In statistics, Cohen's h, popularized by Jacob Cohen, is a measure of distance between two proportions or probabilities. Cohen's h has several related uses:
Contents
When measuring differences between proportions, Cohen's h can be used in conjunction with hypothesis testing. A "statistically significant" difference between two proportions is understood to mean that, given the data, it is likely that there is a difference in the population proportions. However, this difference might be too small to be meaningful—the statistically significant result does not tell us the size of the difference. Cohen's h, on the other hand, quantifies the size of the difference, allowing us to decide if the difference is meaningful.
Uses
Researchers have used Cohen's h as follows.
Calculation
Given a probability or proportion p, between 0 and 1, its "arcsine transformation" is
Given two proportions,
This is also sometimes called "directional h" because, in addition to showing the magnitude of the difference, it shows which of the two proportions is greater.
Often, researchers mean "nondirectional h", which is just the absolute value of the directional h:
In R, Cohen's h can be calculated using the ES.h
function in the pwr
package.
Interpretation
Cohen provides the following descriptive interpretations of h as a rule of thumb:
Cohen cautions that:
As before, the reader is counseled to avoid the use of these conventions, if he can, in favor of exact values provided by theory or experience in the specific area in which he is working.
Nevertheless, many researchers do use these conventions as given.