We can also talk about this circle as showing 100% of the variance (how much people in the study differ from each other) in self-esteem; if we could explain 100% of the variance, we could predict the exact self-esteem everyone in the study has. So when a study reports a statistically significant association between having a sister and self-esteem, that means that having a sister explains more than 0% of the variance in self-esteem. In order to talk about Cohen’s d, we need to think about our example in a slightly different way.
Effect sizes give you some information, like you might expect, about the size of the effect, which is much more useful than simply knowing that the effect is different from 0. When you know something about the effect size, you can understand that the effect of having a sister may not be able to explain everything about self-esteem (hence the counter-examples you can think of) but it can explain something, which makes it useful. Let’s imagine that someone does a study of self-esteem and that all of the self-esteem data from the study is represented in the circle below.
Let me say right off that no study in psychology ever does this; if you find a study that comes even close, be very, very suspicious. If a study reports an R-Squared of .5, that means that 50% of the total variance in self-esteem is explained by having a sister (shown in red below).


For example, if a study says that when trying to explain self-esteem from having a sister, parental relationship, and body image, they found an R-Squared of .62, that means that 62% of the variance in self-esteem was explained by a combination of having a sister, parental relationship, and body image.
It takes the literal difference between the two groups (groupa self-esteem – groupb self-esteem) and then divides it by the standard deviation of the data (a measure of how much the data varies). With regards to the sisters and self-esteem example, this means that the relationship between having a sister and self-esteem is different from 0 at at least 95% certainty.
Remember from before that knowing that there is a statistically significant difference in self-esteem between the two groups means only that the difference between the two groups is different from 0.
It’s easiest to explain why the difference is divided by the standard deviation using an example. She did her undergraduate degree at Yale University where she became interested in deconstructionism, the self, and the nature of “truth.” At UCLA, she does research on the aspects of our social environment that impact the way we interpret our experiences and think about ourselves. Because there is so much that goes into self-esteem, or any other psychological construct, for that matter, that it would be very difficult to capture it all in one study.


That could mean that the self-esteem score in group a is 5 and in group b is 4.5, or that the self-esteem score in group a is 5 and in group b is 2.
For example, part of self-esteem could be explained by having a sister, part of it by how you happened to feel that morning, part of it by your relationship with your parents, part of it by how the experimenter looked at you when you first came in, and so on, so on. Mariana is writing for Psychology in Action because she loves science, and she wants everyone in the world to know how to appreciate and love science, too.



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