ABSTRACT
There is a clear link between correlation and regression analysis and the broader topic of power analysis because both are concerned fundamentally with effect sizes (ES). Throughout this book, we use the percentage of variance in the dependent variable that is explained by treatments, interventions, or other variables (i.e., PV) as our main ES measure. If you square the correlation between two variables, X and Y, what you get is PV (i.e., the proportion of variance in Y that is explained by X). Similarly, in multiple regression, where several X variables are used to predict scores on Y, the squared multiple correlation coefficient (i.e., R2) is a measure of proportion of the variance of Y that is explained. One of the substantial advantages of framing statistical analyses under the general linear model in terms of correlation (e.g., both t-tests and analyses of variance are easily performed using correlational methods) is that it is virtually impossible to make one of the most common mistakes when testing the null hypothesis-i.e., forgetting to examine and report effect size measures. Correlations are effect size measures.
