Systematic review of the use of “magnitude-based inference” in sports science and medicine

Magnitude-based inference (MBI) is a controversial statistical method that has been used in hundreds of papers in sports science despite criticism from statisticians. To better understand how this method has been applied in practice, we systematically reviewed 232 papers that used MBI. We extracted data on study design, sample size, and choice of MBI settings and parameters. Median sample size was 10 per group (interquartile range, IQR: 8–15) for multi-group studies and 14 (IQR: 10–24) for single-group studies; few studies reported a priori sample size calculations (15%). Authors predominantly applied MBI’s default settings and chose “mechanistic/non-clinical” rather than “clinical” MBI even when testing clinical interventions (only 16 studies out of 232 used clinical MBI). Using these data, we can estimate the Type I error rates for the typical MBI study. Authors frequently made dichotomous claims about effects based on the MBI criterion of a “likely” effect and sometimes based on the MBI criterion of a “possible” effect. When the sample size is n = 8 to 15 per group, these inferences have Type I error rates of 12%-22% and 22%-45%, respectively. High Type I error rates were compounded by multiple testing: Authors reported results from a median of 30 tests related to outcomes; and few studies specified a primary outcome (14%). We conclude that MBI has promoted small studies, promulgated a “black box” approach to statistics, and led to numerous papers where the conclusions are not supported by the data. Amidst debates over the role of p-values and significance testing in science, MBI also provides an important natural experiment: we find no evidence that moving researchers away from p-values or null hypothesis significance testing makes them less prone to dichotomization or over-interpretation of findings.