The comparison of two independent proportions via Design Analysis: Theoretical background and an R implementation

In the last decade science has fallen into a replication crisis, this means that researches, when replicated, do not give the same results as the original ones. The difficulty in replicating studies can be due to several reasons, some of which regard the scientific world in general, such as the actual publication system that encourages incorrect behaviours and questionable research practices by scientists, and some that change between scientific fields. In fact, some scientific field feel this crisis more than others, and psychology is one of them. Low statistical power and misuse of statistics in psychology is reported from a long time. The first to criticize psychologist in regards of the use of power has been Cohen in 1962. This crisis can lead to the loss of trust in psychology and in science in general, for this reason it is important to find some solutions to the crisis. Several possible solutions have been proposed. In this work we will focus on Design analysis, that is quite a new notion that can help in the process of getting out of the replication crisis. This analysis consists in calculating (power, and) new type of inferential errors to help researchers to better understand the consequences of low power, small sample sizes and studies started without appropriate planning. Design analysis can be done prospectively and retrospectively, that is different from post-hoc power calculations. The aims of this work are mainly to extend the design analysis to the case of differences between independent proportions and to provide an R implementation that can be used by researchers.