Preprint / Version 1

A Bayesian Approach to Interpret Intervention Effectiveness in Strength and Conditioning Part 2

Effect Size Selection and Application of Bayesian Updating


  • Paul Swinton
  • Katherine Burgess
  • Andy Hall
  • Leon Greig
  • John Psyllas
  • Rodrigo Aspe
  • Patrick Maughan
  • Andrew Murphy



S&C, Evaluation, Effect size, Bayesian, Effectiveness, Statistics


Background Effect sizes are commonly used to assess the effectiveness of interventions in strength and conditioning (S&C). The purposes of this large meta-analysis were to investigate the properties of two different effect size statistics and synthesize the large amount of data available in the form of informative Bayesian priors to quantify effectiveness of future S&C interventions.   

Methods An online database and hand search of published and unpublished S&C intervention studies from the 1950’s onwards was conducted. Pre- and post-intervention data comprising means and standard deviations were extracted from outcomes categorized as: maximum strength, jump performance or sprint performance. Standardised mean difference (SMDpre) and percentage improvement (%Improve) obtained from the response ratio were calculated and modelled with 4-level Bayesian hierarchical meta-analysis models. Results were also used to create normally distributed priors which were incorporated into an accessible tool for assessing the effectiveness of future S&C interventions through the use of Bayesian updating.

Results Data from 628 studies comprising 5468 effect sizes were included in the analyses. Large differences were identified in the effect size distributions for maximum strength (pooled means: SMDpre =0.68 [95%CrI: 0.63 to 0.73]; %Improve = 14.3% [95%CrI: 13.3 to 15.4]) and sprint performance (pooled means: SMDpre =0.46 [95%CrI: 0.43 to 0.50]; %Improve = 6.8% [95%CrI: 6.3 to 7.3]). These differences were also reflected in development of Bayesian priors with the lowest means and largest relative variance obtained for sprint performance reflecting lower improvements in general, but also greater relative dispersion of results. Analysis of the tails of the effect size distributions indicated consistent overestimations of SMDpre values, likely caused by underestimated standard deviations.    

Conclusions Future evaluations of S&C interventions are likely to be better performed and contextualised using Bayesian approaches featuring the information and informative priors developed in this meta-analysis. To facilitate an uptake of Bayesian methods within S&C, an easily accessible tool employing intuitive Bayesian updating was created. It is recommended that researchers and practitioners use the tool alongside the S&C specific threshold values, instead of continual isolated effect size calculations and Cohen’s generic values when evaluating the effectiveness of future S&C interventions. Researchers may choose to evaluate interventions using both SMDpre and percent improvement statistics given their different strengths and limitations.


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