The main objective of this work is to navigate appropriate statistical frameworks with their mathematical characteristics for the AB/BA cross-over design and present a comprehensive comparison of each method by performing a power analysis using a simulation study. Lastly, this study examines how effect size and intra-class correlation influence the accuracy of the applied methods. The comparisons were based on the achieved statistical power and estimated beta coefficient with its standard error. The performance of each method was tested in different situations with respect to effect size and intra-class correlation to demonstrate the most optimal method in a different scenario. At the end of the paper, we applied each method to a real data example to illustrate how the performance suits the theory to provide medical practitioners insight. From the results, LMM was found to be efficient in most cases with respect to effect size and ICC; it was only not eligible when the recruited participants are limited due to its asymptotic estimations. RM-ANOVA and ANCOVAs may take advantage in such cases, but using RM-ANOVA is more restricted due to strong assumptions.