Effect Size

“Statistically significant” results can be of trivial importance in the real world. Because of this, in recent years, many researchers and students have been required to report the effect size in addition to the significance level of their results.

Definition

Effect size is a measurement of how important an obtained effect is in reality, given that we have rejected the null hypothesis (i.e., obtained a significant result). Effect size can be thought of as the number of standard deviation units of difference. But if you don’t understand this, don’t worry about it, and please keep reading!

Note. Effect size is used in two ways. When planning your study, you use an estimate of the typical effect size in similar studies in your field to determine the required sample size for your study. The estimated effect size should represent the smallest effect that would be important for you to detect in your study. After you carry out the study, you calculate what its actual effect size was.

Tip

  • A free trial of the versatile effect size calculator Power and Precision is available at http://www.power-analysis.com.

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Example: Effect Size for a Regression Analysis

A simple regression analysis had an R2 of .20. For a simple regression, the effect size is f2 = R2 / (1 – R2). Thus, the effect size is f2= .25. Using Cohen’s (1988) conventions, this is a medium-to-large effect.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum.

For other effect size reports on this site, see Regression, t-Test and ANOVA.

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