Preprint has been published in a journal as an article
DOI of the published article
Preprint / Version 4

Meta-Analysis of Variation in Sport and Exercise Science

Examples of Application Within Resistance Training Research


  • James Steele Solent University
  • James P. Fisher Solent University
  • Dave Smith Manchester Metropolitan University
  • Brad J Schoenfeld CUNY Lehman College
  • Yefeng Yang University of New South Wales
  • Shinichi Nakagawa University of New South Wales



meta-analysis, intraindividual variability, variability, resistance training, applied statistics


Meta-analysis has become commonplace within sport and exercise science for synthesising and summarising empirical studies. However, most research in the field focuses upon mean effects; particularly the effects of interventions to improve outcomes such as fitness or performance. It is thought that individual responses to interventions vary considerably. Hence, interest has increased in exploring precision or personalised exercise approaches. Not only is the mean often affected by interventions, but variation may also be impacted. Exploration of variation in studies such as randomised controlled trials (RCTs) can yield insight into interindividual heterogeneity in response to interventions and help determine generalisability of effects. Yet, larger samples sizes than those used for typical mean effects are required when probing variation. Thus, in a field with small samples such as sport and exercise science, exploration of variation through a meta-analytic framework is appealing. Despite the value of embracing and exploring variation alongside mean effects in sport and exercise science it is rarely applied to research synthesis through meta-analysis.We introduce and evaluate different effect size calculations along with models for meta-analysis of variation using relatable examples from resistance training RCTs.


Metrics Loading ...


Atkinson, G., & Batterham, A. M. (2015). True and false interindividual differences in the physiological response to an intervention. Experimental Physiology, 100(6), 577–588.

Atkinson, G., Williamson, P., & Batterham, A. M. (2019). Issues in the determination of ‘responders’ and ‘non-responders’ in physiological research. Experimental Physiology, 104(8), 1215–1225.

Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 10.1016/j.jml.2012.11.001.

Bernárdez-Vázquez, R., Raya-González, J., Castillo, D., & Beato, M. (2022). Resistance Training Variables for Optimization of Muscle Hypertrophy: An Umbrella Review. Frontiers in Sports and Active Living, 4.

Bonafiglia, J. T., Swinton, P. A., Ross, R., Johannsen, N. M., Martin, C. K., Church, T. S., Slentz, C. A., Ross, L. M., Kraus, W. E., Walsh, J. J., Kenny, G. P., Goldfield, G. S., Prud’homme, D., Sigal, R. J., Earnest, C. P., & Gurd, B. J. (2022). Interindividual Differences in Trainability and Moderators of Cardiorespiratory Fitness, Waist Circumference, and Body Mass Responses: A Large-Scale Individual Participant Data Meta-analysis. Sports Medicine (Auckland, N.Z.).

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2010). A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods, 1(2), 97–111.

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2021). Introduction to Meta-Analysis. John Wiley & Sons.

Box, G. E. P. (1976). Science and Statistics. Journal of the American Statistical Association, 71(356), 791–799.

Caldwell, A., & Vigotsky, A. D. (2020). A case against default effect sizes in sport and exercise science. PeerJ, 8, e10314.

Carpinelli, R. N. (2017). Interindividual heterogeneity of adaptations to resistance training. Medicina Sportiva Practica, 18(4), 79–94.

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Routledge.

Cortés Martínez, J. (2021). Constant effect in randomized clinical trials with quantitative outcome: A methodological review. TDX (Tesis Doctorals En Xarxa).

Curtis, P. S., & Wang, X. (1998). A meta-analysis of elevated CO2 effects on woody plant mass, form, and physiology. Oecologia, 113(3), 299–313.

Deb, S. K., Brown, D. R., Gough, L. A., Mclellan, C. P., Swinton, P. A., Andy Sparks, S., & Mcnaughton, L. R. (2018). Quantifying the effects of acute hypoxic exposure on exercise performance and capacity: A systematic review and meta-regression. European Journal of Sport Science, 18(2), 243–256.

Esteves, G. P., Swinton, P., Sale, C., James, R. M., Artioli, G. G., Roschel, H., Gualano, B., Saunders, B., & Dolan, E. (2021). Individual Participant Data Meta-Analysis Provides No Evidence of Intervention Response Variation in Individuals Supplementing With Beta-Alanine. International Journal of Sport Nutrition and Exercise Metabolism, 31(4), 305–313.

