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.