Power Estimates in the Presence of a Covariate and Measurement Error

The statistical power of a test of significance for the difference among means is dependent upon a number of factors, among them the presence of a covariate, which often serves to increase power, as well as measurement error, which reduces power. Formulas are provided for adjusting Cohen's (1977) f value for these two sources of variability. These adjusted f values can then be used with Cohen's power tables. An example of the use of these formulas in the planning stage of a study is given, followed by a description of the complex nature of the relationship between power and covariance and measurement error.