Introduction
Let’s say you know how to test hypotheses and interpret p values. Where do you go from there? Oftentimes, in order to improve the quality of an academic paper or thesis, you need to know how to generate and interpret effect sizes. The best way to understand effect sizes is through examples, so let’s walk you through one.
Let’s say you’re writing an academic paper on whether men are taller than women. You collect data from 15 men and 15 women in your class as part of this academic paper. We can now discuss what effect sizes are, how to generate them, and how to interpret them.
Findings
You have just conducted an independent samples t-test to determine whether men are taller than women. Your readout looks like this:
We see that women’s average height, in centimeters, is 151.42, with a standard deviation of 23.08. Men’s average height, also in centimeters, is 164.65, with a standard deviation of 20.46. You rejected the null at p < .10 and concluded that the men in your sample were taller than the women.
Effect Size
Now your statistical program (Stata, in this case) generated an effect size for you. That effect size is Cohen’s d, which is the most frequent measure of effect size. Cohen’s d is calculated on the basis of standard deviations, but the easiest way to understand it is as a real-world measure of what counts as ‘small’ or ‘big’ differences. Here, for example, d = -0.61, so women’s lower height as compared to men, on the basis of your data, counts as a medium-sized difference.
Conclusion
Statistical significance is extremely important, but, oftentimes, adding and interpreting an effect size adds an important dimension to academic papers that include statistical findings. Cohen’s d is both a common and an easily interpreted measure of effect size.
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