Size-distance rescaling in the ensemble representation of variance
Numerous studies report that observers are good at evaluating various ensemble statistics, such as mean or range. Recent studies have shown that, in the perception of mean size, the visual system relies on size information individually rescaled to distance for each item (Utochkin & Tiurina, 2018). Here, we directly tested this rescaling mechanism on the perception of variance. In our experiment, participants were stereoscopically shown a sample set of circles with different sizes and in different apparent depths. Then they had to adjust a test set so that the range of sizes to match the range of the sample. We manipulated the correlation between sizes and depth for both samples and tests. In positive size-depth correlation, bigger circles were presented farther and had to seem larger and small circles were presented closer and had to seem smaller; therefore, the apparent range had to increase. In negative size-depth correlation, the apparent range had to decrease, since bigger circles had to become smaller, and vice versa. We tested all possible couplings of correlation conditions between samples and tests. We found that in general, observers tended to overestimate the range of the sample (over-adjusted it on the test). Yet, the strongest underestimation was shown when the sample had a negative correlation and the test had a positive correlation. This pattern is consistent with the prediction following from the idea of rescaling. As the negative correlation reduced an apparent range, participants had to under-adjust the range of a positively correlated test to compensate for the difference in variance impressions. We conclude, therefore, that multiple sizes are automatically rescaled in accordance with their distances and this rescaling can be used to judge ensemble variance.