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

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].

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.

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.

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.

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.