Abstract
Data binning can deal with overplotting and noise. As such, it has become integral to population receptive field (pRF) analyses aimed at contrasting visual field maps with many observations. However, such differential data binning is flawed if the same observations are used for binning and contrasting. This creates circularity, eventually biasing noise components. To expose this flaw, we perturbed pRF position estimates of an empirical visual field map with random Gaussian noise. We repeated this to simulate an Interest, Baseline, and Independent condition. The Interest and Baseline condition can be regarded as different attention conditions and the Independent condition as a replication of the Baseline condition – to give but one example. We then binned pRF positions from the Interest and Baseline condition and calculated bin-wise means. The binning was based on pRF positions from any of the three conditions. Since there were no systematic differences between conditions, the bin-wise means for the Interest and Baseline condition should always coincide. Although this was true when using the Independent condition for binning, artifactual differences occurred when using the Baseline condition instead. Strikingly, these differences flipped when using the Interest condition for binning. This bidirectionality is characteristic of regression to the mean and occurred because the same condition (e.g. Baseline) was used for contrasting and binning. This circularity skewed the bin-wise noise components for this condition on average, rendering the bin-wise means more extreme. As a consequence, the bin-wise means in the other condition (e.g. Interest) regressed – by statistical necessity – to the overall mean. This regression artifact replicated with empirical repeat data and was modulated substantially by data cleaning and heteroscedasticity, rendering it easy to mistake for a real effect. Consequently, flawed differential binning may have resulted in spurious claims about the plasticity of pRFs in previous research.