The power of a paired t-test with a covariate

Many researchers employ the paired t-test to evaluate the mean difference between matched data points. Unfortunately, in many cases this test in inefficient. This paper reviews how to increase the precision of this test through using the mean centered independent variable x, which is familiar to researchers that use analysis of covariance (ANCOVA). We add to the literature by demonstrating how to employ these gains in efficiency as a factor for use in finding the statistical power of the test. The key parameters for this factor are the correlation between the two measures and the variance ratio of the dependent measure on the predictor. The paper then demonstrates how to compute the gains in efficiency a priori to amend the power computations for the traditional paired t-test. We include an example analysis from a recent intervention, Families Preparing the New Generation (Familias Preparando la Nueva Generación). Finally, we conclude with an analysis of extant data to derive reasonable parameter values.