How Statistical Power Works | NEJM Evidence (December 5, 2023 via “NEJM Group”): 4-min video.

• Summary: Introduces the concept of the null hypothesis, statistical power, type I error, type II error, statistical significance level, effect size, variance, and their roles as parameters in sample size calculations.

Hickey GL, et al. Statistical primer: sample size and power calculations-why, when and how? Eur J Cardiothorac Surg. 2018 Jul 1;54(1):4-9. (8-page paper)

• Summary: Describes the basis for sample size calculations and describes the components necessary to complete the calculation (i.e., type I error, statistical power, minimal clinically relevant difference, and variance). In many cases, it is necessary to collaborate with a (bio)statistician who may use statistical software packages (several are described in the paper, including packages that exist in R, SAS, SPSS, Stata, and Excel) and/or complete simulation studies. Guidance on the reporting of sample size and power calculations, as well as what to do when an estimated sample size is not achievable in practice, is also provided.

Sample Size and Power: Fundamentals Part 1 (April 19, 2022 via “NIH VideoCast”): 24-min video.

• Summary: Dr. Laura Lee Johnson introduces the concepts of sample size and statistical power and emphasizes the need for input from a statistician during the design of a trial. Effect size, variance, and significance level are introduced, as well as the relationships between these parameters. Discusses that sample size and power calculations are study design-specific, and that many software packages can be used to support a researcher’s efforts in such calculations. A basic sample size formula is introduced for illustrative purposes, along with advice on what a researcher should consider before consulting with a statistician.

Röhrig B, et al. Sample size calculation in clinical trials: part 13 of a series on evaluation of scientific publications. Dtsch Arztebl Int. 2010 Aug;107(31-32):552-6. (5-page paper)

• Summary: Sample size planning is essential for robust epidemiologic research; samples that are either too small or too large are often unacceptable for clinical, methodological, and/or ethical reasons. This paper discusses the purpose of sample size calculations in trials, the need for such calculations, and the methods by which such calculations are completed. As consistent with many other resources, it is advised that such work be carried out in collaboration with an experienced statistician.

CAPER - Center for Access Policy, Evaluation and Research: Sample Size Calculations for Pragmatic Trials (Nicolae Done, June 25, 2017): 20-slide presentation.

• Summary: Contrasts calculating sample sizes using analytical methods (e.g., existing formulas with specific assumptions) vs. using simulation approaches, which, while more complicated to perform, are often better able to incorporate unique design elements. Discusses parallel cluster randomized trials - which are a common approach to randomization in pragmatic trials - and introduces the design effect (a factor that quantifies the loss of information due to correlation of data within clusters), and the intraclass correlation coefficient (ICC). Considerations related to unequal cluster sizes, as well as a statistical package (in Stata) to complete relevant power calculations are discussed. The design effect and statistical package (in Stata) for power calculations for stepped-wedge cluster trials are also described.

Rutterford C, et al. Methods for sample size determination in cluster randomized trials. Int J Epidemiol. 2015 Jun;44(3):1051-67. (17-page paper)

• Summary: Summarizes approaches for sample size calculations for cluster randomized trials*. Presents methods applicable to two-arm, parallel group, completely randomized designs, followed by approaches that incorporate deviations from this design such as: variability in cluster sizes, attrition, non-compliance, and/or the inclusion of baseline covariates or repeated measurements. Concludes with recommendations for alternative designs (e.g., stepped-wedge). *Note: Acknowledging that the decision to randomize at the cluster-level needs to be given thoughtful consideration, and that not all pragmatic trials are cluster trials, sample size calculations often become more complex in this setting. Therefore, this paper (and other resources provided below) will help trialists navigate these additional considerations when necessary. 

Hemming, K. Cluster randomized trials sample size calculator. University of Birmingham: sample size calculator.

• Summary: A Shiny App for power and sample size calculations for cluster trials. Provides calculations for parallel, parallel with baseline measures, two-period cross-over, stepped-wedge, and multiple-period cross-over designs. Sampling structure, correlation structure, cluster size variation, number of clusters, cluster size, intraclass correlation coefficient (ICC), outcome type, mean difference, standard deviation, and significance level can all be adjusted in the calculator.

National Institutes of Health (Research Methods Resources) - Sample Size Calculators (Last updated March 31, 2025): 4 sample size calculators.

• Summary: Browser-based sample size calculators for parallel group- or cluster-randomized trials (GRTs), individually randomized group-treatment (IRGT) trials, stepped wedge group- or cluster-randomized trials (SWGRTs), and group or cluster regression discontinuity designs (GRDDs).

National Cancer Institute - Division of Cancer Control & Population Sciences (Healthcare Delivery Research Program - Cluster Randomized Designs in Cancer Care Delivery Research (Last Updated January 17, 2025): "Session 4" presentations.

• Summary: Session 4 (“Sample Size and Statistical Efficiency”) provides resources for researchers to design cluster randomized trials to maximize statistical efficiency. One presentation (29-min) discusses the optimal choice of cluster size, number of clusters, and the number of crossovers, for parallel, stepped-wedge, and cross-over designs. A follow-up presentation (32-min) reviews sample size calculations for parallel cluster trials, where concepts are illustrated with worked examples. Another presentation (56-min) reviews sample size calculations for stepped-wedge trials and other multiple period cluster trial designs. A final presentation (1-hr 3-min) overviews a sample size calculator that can incorporate different design features and illustrates the implications of different design choices.

Hemming K, et al. Sample size calculations for cluster randomised controlled trials with a fixed number of clusters. BMC Med Res Methodol. 2011 Jun 30;11:102. Erratum in: BMC Med Res Methodol. 2017 Jan 19;17(1):8. (11-page paper)

• Summary: Outlines the components of sample size calculations (e.g., the required number of randomization units, detectable difference, and statistical power) for cluster trials with a fixed number of clusters. Extensions to trials with unequal cluster sizes are also discussed.

Leyrat C, et al. Practical considerations for sample size calculation for cluster randomized trials. J Epidemiol Popul Health. 2024 Feb;72(1):202198. (7-page paper)

• Summary: Standard approaches to sample size calculations are not valid for cluster trials as they underestimate the number of clusters needed for a study. This paper sets out principles for sample size calculations, including parallel-arm designs with or without a baseline period, cluster cross-over, and stepped-wedge trial designs, and provides tools to help researchers perform these calculations.

Lauer SA, et al. The effect of cluster size variability on statistical power in cluster-randomized trials. PLoS One. 2015 Apr 1;10(4):e0119074. (13-page paper)

• Summary: One of the key components to designing a successful cluster trial is calculating the necessary sample size (i.e., the number of clusters) needed to attain an acceptable level of statistical power. This paper overviews a simulation study that investigated how the statistical power of cluster trials changes with variable cluster sizes.