Exner, R. J., Patel, M. H., Whitener, D. V., Buckner, S. L., Jessee, M. B., & Dankel, S. J. (2022). Does performing resistance exercise to failure homogenize the training stimulus by accounting for differences in local muscular endurance? European Journal of Sport Science, 1–10.

Fisher, J., Steele, J., Wolf, M., Korakakis, P. A., Smith, D., & Giessing, J. (2022). The Role of Supervision in Resistance Training; an Exploratory Systematic Review and Meta-Analysis: International Journal of Strength and Conditioning, 2(1), Article 1.

Glass, G. V. (1976). Primary, Secondary, and Meta-Analysis of Research. Educational Researcher, 5(10), 3–8.

Gurevitch, J., Morrison, J. A., & Hedges, L. V. (2000). The Interaction between Competition and Predation: A Meta-analysis of Field Experiments. The American Naturalist, 155(4), 435–453.

Hagger, M. (2006). Meta-analysis in sport and exercise research: Review, recent developments, and recommendations. European Journal of Sport Science, 6(2), 103–115.

Hagger, M. (2022). Meta-analysis. International Review of Sport and Exercise Psychology, 15(1), 120–151.

Halliday, T. M., Savla, J., Marinik, E. L., Hedrick, V. E., Winett, R. A., & Davy, B. M. (2017). Resistance training is associated with spontaneous changes in aerobic physical activity but not overall diet quality in adults with prediabetes. Physiology & Behavior, 177, 49–56.

Halperin, I., Malleron, T., Har-Nir, I., Androulakis-Korakakis, P., Wolf, M., Fisher, J., & Steele, J. (2022). Accuracy in Predicting Repetitions to Task Failure in Resistance Exercise: A Scoping Review and Exploratory Meta-analysis. Sports Medicine, 52(2), 377–390.

Hecksteden, A., Kraushaar, J., Scharhag-Rosenberger, F., Theisen, D., Senn, S., & Meyer, T. (2015). Individual response to exercise training—A statistical perspective. Journal of Applied Physiology (Bethesda, Md.: 1985), 118(12), 1450–1459.

Hedges, L. V., Gurevitch, J., & Curtis, P. S. (1999). The Meta-Analysis of Response Ratios in Experimental Ecology. Ecology, 80(4), 1150–1156.[1150:TMAORR]2.0.CO;2

Hedges, L. V., & Nowell, A. (1995). Sex differences in mental test scores, variability, and numbers of high-scoring individuals. Science (New York, N.Y.), 269(5220), 41–45.

Hedges, L. V., & Olkin, I. (2014). Statistical Methods for Meta-Analysis. Academic Press.

Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods, 1(1), 39–65.

Heidel, K. A., Novak, Z. J., & Dankel, S. J. (2022). Machines and free weight exercises: A systematic review and meta-analysis comparing changes in muscle size, strength, and power. The Journal of Sports Medicine and Physical Fitness, 62(8), 1061–1070.

Hopkins, W. G. (2015). Individual responses made easy. Journal of Applied Physiology (Bethesda, Md.: 1985), 118(12), 1444–1446.

Hrubeniuk, T. J., Bonafiglia, J. T., Bouchard, D. R., Gurd, B. J., & Sénéchal, M. (2022). Directions for Exercise Treatment Response Heterogeneity and Individual Response Research. International Journal of Sports Medicine, 43(1), 11–22.

Kass, R. E., & Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90(430), 773–795.

Kelley, G. A. (2022). Precision exercise medicine in rheumatology: Don’t put the cart before the horse. Clinical Rheumatology, 41(8), 2277–2279.

Kelley, G. A., Kelley, K. S., & Callahan, L. F. (2022). Are There Interindividual Differences in Anxiety as a Result of Aerobic Exercise Training in Adults with Fibromyalgia? An Ancillary Meta-analysis of Randomized Controlled Trials. Archives of Physical Medicine and Rehabilitation, S0003-9993(22)00007-7.

Kelley, G. A., Kelley, K. S., & Pate, R. R. (2020). Are There Inter-Individual Differences in Fat Mass and Percent Body Fat as a Result of Aerobic Exercise Training in Overweight and Obese Children and Adolescents? A Meta-Analytic Perspective. Childhood Obesity (Print), 16(5), 301–306.

