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Introduction to Power Analysis

Introduction to Power Analysis
Two-Group Studies

December 2017 | 160 pages | SAGE Publications, Inc

Introduction to Power Analysis: Two-Group Studies provides readers with the background, examples, and explanation they need to read technical papers and materials that include complex power analyses.  This clear and accessible guide explains the components of test statistics and their sampling distributions, and author Eric Hedberg walks the reader through the simple and complex considerations of this research question. Filled with graphics and examples, the reader is taken on a tour of power analyses from covariates to clusters, seeing how the complicated task of comparing two groups, and the power analysis, can be made easy.

Chapter 1: The what, why, and when of power analysis
What is statistical power?

Why should power be a consideration when planning studies?

When should you perform a power analysis?

Significance and Effect 8

What do you need to know to perform a power analysis?

The structure of the volume

Chapter 2: Statistical distributions
Normally distributed random variables

The x^2 distribution

The t distribution

The F distribution

F to t

Chapter 3: General topics in hypothesis testing and power analysis when the population standard deviation is known: the case of two group means
The difference in means as a normally distributed random variable when the population standard deviation is known

Hypothesis testing with the difference between two group means when the population standard deviation is known

Power analysis for testing the difference between two group means when the population standard deviation is known

Scale-free parameters

Balance or unbalanced?

Types of power analyses

Power tables

Chapter 4: The difference between two groups in simple random samples where the population standard deviation must be estimated
Data generating process

Testing the difference between group means with samples

Power analysis for samples without covariates

Chapter 5: Using covariates when testing the difference in sample group means for balanced designs
Example analysis

Tests employing a covariate (ANCOVA) with balanced samples

Power analysis with a covariate correlated with the treatment indicator

Power analysis with a covariate uncorrelated to the treatment indicator

Chapter 6: Multilevel Models I: Testing the difference in group means in two-level cluster randomized trials
Example data

Understanding the single level test as an ANOVA

The hierarchical mixed model for cluster randomized trials

Power parameters for cluster randomized trials

Example analysis of a cluster randomized trial

Power analyses for cluster randomized trials

Chapter 7: Multilevel Models II: Testing the difference in group means in two-level multisite randomized trials
Power parameters for multisite randomized trials

Example analysis of a multisite randomized trial

Power analyses for multisite randomized trails

Chapter 8: Reasonable assumptions
Power analyses are arguments

Strategies for using the literature to make reasonable assumptions

Chapter 9: Writing about power
What to include


Chapter 10: Conclusions, further reading, and regression
The case study of comparing two groups

Further reading

Observational regression



Student Study Site
The open-access Student Study Site includes example power analyses using the major software packages (SPSS, Stata, and R), complete with code and output.

Introduction to Power Analysis provides detailed coverage of the topic in a succinct and concise way. Graduate students and others (including faculty who are also researchers) can benefit from this resource as it outlines the steps to conduct and evaluate power analysis to produce rigorous quantitative research in the social sciences, as well as why power analysis and effects are important to understand and apply in research.”

Stephanie Jones
Texas Tech University

“Although there are a number of software programs available for power analysis, this volume teaches the reader how to employ power analysis using a popular software program (R) that can also be used to perform the desired statistical analyses on the data.”

Leslie Echols
Missouri State University
Key features


  • Examples for each statistical expression help readers understand complex formulas
  • A chapter on how to use the literature for power analysis walks readers through the process of making good assumptions
  • A chapter on how to write about power analysis offers 7 key points on what needs to be included in a power analysis

For instructors

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