Introduction to Power Analysis

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