Lajeunesse, M. J. (2011). On the meta-analysis of response ratios for studies with correlated and multi-group designs. Ecology, 92(11), 2049–2055.

Lajeunesse, M. J. (2015). Bias and correction for the log response ratio in ecological meta-analysis. Ecology, 96(8), 2056–2063.

Mills, H. L., Higgins, J. P. T., Morris, R. W., Kessler, D., Heron, J., Wiles, N., Davey Smith, G., & Tilling, K. (2021). Detecting Heterogeneity of Intervention Effects Using Analysis and Meta-analysis of Differences in Variance Between Trial Arms. Epidemiology (Cambridge, Mass.), 32(6), 846–854.

Morris, S. B. (2008). Estimating Effect Sizes From Pretest-Posttest-Control Group Designs. Organizational Research Methods, 11(2), 364–386.

Morris, W. F., Hufbauer, R. A., Agrawal, A. A., Bever, J. D., Borowicz, V. A., Gilbert, G. S., Maron, J. L., Mitchell, C. E., Parker, I. M., Power, A. G., Torchin, M. E., & Vázquez, D. P. (2007). Direct and interactive effects of enemies and mutualists on plant performance: A meta-analysis. Ecology, 88(4), 1021–1029.

Nakagawa, S., & Cuthill, I. C. (2007). Effect size, confidence interval and statistical significance: A practical guide for biologists. Biological Reviews of the Cambridge Philosophical Society, 82(4), 591–605.

Nakagawa, S., Poulin, R., Mengersen, K., Reinhold, K., Engqvist, L., Lagisz, M., & Senior, A. M. (2015). Meta-analysis of variation: Ecological and evolutionary applications and beyond. Methods in Ecology and Evolution, 6(2), 143–152.

Nakagawa, S., & Schielzeth, H. (2012). The mean strikes back: Mean-variance relationships and heteroscedasticity. Trends in Ecology & Evolution, 27(9), 474–475; author reply 475-476.

Nuzzo, J., Pinto, M. D., Nosaka, K., & Steele, J. (2023a). The Eccentric:Concentric Strength Ratio of Human Skeletal Muscle In Vivo: Meta-analysis of the Influences of Sex, Age, Joint Action, and Velocity. Sports Medicine, 53(6), 1125–1136.

Nuzzo, J., Pinto, M., Nosaka, K., & Steele, J. (2022). How much stronger are muscles eccentrically than concentrically? : Meta-analysis of the influences of sex, age, joint action, and velocity. SportRxiv.

Nuzzo, J., Pinto, M., Nosaka, K., & Steele, J. (2023b). Maximal number of repetitions at percentages of the one repetition maximum: A meta-regression and moderator analysis of sex, age, training status, and exercise. SportRxiv.

Olsson-Collentine, A., Van Aert, R. C. M., Bakker, M., & Wicherts, J. (2023). Meta-analyzing the multiverse: A peek under the hood of selective reporting. Psychological Methods.

Pickering, C., & Kiely, J. (2019). Do Non-Responders to Exercise Exist-and If So, What Should We Do About Them? Sports Medicine (Auckland, N.Z.), 49(1), 1–7.

Plackett, R. L. (1958). Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean. Biometrika, 45(1/2), 130–135.

Polito, M. D., Papst, R. R., & Farinatti, P. (2021). Moderators of strength gains and hypertrophy in resistance training: A systematic review and meta-analysis. Journal of Sports Sciences, 39(19), 2189–2198.

Raudenbush, S. W., & Bryk, A. S. (1987). Examining Correlates of Diversity. Journal of Educational Statistics, 12(3), 241–269.

Robinson, Z., Helms, E., Trexler, E., Steele, J., Hall, M., Huang, C.-J., & Zourdos, M. (2023). Optimizing Research Methodology for the Detection of Individual Response Variation in Resistance Training. SportRxiv.

Ross, R., Goodpaster, B. H., Koch, L. G., Sarzynski, M. A., Kohrt, W. M., Johannsen, N. M., Skinner, J. S., Castro, A., Irving, B. A., Noland, R. C., Sparks, L. M., Spielmann, G., Day, A. G., Pitsch, W., Hopkins, W. G., & Bouchard, C. (2019). Precision exercise medicine: Understanding exercise response variability. British Journal of Sports Medicine, 53(18), 1141–1153.

Senior, A. M., Viechtbauer, W., & Nakagawa, S. (2020). Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio. Research Synthesis Methods, 11(4), 553–567.

