Stata's power
command performs power and sample-size analysis (PSS). Its features now include PSS for linear regression.
As with all other power
methods, the new methods allow you to specify multiple values of parameters and to automatically produce tabular and graphical results.
Stata's power
command provides three new PSS methods for linear regression.
power oneslope
performs PSS for a slope test in a simple linear regression. It computes one of the sample size, power, or target slope given the other two and other study parameters. See [PSS] power oneslope.
power rsquared
performs PSS for an R^{2} test in a multiple linear regression. An R^{2} test is an F test for the coefficient of determination (R^{2}). The test can be used to test the significance of all the coefficients, or it can be used to test a subset of them. In both cases power rsquared
computes one of the sample size, power, or target R^{2} given the other two and other study parameters. See [PSS] power rsquared.
power
pcorr performs PSS for a partial-correlation test in a multiple linear regression. A partial-correlation test is an F test of the squared partial multiple correlation coefficient. The command computes one of the sample size, power, or target squared partial-correlation coefficient given the other two and other study parameters. See [PSS] power pcorr.
Here, we demonstrate PSS for an R^{2} test of a subset of coefficients in a multiple linear regression.
Consider a test of the significance of two covariates in a multiple linear regression adjusting for three other covariates. We will call the two covariates the tested covariates and the three others control covariates. The reduced model with the control covariates has an R^{2} of 0.1, and the full model with all five covariates has an R^{2} of 0.2. We want to compute the required sample size for the two-sided R^{2} test to achieve 80% power with a 5% significance level—power rsquared
defaults.
We need 81 observations.
Suppose that we want to investigate the impact of the effect size on the required sample size. We plot below the sample-size curve as a function of the R^{2} values of the full model.
As the R^{2} of the full model increases, the required sample size decreases. When the R^{2} is closer to 0.2, the curve is steeper.