158 PART 4 Comparing Groups

Estimating the Sample Size You Need

for Comparing Averages

There are several ways to estimate the sample size you need in order to be able to

detect if there is a significant result on a t test or an ANOVA. (Check out Chapter 3

for a refresher on the concepts of power and sample size.)

Using formulas for manual calculation

Chapter 25 provides a set of formulas that let you estimate how many participants

you need for several kinds of t tests and ANOVAs. As with all sample-size

­calculations, you need to be prepared to specify two parameters: the effect size of

importance, which is the smallest between-group difference that’s worth knowing

about, and the amount of random variability in your data, expressed as the

within-group SD. If you plug these values into the formulas in Chapter 25, you

can calculate desired sample size.

Software and web pages

All the modern statistical programs covered in Chapter  4 provide power and

sample-size calculations for most standard statistical tests. As described in

Chapter 4, G*Power is menu-driven, and can be used for sample size calculations

for many tests, including t tests and ANOVAs. If you are using G*Power, to

estimate sample size for t tests, choose t tests from the test family drop-down

menu, and for ANOVA, choose F tests. Then, from the statistical test drop-down

menu, choose the test you plan to use and set type of power analysis to “A priori:

Compute required sample size – given α, power, and effect size.” Then enter the

parameters and click determine to calculate the sample size.

In terms of web pages, the website https://statpages.info lists several dozen

web pages that perform power and sample-size calculations for t tests and

ANOVAs.