“…The robustness of OLS methods to heteroscedasticity guarantees only that they will compute statistics as if error were, in reality, homogeneously distributed between participants, across time, and across measurement, but there is no guarantee against distortion of the actual longitudinal structure (Molenaar, 2008). The individual differences in perceptual learning (Withagen & van Wermeskerken, 2009) suggest heteroscedasticity in the trajectories of perceptual learning. ML estimation controls for heteroscedasticity by estimating random effects for each participant and for the finest-grain by- To quantify this change in discrepancies, we used a growth curve to model, in the first place, a quadratic function of log(I 1 ) [i.e., a function of log(I 1 ) * log(I 1 ); see Table 4] and, in addition, the effects of block, strike, and hadS as they interact with this quadratic relationship.…”