Steegen, S., Tuerlinckx, F., Gelman, A., & Vanpaemel, W. (2016). Increasing Transparency Through a Multiverse Analysis. Perspectives on Psychological Science, 11(5), 702–712.

Steele, J., Fisher, J. P., Giessing, J., Androulakis-Korakakis, P., Wolf, M., Kroeske, B., & Reuters, R. (2022). Long-Term Time-Course of Strength Adaptation to Minimal Dose Resistance Training Through Retrospective Longitudinal Growth Modeling. Research Quarterly for Exercise and Sport, 0(0), 1–18.

Steele, J., Fisher, J., Skivington, M., Dunn, C., Arnold, J., Tew, G., Batterham, A. M., Nunan, D., O’Driscoll, J. M., Mann, S., Beedie, C., Jobson, S., Smith, D., Vigotsky, A., Phillips, S., Estabrooks, P., & Winett, R. (2017). A higher effort-based paradigm in physical activity and exercise for public health: Making the case for a greater emphasis on resistance training. BMC Public Health, 17(1), 300.

Steele, J., Malleron, T., Har-Nir, I., Androulakis-Korakakis, P., Wolf, M., Fisher, J. P., & Halperin, I. (2022). Are Trainees Lifting Heavy Enough? Self-Selected Loads in Resistance Exercise: A Scoping Review and Exploratory Meta-analysis. Sports Medicine.

Steele, J., Plotkin, D., Van Every, D., Rosa, A., Zambrano, H., Mendelovits, B., Carrasquillo-Mercado, M., Grgic, J., & Schoenfeld, B. J. (2021). Slow and Steady, or Hard and Fast? A Systematic Review and Meta-Analysis of Studies Comparing Body Composition Changes between Interval Training and Moderate Intensity Continuous Training. Sports (Basel, Switzerland), 9(11), 155.

Swinton, P. A., Hemingway, B. S., Saunders, B., Gualano, B., & Dolan, E. (2018). A Statistical Framework to Interpret Individual Response to Intervention: Paving the Way for Personalized Nutrition and Exercise Prescription. Frontiers in Nutrition, 5, 41.

Swinton, P. A., Katherine, B., Andy, H., Leon, G., John, P., Rodrigo, R. A., Patrick, M., & Andrew, M. (2022). Interpreting magnitude of change in strength and conditioning: Effect size selection, threshold values and Bayesian updating Journal of Sports Sciences. Journal of Sports Sciences.

Taylor, L. R. (1961). Aggregation, Variance and the Mean. Nature, 189(4766), Article 4766.

Tenan, M. S., Vigotsky, A. D., & Caldwell, A. R. (2020). Comment on: “A Method to Stop Analyzing Random Error and Start Analyzing Differential Responders to Exercise”. Sports Medicine, 50(2), 431–434.

Usui, T., Macleod, M. R., McCann, S. K., Senior, A. M., & Nakagawa, S. (2021). Meta-analysis of variation suggests that embracing variability improves both replicability and generalizability in preclinical research. PLOS Biology, 19(5), e3001009.

Van den Noortgate, W., López-López, J. A., Marín-Martínez, F., & Sánchez-Meca, J. (2013). Three-level meta-analysis of dependent effect sizes. Behavior Research Methods, 45(2), 576–594.

Viechtbauer, W. (2010). Conducting Meta-Analyses in R with the metafor Package. Journal of Statistical Software, 36, 1–48.

Vigotsky, A., Nuckols, G. L., Fisher, J., Heathers, J., Krieger, J., Schoenfeld, B. J., Giessing, J., & Steele, J. (2020). Improbable data patterns in the work of Barbalho et al. SportRxiv.

Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems ofp values. Psychonomic Bulletin & Review, 14(5), 779–804.

Wolf, M., Androulakis-Korakakis, P., Fisher, J., Schoenfeld, B., & Steele, J. (2023). Partial Vs Full Range of Motion Resistance Training: A Systematic Review and Meta-Analysis. International Journal of Strength and Conditioning, 3(1), Article 1.

Yang, Y., Hillebrand, H., Lagisz, M., Cleasby, I., & Nakagawa, S. (2022). Low statistical power and overestimated anthropogenic impacts, exacerbated by publication bias, dominate field studies in global change biology. Global Change Biology, 28(3), 969–989.


2022-10-26 — Updated on 2023-11-13