—for selectivity, Δ = 0.318, t(7) = 1.861, p = 0.112, BF = 0.91—but what difference there was did show that experts still performed better than novices on average. There was no significant difference in efficiency between novices and experts in any of the four tasks. There were also no significant interactions, suggesting that the effects of target and distractor homogeneity versus heterogeneity generalize across skill levels. The effects we found for target and distractor heterogeneity are therefore not driven by practice with the centroid task. Experts were more selective for targets overall, but their performance in the heterogeneous conditions worsened as much as the novices'. This suggests that the effects are not task specific.