Power Analysis for Logistic Regression: Examples for
Dissertation Students & Researchers
It is hoped that a desired sample size of at least 150 will be achieved for the study. A power analysis was conducted to determine the number of participants needed in this study (Cohen, 1988). The primary model will be examined using logistic regression. The model will test whether the independent variables (the Multidimensional Health Locus of Control subscales: Internal, Chance, Powerful-Others and Doctors) predict the dependent/criterion variable (attendance in a cardiac support group, Yes/No). The α for the test of this model will be set at .05. To achieve power of .80 and a medium effect size a sample size of 300 is required to detect a significant model.
For logistic regression of a binary dependent variable using several continuous, normally distributed independent variables, at 80% power at a 0.05 significance level, to detect a change in Prob (Y = 1) from the value of 0.050 at the mean of X to 0.100 when X is increased to one standard deviation above the mean, requires a sample size of 150. This change corresponds to an odds ratio of 2.61.
You may want to cite this reference: Hsieh, F.Y., Block, D.A., and Larsen, M.D. (1998). A Simple Method of Sample Size Calculation for Linear and Logistic Regression. Statistics in Medicine, Volume 17, pages 1623-1634.
||Power is the probability of rejecting a false null hypothesis. It should be close to one.
||N is the size of the sample drawn from the population.
||P0 is the response probability at the mean of X.
||P1 is the response probability when X is increased to one standard deviation above the mean.
||Odds Ratio is the odds ratio when P1 is on top. That is, it is [P1/(1-P1)]/[P0/(1-P0)].
||R-Squared is the R² achieved when X is regressed on the other independent variables in the regression.
||Alpha is the probability of rejecting a true null hypothesis.
||Beta is the probability of accepting a false null hypothesis.
Conducting a logistic regression with other binary independent variables will require you to have almost 1000 participants to achieve 80% power. I imagine it would be difficult to achieve this for your dissertation. For this reason, only mention the power analysis above, requiring 300 participants for your four primary independent variables of interest.