The Standard Error/Standard Deviation Mix-Up: Potential Impacts on Meta-Analyses in Sports Medicine

Abstract

Abstract Background A recent review found that 45% of meta-analyses included statistical errors, of which, the most common was the calculation of effect sizes based on standard error (SE) rather than standard deviation (SD) [the SE/SD mix-up]. Objectives The first aim of this study was to assess the impact of the SE/SD mix-up on the results of one highly cited meta-analysis. Our second aim was to identify one potential source of the SE/SD mix-up, by assessing how often SE is reported as a measure of sample variability in randomised controlled trials in sports medicine. Methods We checked for potential SE/SD mix-ups in a 2015 meta-analysis of randomised controlled trials reporting the effects of recreational football interventions on aerobic fitness in adults. We corrected effect sizes affected by SE/SD mix-ups and re-analysed the data according to the original methodology. We compared pooled estimates of effect sizes from our re-analysis of corrected values with those of the original study. To assess how often SE was reported instead of SD as a measure of sample variance, we text mined results of randomised controlled trials from seven sports medicine journals and reported the proportion reporting of SE versus SD. Results We identified potential SE/SD mix-ups in 9/16 effect sizes included in the meta-analysis describing the effects of football-based interventions versus non-exercise control. The published effect size was standardised mean difference (SMD) = 1.46 (95% confidence interval [CI] 0.91, 2.01). After correcting for SE/SD mix-ups, our re-analysis produced a smaller pooled estimate (SMD = 0.54 [95% CI 0.37, 0.71]). The original pooled estimate for trials comparing football versus running interventions was SMD = 0.68 (95% CI 0.06, 1.4). After correcting for SE/SD mix-ups and re-analysis, the effect was no longer statistically significant (SMD = 0.20 [95% CI − 0.10, 0.49)]). We found that 19.3% of randomised controlled trials reported SE rather than SD to describe sample variability. The relative frequency of the practice ranged from 0 to 25% across the seven journals sampled. Conclusions We found the SE/SD mix-up had inflated estimates for the effects of football on aerobic fitness. Meta-analysts should be vigilant to avoid miscalculating effect sizes. Authors, reviewers and editors should avoid and discourage (respectively) the practice of reporting SE as a measure of sample variability in sports medicine research.