Equality judgments cannot distinguish between attention effects on appearance and criterion: a reply to Schneider (2011).

Whether attention modulates the appearance of stimulus features is debated. Whereas many previous studies using a comparative judgment have found evidence for such an effect, two recent studies using an equality judgment have not. Critically, these studies have relied on the assumption that the equality paradigm yields bias-free PSE estimates and is as sensitive as the comparative judgment, without testing these assumptions. Anton-Erxleben, Abrams, and Carrasco (2010) compared comparative judgments and equality judgments with and without the manipulation of attention. They demonstrated that the equality paradigm is less sensitive than the comparative judgment and also bias-prone. Furthermore, they reported an effect of attention on the PSE using both paradigms. Schneider (2011) questions the validity of the latter finding, stating that the data in the equality experiment are corrupted because of skew in the response distributions. Notably, this argument supports the original conclusion by Anton-Erxleben et al.: that the equality paradigm is bias-prone. Additionally, the necessary analyses to show that the attention effect observed in Anton-Erxleben et al. was due to skew in the data were not conducted. Here, we provide these analyses and show that although the equality judgment is bias-prone, the effects we observe are consistent with an increase of apparent contrast by attention.