## Sunday, April 12, 2009

### Effect Size

Effect size (ES) is a name given to a family of indices that measure the magnitude of a treatment effect. Unlike significance tests, these indices are independent of sample size. Effect size has been frequently linked to the power analysis (or sample size calculation) and Meta analysis.

The concept of effect size seems to come from Cohen's book "Statistical Power Analysis for the Behavioral Sciences". Effect size is not just for the continuous variable, it could also be for rates and proportions, and other type of data.

The following weblinks provide good summaries on effect size:

Recently, I came across a paper that described the use of effect size as Benchmarks for Interpreting Change - one of many ways to determine the sensitivity of the measurement and subsequently the minimal clinically important difference (MCID) or minimal important difference (MID).

In a paper by Kazis LE, Anderson JJ, Meenan RF (Effect sizes for interpreting changes in health status. Med Care 1989;27:S178-S189), they described the following:

"Effect size as used in this study is calcu-lated by taking the difference between the means before treatment and after treatment and dividing it by the standard deviation of the same measure before treatment. This method of calculating effect sizes can be expressed mathematically as ES = (mi - m2)/sl, where m, is the pretreatment mean, m2 the posttreatment mean, and s, the pretreatment standard deviation. In this instance the before-treatment scores are used as a proxy for control group scores. This approach treats the effect size as a standard measure of change in a "before and after study" context. We are interested in the magnitude or size of the change rather than statistical significance, so we use the standard deviation at baseline rather than the standard deviation of the differ-ence between the means.8 Effect sizes can be used to translate changes in health status into a standard unit of measurement that will provide a clearer interpretation of the results. This can be ac-complished by using effect sizes as bench-marks for measuring changes or as a means for taking comparisons between measures in the same study or across studies. "

Here the effect size is not to compare the two treatmetn groups, rather compare the differences pre and post. The formula for effect size can be explicitly rewritten to represent the mean change from pre treatment to the post treatment divided by the standard deviation of the baseline measures (effect size = (mui - mu0/SDmu0; mui = mean value of the post-baseline measure; mu0 = mean value at baseline).

If we calculate the effect size for both treatment group and placebo group, we should expect a very small effect size for Placebo group and a rather large effect size for treatment group - an indicator of a good measurement.