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. This article exposes two related common misconceptions in statistics, the effect size (ES) based on correlation (CBES) and a misconception of contingency tables (MCT). CBES is a fallacy based on misunderstanding of correlation and ES and confusion with 2 × 2 tables, which makes no distinction between gross crosstabs (GCTs) and contingency tables (CTs). This leads to misapplication of Pearson’s Phi, designed for CTs, to GCTs and confusion of the resulting gross Pearson Phi, or mean-square effect half-size, with the implied Pearson mean square contingency coefficient. Generalizing this binary fallacy to continuous data and the correlation in general (Pearson’s r) resulted in flawed equations directly expressing ES in terms of the correlation coefficient, which is impossible without including covariance, so these equations and the whole CBES concept are fundamentally wrong. MCT is a series of related misconceptions due to confusion with 2 × 2 tables and misapplication of related statistics. The misconceptions are threatening because most of the findings from contingency tables, including CBES-based meta-analyses, can be misleading. Problems arising from these fallacies are discussed and the necessary changes to the corpus of statistics are proposed resolving the problem of correlation and ES in paired binary data. Since exposing these fallacies casts doubt on the reliability of the statistical foundations of EBM in general, we urgently need to revise them.