Biostatistics Guide: Power Analysis & Sample Size

Welcome to Power Analysis & Sample Size Resources!

This guide provides resources related to power analysis and sample size calculations that are applicable to a broad audience from a clinical researcher looking for introductory education material to a statistician looking for a specialized calculator. Resources include:

• Introductory readings and references
• A statistics handbook to help grant applicants avoid statistical pitfalls in their application
• How-to guides with illustrated examples
• Tools to select the correct statistical test and effect size measurement for a power calculation
• Validated power calculators, free and for purchase
• Articles that discuss post-hoc power analysis (i.e., analyses that are done after the study has been completed)

Introductory Reference Material

Fundamentals

• Introduction to Power Analysis UCLA offers this comprehensive introduction on conducting power analyses. The article includes relevant definitions, what you need to know to do a power analysis, obtaining the necessary numbers to do a power analysis, the factors that affect power, and cautions about small sample sizes.    
• Quick Start Guide to Power Analysis & Sample Size WUSM Biostatistics Consulting Service offers this quick start guide. These slides describe the basic mechanics of power, the importance of sample size calculations, and walks through each step from identifying your outcome(s) to writing a sample size justification.
• Power Analysis and Sample Size Calculations Lecture UC-Davis offers this excellent introduction to get you started with power computations. These slides with one-hour video describe the importance of sample size calculations, where calculations fit in study planning, what is needed to calculate sample size, how to conduct simple calculations, and when to seek help from a statistician.
• Statistics Guide for Research Grant Applicants (see Section D) St. George’s Hospital Medical School (London) has an excellent statistics handbook intended to help research grant applicants avoid statistical pitfalls in their application. The handbook should make grant applicants more aware of the questions to ask and the information to take along to a statistical consultation and in addition, help them understand any statistical advice given. Section D discusses the importance of sample size calculations, the information required to calculate sample size, an explanation of related statistical terms, the importance of consistency with aims and analysis, and examples (single proportion, comparison of two means, and comparison of two proportions). There is an interactive online version and a PDF version of the guide.

How-To Guides and Examples 

• Power and Sample Size How-To Guides (select ‘Power and Sample Size Calculations’) UC-Davis offers several how-to guides with illustrated examples using freely available software to estimate sample size for several statistical procedures including t-tests, ANOVA, correlation, equivalence tests, non-inferiority tests, logistic regression, and survival. On the webpage, select ‘Power and Sample Size Calculations’.       
• Examples of Simple Power Analyses (scroll down to the section ‘Power Analyses’) UCLA offers power analysis examples using G*Power, Stata, SAS and R. Power analysis examples include t-tests, proportions, ANOVA, and multiple regression. On the webpage, scroll down to the section ‘Power Analyses’.

Tools to Select the Right Statistical Test and Effect Size Measurement

• Choosing a Statistical Test GraphPad offers this tool for choosing the correct statistical test based upon the nature of the data (i.e., interval and normally distributed, rank/score/not normally distributed, binomial, survival time) and the analysis goal. Includes additional discussion of parametric vs. nonparametric tests, one vs. two-sided p-values, paired vs. unpaired tests, and regression vs. correlation.
• Choosing the Correct Statistical Test UCLA offers general guidelines for choosing the correct statistical test based upon the nature of the outcome variable (i.e., interval and normally distributed, ordinal, categorical) and independent variable(s).
• Tool to Select the Correct Effect Size Measurement WUSM Department of Otolaryngology offers this web tool to help you select the appropriate effect size measurement for planning and reporting the results of your research.