Samples, Trial Size

In statistics, 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 summarize 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 many people would you need to see before you realize 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 helps to determine whether a statistically significant difference is a difference of practical concern. In other words, given a sufficiently large sample size, it is always possible to show that there is a difference between two means being compared out to some decimal position. The effects size helps us to know whether the difference observed is a difference that matters. Effect size, along with sample size and critical significance level α, and power in statistical hypothesis testing are related, and any one of these values can be determined given the others. In meta-analysis, effect sizes are used as a common measure that can be calculated for different studies and then combined into overall analyses.

The term effect size is most commonly used to described standardized measures of effect (e.g., r, Cohen's d, odds ratio, etc.). However, unstandardized measures (e.g., the raw difference between group means, unstandardized regression coefficients, etc.) can equally be effect size measures. Standardized effect size measures are typically used when the metrics of variables being studied do not have intrinsic meaning to the reader (e.g., a score on a personality test on an arbitrary scale), or when results from multiple studies are being combined when some or all of the studies use different scales. Some students mistook the recommendation of Wilkinson & APA Task Force on Statistical Inference (1999, p. 599)--Always present effect sizes for primary outcomes--as that reporting standardized measures of effect like Cohen's d is the default requirement. Actually, just following the sentence the authors added that -- If the units of measurement are meaningful on a practical level (e.g., number of cigarettes smoked per day), then we usually prefer an unstandardized measure (regression coefficient or mean difference) to a standardized measure (r or d).

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