4.0 Discussion

We have shown that apparent non-uniform reductions in contrast sensitivity can be explained by the heteroscedastic/skewed distribution of the contrast sensitivity data and by group differences in visual acuity. Our analysis gives reason to be cautious when interpreting interactions with spatial frequency in past studies; it also explains why the log-transformed data of Zemon et al. (2020) and Keri et al. (2002) yielded interactions that were opposite in sign to the interactions reported in certain previous studies (Butler et al., 2005; Martinez et al., 2012; Revheim et al., 2014) that did not transform the data.
Note that the pitfalls identified above have been discussed in other corners of science. For example, in the memory literature, it has been known that some “removable” interactions in two-way designs arise from non-linearities in the dependent variable (e.g., response probability) and can often be abolished by applying a transformation that conserves monotonicity (Wagenmakers et al., 2012; Loftus, 1978). In the vision literature, refractive errors have been shown to compromise contrast sensitivity at high but not low spatial frequencies, with smaller but still detectable effects in the mid-spatial frequency range (Keane et al., 2014; Keane et al., 2022; Charman & Heron, 1979; Johnson & Casson, 1995). Despite the long-standing nature of these problems, non-log-transformed data and their interactions continue to be discussed and interpreted in cognitive science, behavioral neuroscience, and vision science (Arnold et al., 2016; Jackson et al., 2012; Abrahamsson & Sjöstrand, 1986). Likewise, refractive error is often not regarded as a potential confound even when group differences increase with spatial frequency (Keri et al., 2002; Wesner & Tan, 2006).
While our focus was on spatial frequency interactions, our re-analysis also demonstrated that patient contrast sensitivity deficits could not be erased simply by matching groups on visual acuity. This shows that not matching groups on visual acuity can be a missed opportunity; when groups are well-matched in this regard, contrast sensitivity deficits (or enhancements) can be more definitively established.