Abstract

The replication crisis weakens the credibility of statistical science. Although the reasons usually given for this (e.g. questionable research practices, statistical errors) are important, but it is often overlooked that hypotheses are often not complex enough to accurately represent empirical phenomena. This means that statistical methods will have to be better suited to more complex hypotheses than in the past. The Relation Analysis (RELAN), theoretical framework and software, allows the logical analysis, statistical testing, and simulation (modelling) of simple and highly complex logical hypotheses and also an extensive exploration of multivariate data sets. The approach of RELAN is grounded in the mathematical framework of relations, which permits the identification of all relationships - causes, effects, moderators, and mediators - among up to ten binary variables. To adequately describe complex empirical associations, the method employs six logical functions between variables (e.g. AND, OR, IF-THEN) as opposed to relying on a single function, namely (bidirectional) correlation, as is the case with the majority of multivariate statistical methods. Furthermore, most multivariate statistical analyses are based on pairwise correlations between variables; RELAN takes into account all potential relationships, that means the interactions between all variables; this multivariate and multifunctional complexity allows for highly specific hypotheses (alternative hypotheses) that are often very ‘far’ (effect size) from the random probability (null hypothesis), so that (with a constant sample size and significance level) the statistical power generally also increases. Moreover, the logical association analysis, RELAN, can be conducted for up to one hundred variables. Consequently, this method serves as a potential remedy for the replication crisis observed in numerous scientific disciplines. Additionally, the logical formulation of hypotheses clarifies their theoretical structure and enhances communication within the research community. This article provides a brief overview of the method and illustrates its application through several straightforward examples.

Keywords

logical-statistical analysis, hypothesis testing, exploration, modelling, propositional logic, software.