3. Results

Detailed side-by-side descriptions of the interaction effects for each analysis may be found in Supplementary Tables S1, S2, and S3. For the non-transformed short stimulus duration data (33 ms), there was a main effect of subject group (F (1,141)=22.4, p <.001,\(\eta_{p}^{2}\)=.14), spatial frequency (F (1,141)=637.2,p <.001 , \(\eta_{p}^{2}\)=.82), and an interaction (F (1,141)=12.7, p <.001, \(\eta_{p}^{2}\)=.083). Follow-up t-tests showed a larger contrast sensitivity deficit at the low spatial frequency condition (t (141)=4.2,p <.001, Hedges’ g =.70) versus the high spatial frequency condition (t (111.2)=3.7, p <.001,Hedges’ g =.60), consistent with certain previous studies (Butler et al., 2005; Revheim et al., 2014).
Log transforms are often implemented because contrast sensitivity values are thought to vary according to a power law distribution and because such values can differ by order of magnitude across spatial frequencies. Log-transformations mitigate positive skew and heteroscedasticity and likely facilitate more accurate statistical inferences. We, therefore, re-ran the ANOVA on the log-transformed data. There was a main effect of spatial frequency and subject group, as before, but the direction of the significant interaction reversed (F (1,141)=41.9,p <.001, \(\eta_{p}^{2}\) =.229; F (1,141)=1861.3,p <.001, \(\eta_{p}^{2}\) = .930; F (1,141)=4.2,p =.04, \(\eta_{p}^{2}\) =.029). Follow-up t-tests revealed more pronounced deficits at the high spatial frequency condition (t (141)=5.2, p <.001, Hedges’ g=.86) versus the low spatial frequency condition (t (120.3)=4.6,p <.001, Hedges’ g =.77).
Despite the nearly ubiquitous use of log-transforms throughout the life sciences, some have found fault with this practice because, for example, the magnitude of skew can be equal and opposite after the transformation and because parameter estimates can have more significant standard errors after the transformation (Feng et al., 2014). Generalized estimating equations (GEE) have been recommended as an alternative because they can flexibly account for differences in variance and rightward skew and are robust to the misspecification of the covariance structure (Feng et al., 2014; Pekár & Brabec, 2018). Our GEEs revealed results that were qualitatively the same as the ANOVAs with the log-transformed data: patients exhibited contrast sensitivity deficits that worsened from low to high spatial frequencies (Wald Chi-square (1) = 4.87, B =-.419, SEB =.19, p =.027).