Revisiting Statistics and Evidence-Based Medicine: On the Fallacy of the Effect Size Based on Correlation and the Misconception of Contingency Tables

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 studyquestions the correctness of the basic statistics related to the effect size (ES) based oncorrelation (CBES). METHODS: Monte Carlo simulation of paired samples, mathematicalanalysis, conceptual analysis, bias analysis. RESULTS: Correlation and ES are not related.CBES is a fallacy, mainly based on the point biserial correlation (PBC) fallacy andmisconception of contingency tables (MCT), which makes no distinction between grosscrosstabs (GCTs) and contingency tables (CTs). Misapplication of Pearson’s correlationcoefficient to point biserial datasets and GCTs gives ES parameters that are not related tocorrelation. Equations directly expressing ES in terms of correlation coefficient are flawed,since it is impossible without including covariance. Generalization of these fallacies leads toerroneous inferences, conversions, transformations, meta-analyses, and misunderstandingof the nature of correlation. MCT leads to misuse of the relevant statistics and is soubiquitous that all findings from CTs are suspect. CONCLUSIONS: Two related commonstatistical misconceptions, CBES and MCT, have been exposed and fixed. Thesemisconceptions are threatening because most of the findings from correlation, pairedsamples and CTs, including meta-analyses, can be misleading. Since exposing these fallaciescasts doubt on the reliability of the statistical foundations of EBM in general, we urgentlyneed to revise them.