<Fig. 2. here>
Figure 2. Contrast sensitivity results for controls (green) and patients (red) for longer presentation times (500 ms) . Results were qualitatively the same as with the short presentation data (33 ms), suggesting, again, that spatial frequency interactions depend on whether the data were log transformed and whether groups differed in visual acuity.
To show that these results generalize to other viewing conditions, we also considered data from the longer presentation condition (500 ms). The interactions and main effects were similar to before (see Figure 2; Tables S3). In particular, using all subjects, the interaction was significant in opposite ways depending on whether the log-transform was applied or not (raw data: F (1,141)=7.6, p =.006,\(\eta_{p}^{2}\) =.05; log-transformed: F (1,141)=17.7,p <.001, \(\eta_{p}^{2}\)=.11). Using the matched subsample of controls, we found that the interaction showed reduced contrast sensitivity deficits at higher spatial frequencies before but not after the log-transform (raw data: F (1,100)=4.7,p =.03, \(\eta_{p}^{2}\)=.05; log-transformed:F (1,100)=2.6, p =.11, \(\eta_{p}^{2}\)=.03). In each of the above cases, there were main effects of group and spatial frequency (allp <.001; all \(\eta_{p}^{2}\)>.14). GEEs yielded results that were qualitatively the same as the log-transformed results with one exception: using the subsample matched on acuity, there was now an interaction with spatial frequency such that patient deficits tended to worsen at the higher spatial frequency (B =-.436,SEB =.19, Wald Chi-square(1)=5.26, p =.02). However, adding logMAR as a covariate would nudge the interaction out of significance territory (B =-.37, SEB =.20, Wald Chi-square(1)=3.7, p =.06). Moreover, if we were to more closely match groups on acuity, then the interaction would likely be pushed further from significance by reducing the high spatial frequency group difference. To summarize, the results for the long presentation condition were largely the same as the short presentation condition.
Our focus in the study was on spatial frequency interactions. However, it is worth noting that–in all the foregoing analyses, including acuity matching–patients had worse contrast sensitivity than controls (allp <.05). If we were to remove patients whose vision was worse than 20/25–so that the groups would become even more closely matched on logMAR acuity (MHC=.02, MSZ=.02, p =.96, Hedges’ g=.01; n =34 SZ, 58 HC)–the log-transformed ANOVA results would again reveal a strong group deficit in the short duration condition (\(\eta_{p}^{2}\)>.10, p <.004) and the long duration condition (\(\eta_{p}^{2}\)>.11,p <.004) with or without a logMAR covariate.