We have presented the Pearson r correlation coefficient as the appropriate way to describe the relationship between two variables with interval or ratio scale properties. Researchers also want to describe the strength of relationships between variables in all studies. Effect size refers to the strength of association between variables. The Pearson r correlation coefficient is one indicator of effect size; it indicates the strength of the linear association between two variables. In an experiment with two or more treatment conditions, other types of correlation coefficients can be calculated to indicate the magnitude of the effect of the independent variable on the dependent variable. For example, in our experiment on the effects of witnessing an aggressive model on children’s aggressive behavior, we compared the means of two groups. In addition to knowing the means, it is valuable to know the effect size. An effect size correlation coefficient can be calculated for the modeling and aggression experiment. In this case, the effect size correlation value is .69. As with all correlation coefficients, the values of this effect size correlation can range from 0.00 to 1.00 (we do not need to worry about the direction of relationship, so plus and minus values are not used).
The advantage of reporting effect size is that it provides us with a scale of values that is consistent across all types of studies. The values range from 0.00 to 1.00, irrespective of the variables used, the particular research design selected, or the number of participants studied. You might be wondering what correlation coefficients should be considered indicative of small, medium, and large effects. A general guide is that correlations near .15 (about .10 to .20) are considered small, those near .30 are medium, and correlations above .40 are large.
It is sometimes preferable to report the squared value of a correlation coefficient; instead of r, you will see r2. Thus, if the obtained r = .50, the reported r2 = .25.
Why transform the value of r? This reason is that the transformation changes the obtained r to a percentage. The percentage value represents the percent of variance in one variable that is accounted for by the second variable. The range of r2 values can range from 0.00 (0%) to 1.00 (100%). The r2 value is sometimes referred to as the percent of shared variance between the two variables. What does this mean, exactly? Recall the concept of variability in a set of scores—if you measured the weight of a random sample of American adults, you would observe variability in that weights would range from relatively low weights to relatively high weights. If you are studying factors that contribute to people’s weight, you would want to examine the relationship between weights and scores on the contributing variable.
One such variable might be gender: In actuality, the correlation between gender and weight is about .70 (with males weighing more than females). That means that 49% (squaring .70) of the variability in weight is accounted for by variability in gender. You have therefore explained 49% of the variability in the weights, but there is still 51% of the variability that is not accounted for. This variability might be accounted for by other variables, such as the weights of Page 257the biological mother and father, prenatal stress, diet, and exercise. In an ideal world, you could account for 100% of the variability in weights if you had enough information on all other variables that contribute to people’s weights: Each variable would make an incremental contribution until all the variability is accounted for.