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).