Introduction to effect size

¶ … Size

In the field of statistics, the term effect size is used to refer to the degree of relationship between two variables. Quite simply, it is the size of the effect that one thing has on another. There are many different examples of effect size that we encounter in our daily lives; it is a comparison and judgment we are so used to main that it appears like second nature. Think about the last time you saw a commercial for a product that advertised itself as "30% more effective than the leading brand," or made some similar "more-than" claim. This is a very direct and open use of effect size -- or at least claimed effect size -- to make what the advertisers want you to believe is a mathematical point. They are basically saying that their product, whatever it is, has a bugger effect size on whatever that products is intended to do. For instance, if a commercial for Brand X weight-gain powder for body builders claimed it was 20% more effective than Brand Y, they would be saying that their powder makes your muscles grow 20% more than the other powder -- that their powder has a larger effect size on muscles.

Though understanding effect size is relatively simple, understanding the mathematical formula behind it can be a little trickier. There are actually many different ways to measure effect size, some of them more reliable for certain cases than others. In general, effect size applies to the meta-analysis aspects of statistics. This means it is used to analyze the analysis, in a way -- while other data is analyzed to establish a correlation, effect size is used to measure the strength or degree of that correlation -- or rather, effect size is the measure of that correlation. According to Professor Becker's overview of effect size on the University of Colorado website (2000), one of the most commonly used measures of effect size is Cohen's d (section II). The "d" stands for difference, and this measure is used to measure effect size between two independent groups of data points. The formula for calculating Cohen's d is (M1-M2)/s, where M1 is the mean of the first set of data points, M2 is the mean of the second set, and s is the standard deviation of either group. The larger the value of "d," the larger the effect size. This means that the larger the value of "d" gets, the stronger the correlation between the two data sets is.

There are many uses for effect size, in practically any field imaginable. We have already seen how they are used in advertising, although this might not be the best mathematical example. We do not have to look very far to find such an example, however. Professor Becker at the University of Colorado is actually a psychologist, and his website (2000) explains effect size using practical examples from various psychological and medical research. The efficacy of medicines and other treatments, for example, is a very important use of effect size, it can determine the suitability of risks associated with a medicine compared to its likely benefits, and give a mathematical model for when certain patients should take that medication, and when the risks outweigh the correlative benefits.