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 correctness of the basic statistics related to the effect size (ES) based on correlation (CBES) was questioned. METHODS: Monte Carlo simulation of two paired binary samples, mathematical analysis, conceptual analysis, bias analysis. RESULTS: Actual effect size and CBES are not related. CBES is a fallacy based on misunderstanding of correlation and ES and confusion with 2 × 2 tables that 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. misconception of contingency tables (MCT) is a series of related misconceptions due to confusion with 2 × 2 tables and misapplication of related statistics. 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. CONCLUSIONS: Two related common misconceptions in statistics have been exposed, CBES and MCT. The misconceptions are threatening because most of the findings from contingency tables, 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.