Interpreting Correlations and Effect Sizes

Throughout this chapter, common statistical methods are used to report results, such as correlation coefficients and effect sizes. In addition to tests of statistical significance, correlations and effect sizes help communicate the magnitude of an observed effect. Correlation coefficients provide us with a statistical measure of the degree of association between two variables. The correlation coefficients presented in this chapter are Pearson’s correlations, ranging from -1 to 1, with higher values indicating greater consistency or agreement between ratings. Although there are several approaches to interpretation, the correlation coefficients are categorized herein as follows: absolute values lower than .20 are classified as very weak; values of .20 to .39 are considered weak; values of .40 to .59 are moderate; values of .60 to .79 are strong; and absolute values greater than or equal to .80 are very strong (Evans, 1996).

Additionally, a variety of effect sizes are presented, including Cohen’s d, Cliff’s d, and eta-squared (η²; see Cohen, 1973). Cohen’s d absolute values are measures of the size of the standardized difference between groups and are typically quantified as negligible effects if they are less than .20, small effects if they are .20 to .49, medium-sized effects if they are .50 to .79, and large effects if they are greater than or equal to .80. Guidelines for interpreting Cliff’s d absolute values (non-parametric effect size metric values) are often quantified as negligible effects if they are less than .15, a small effect if they are .15 to .32, a medium effect if they are .33 to .44, and a large effect if they are greater than or equal to .45. Effect sizes as measured by eta-squared (η²; see Cohen, 1973), a statistic that communicates the percent of variance explained, are also provided. Commonly used guidelines for interpreting η² include negligible effect sizes for values less than .01, small effect sizes for values of .01 to .05, medium effect sizes for values of .06 to .13, and large effect size for values greater than or equal to .14. Additional statistical methods and guidelines for interpretation are explained within the relevant sections of this chapter.