BACKGROUND: Evidence-based medicine (EBM) is in crisis, in part due to bad methods, which are understood as misuse of statistics that is considered correct in itself. The study questions the correctness of the basic statistics related to the effect size (ES) based on correlation (CBES).
METHODS: Monte Carlo simulation of paired samples, mathematical analysis, conceptual analysis, bias analysis.
RESULTS: Correlation and ES are not related. CBES is a fallacy, mainly based on the point biserial correlation (PBC) fallacy and misconception of contingency tables (MCT), which makes no distinction between gross crosstabs (GCTs) and contingency tables (CTs). Misapplication of Pearson’s correlation coefficient to point biserial datasets and GCTs gives ES parameters that are not related to correlation. Equations directly expressing ES in terms of correlation coefficient are flawed, since it is impossible without including covariance. Generalization of these fallacies leads to erroneous inferences, conversions, transformations, meta-analyses, and misunderstanding of the nature of correlation. MCT leads to misuse of the relevant statistics and is so ubiquitous that all findings from CTs are suspect.
CONCLUSIONS: Two related common statistical misconceptions, CBES and MCT, have been exposed and fixed. These misconceptions are threatening because most of the findings from correlation, paired samples and CTs, including meta-analyses, can be misleading. Since exposing these fallacies casts doubt on the reliability of the statistical foundations of EBM in general, we urgently need to revise them.