# Mende Davis and Mei-kuang Chen on Estimating Power and Sample Size

Hi, we are Mende Davis (assistant research professor) and Mei-kuang Chen (advanced graduate student) in the department of Psychology at the University of Arizona. We are also members of the Evaluation Group for Analysis of Data (EGAD) led by Lee Sechrest. G*power is a useful tool to estimate minimum sample size or possible power of a potential study. In our own work as researchers applying for numerous grants, G*power has been a handy tool.

Hot Tip: An evaluation without enough cases may not be able to answer the research questions. You don’t want to be in the position of telling stakeholders that the study was only powered to detect a real difference 15% of the time. Power analysis is used to estimate the number of cases needed to detect a true difference if it exists. Three things are needed for a run-of-the-mill power analysis; alpha (probability of committing a type I error, i.e., rejecting a “true” null hypothesis), beta (probability of committing a type II error, i.e., accepting a “false” null hypothesis), and the expected effect size. Alpha is the familiar ‘type I error rate’ that is often set at .05 (p=.05, meaning you are willing to accept a false positive one time out of twenty). Beta is related to the value of statistical power (power= 1- beta) that you select, which is often set at .80. This means you want to be able to detect a real difference 80% of the time. The effect size is the strength of the relationship between two variables (e.g., the amount of change you expect in your outcome variable). Effect sizes are usually reported in standardized units, such as r, f2, or odds-ratios. Pilot studies and the literature can help us make an educated guess about the effect size. Checking the literature for an effect size can be a real eye opener. With the statistical analysis to be used (e.g., t-test, or regression equation), plus the levels of alpha, beta, and the estimated effect size at hand, you can use G*power to estimate the minimum sample size. If you have the information about the available sample size instead of the effect size, G*power can tell you how much statistical power you would have in your study.

Rad Source: G*power is free. Where can you get G*power? The newest G*power 3 can be obtained at http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/ and the G*Power 2 manual will still be useful for using G*power 3. It can be found at http://bit.ly/GPower2Manual.

Rad Source: The calculating of power and required sample size depends on which statistical tool you will use in your study. Some knowledge about power analysis will be helpful for evaluators: http://www.statsoft.com/textbook/power-analysis/

References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd edition). Hillsdale, NJ: Erlbaum.

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