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.