Error Rates, Decisive Outcomes and Publication Bias with Several Inferential Methods


Will G. Hopkins Alan M. Batterham


Institute of Sport Exercise and Active Living, Victoria University, Melbourne, Victoria, Australia; Health and Social Care Institute, Teesside University, Middlesbrough, United Kingdom



Background Statistical methods for inferring true magnitude of an effect from a sample should have acceptable error rates when the true effect is trivial (Type-I rates) or substantial (Type-II rates).

Objectives To quantify error rates, rates of decisive (publishable) outcomes, and publication bias of five inferential methods commonly used in sports medicine and science. The methods were conventional null-hypothesis significance testing (NHST; significant and non-significant imply respectively substantial and trivial true effects); conservative NHST (the observed magnitude is interpreted as the true magnitude only for significant effects); non-clinical magnitude-based inference (MBI; the true magnitude is interpreted as the magnitude range of the 90% confidence interval only for intervals not spanning substantial values of opposite sign); clinical MBI (a possibly beneficial effect is recommended for implementation only if it is most unlikely harmful); and odds-ratio clinical MBI (implementation is also recommended when odds of benefit outweigh odds of harm, with odds ratio >66).

Methods Simulation was used to quantify standardized mean effects in 500,000 randomized controlled trials each for true standardized magnitudes ranging from null through marginally moderate with three sample sizes: suboptimal (10+10), optimal for MBI (50+50), and optimal for NHST (144+144).

Results Type-I rates for non-clinical MBI were always lower than for NHST. When Type-I rates for clinical MBI were higher, most errors were debatable, given the probabilistic qualification of those inferences (unlikely or possibly beneficial). NHST often had unacceptable rates either for Type-II errors or decisive outcomes, and it had substantial publication bias with the smallest sample size, whereas MBI had no such problems.

Conclusion Magnitude-based inference is a trustworthy nuanced alternative to null hypothesis significance testing, which it outperforms on sample size, error rates, decision rates, and publication bias.


Key Points

Null-hypothesis significance testing (NHST) is increasingly criticised for its failure to deal adequately with conclusions about the true magnitude of effects in research on samples.

A relatively new approach, magnitude-based inference (MBI), provides up-front comprehensible nuanced uncertainty in effect magnitudes.

In simulations of randomised controlled trials, MBI outperforms NHST in respect of inferential error rates, rates of publishable outcomes with suboptimal sample sizes, and publication bias with such samples.

Back to In-brief article