Various statistical hyphotesis testing (such as Pearson’s Chi-Square, McNemar, Bowker, Cochran-Mantel-Hanszel, Stuart-Maxwell, etc.) for discrete categorical (binary) data have been extensively discussed in the literature. In this research we give a comprehensive review of the two-sample categorical/binary data testing methods on data with or without Stratum Effects along with Homogeneity Testing and Estimation of Common Risk Difference. We also provide detailed implementation of these testing methods and the roadmap to which methods are available in the literature. In addition, the implementation of these methods in popular statistical software packages is also presented. This article will be very helpful for researchers to determine which test or method is available to use in both clinical trials and epidemiology fields, both for the design phase of a study in prospective study, or retrospective study analysis