Correlation and Regression
There is a clear link between correlation and regression analysis and the broader topic of power analysis, because both are concerned fundamentally with effect size (ES) values. Throughout this book, we have used 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 that is made when testing the null hypothesis-i.e., forgetting to examine and report ES measures. Correlations are ES measures.