Many experiments in psychology, biology, medicine, etc. result in one-way repeated measures data. However, it is often difficult to make common distributional assumptions such as normality in these settings due to small sample sizes, for example, making nonparametric alternatives to traditional parametric testing procedures desirable. Furthermore, researchers in these fields are often interested in reporting effect sizes such as the common log odds effect size. To that end, we present a nonparametric multiple comparison procedure in the repeated measures setting using log odds as the effect size for the corresponding component test statistics. Moreover, we suggest a novel wild bootstrap algorithm that can be applied to the suggested procedure. Our simulation results indicate that the proposed wild bootstrap-based method performs well relative to traditional procedures based on asymptotic or approximate multivariate distributions.