Sample Size Requirements for Accurate Estimation of Squared Semi-Partial Correlation Coefficients

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Abstract
The increase in the squared multiple correlation coefficient associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. An alternative measure of importance is the difference in the adjusted squared multiple correlation coefficients. Both estimate the difference in the population squared multiple correlation coefficients (Δρ2), a quantity also called a squared semi-partial correlation coefficient. In planning a study that will use regression analysis, it is important to select a sample size that will allow Δρ2 to be estimated with adequate accuracy. Results showed that the sample size necessary for adequate accuracy depend strongly on three factors: (a) the population squared multiple correlation coefficient (ρ2), (b) the population increase in ρ2, and (c) the desired degree of accuracy. The number of predictors had a small effect on the required sample size. Tables to facilitate sample size selection were presented.