Cohen's h

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:

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, and , h is defined as the difference between their arcsine transformations.[1] Namely,

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.[6]

Interpretation

Cohen[1] 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.

See also

References

  1. 1 2 3 Cohen, Jacob (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
  2. ↑ Yu, Xiaonan; et al. (2012). "The Patient Health Questionnaire-9 for measuring depressive symptoms among the general population in Hong Kong". Comprehensive Psychiatry. 53: 95–102. doi:10.1016/j.comppsych.2010.11.002.
  3. ↑ Titus, Janet C.; et al. (February 2008). "Characteristics of Youths With Hearing Loss Admitted to Substance Abuse Treatment". Journal of Deaf Studies and Deaf Education. doi:10.1093/deafed/enm068.
  4. 1 2 Reavley, Nicola J.; et al. (2012). "Stigmatising attitudes towards people with mental disorders: Changes in Australia over 8 years". Psychiatry Research. 197: 302–306. doi:10.1016/j.psychres.2012.01.011.
  5. ↑ Yap, Marie Bee Hui; et al. (2012). "Intentions and helpfulness beliefs about first aid responses for young people with mental disorders: Findings from two Australian national surveys of youth". Journal of Affective Disorders. 136: 430–442. doi:10.1016/j.jad.2011.11.006.
  6. ↑ Champely, Stephane (2015). "pwr: Basic Functions for Power Analysis".
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