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Samples, Trial Size

Effect size is a measure of the strength of the relationship between two variables. In scientific experiments, it is often useful to know not only whether an experiment has a statistically significant effect, but also the size of any observed effects. more...

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In practical situations, effect sizes are helpful for making decisions. Effect size measures are the common currency of meta-analysis studies that summarise the findings from a specific area of research.

Summary

The concept of effect size appears in everyday language. For example, a weight loss program may boast that it leads to an average weight loss of 30 pounds. In this case, 30 pounds is an indicator of the claimed effect size. Another example is that a tutoring program may claim that it raises school performance by one letter grade. This grade increase is the claimed effect size of the program.

An effect size is best explained through an example: if you had no previous contact with humans, and one day visited England, how long would it take you to realise that, on average, men are taller than women there? The answer relates to the effect size of the difference in average height between men and women. The larger the effect size, the easier it is to see that men are taller. If the height difference were small, then it would require knowing the heights of many men and women to notice that (on average) men are taller than women. This example is demonstrated further below.

In inferential statistics, an effect size is the size of a statistically significant difference. Effect sizes, along with N and critical alpha determine power in statistical hypothesis testing. In meta-analysis, effect sizes are used as a common measure which can be calculated for different studies and then combined into overall analyses.

Types

Pearson r correlation

Pearson's r correlation is one of the most widely used effect sizes. It can be used when the data are continuous or binary, thus the Pearson r is arguably the most versatile effect size. This was the first important effect size to be developed in statistics, and it was introduced by Karl Pearson. Pearson's r can vary in magnitude from -1 to 1, with -1 indicating a perfect negative relationship, 1 indicating a perfect positive relationship, and 0 indicating no relationship between two variables.

Another often used measure of the size of the relationship between two variables is the square of r, often referred to as "r-squared" or the coefficient of determination. It is a measure of the proportion of variance shared by the two variables and varies from 0 to 1. An r² of 0.21 would suggest that 21% of the variance is shared by these two variables.