Cohen g
Introduction
Cohen g is an effect size measure if you have a single binary variable, and performed for example a one-sample binomial (Rosnow & Rosenthal, 2003), score, or Wald test.
Cohen g is perhaps the most simple effect size there is. It is simply the difference between the sample proportion and 0.5 (Cohen, 1988, p. 147). It can therefor only be used, if indeed for the test the assumption about the population was, that the proportion was 0.5.
Obtaining the Measure
with Flowgorithm
A basic implementation for Cohen g is shown in the flowchart in figure 1
Figure 2
Flowgorithm for Cohen g
It takes as input the frequency of one of the categories (k) and the sample size (n).
Flowgorithm file: ES - Cohen g.fprg.
with R (Studio)
with stikpetR
Jupyter Notebook from video ES - Cohen g (R).ipynb.
without stikpetR
R script from video: binary - effect sizes.R.
Datafile used in video: StudentStatistics.sav
with SPSS
Datafile used in video: StudentStatistics.sav
Online calculator
Enter the number of cases of the first category, then the total sample size:
Manually (using Formula)
Given a sample proportion (p) and the expected proportion in the population (π), the formula for Cohen's g will be:
\(g=p-\pi\)
The sample proportion in the example was 0.26 and the expected proportion was 0.50, in the example this therefor gives:
\(g=0.26-0.50=-0.24\)
Often the absolute value is used (the so-called nondirectional Cohen's g):
\(g=|0.26-0.50|=|-0.24|=0.24\)
Interpretation
A Cohen g of for example 0.1 would mean that in the sample the proportion was either 0.4 (40%) or 0.6 (60%).
Cohen g can range from -0.5 to 0.5, and often the absolute value is taken, which make it range from 0 to 0.5. Cohen provided some rule of thumb to interpret this, shown in Table 1.
| |g| | Interpretation |
|---|---|
| 0.00 < 0.05 | Negligible |
| 0.05 < 0.15 | Small |
| 0.15 < 0.25 | Medium |
| 0.25 or more | Large |
| Note: Adapted from Statistical power analysis for the behavioral sciences (2nd ed., pp. 147-149) by J. Cohen, 1988, L. Erlbaum Associates. | |
Alternatives
Alternatives for this effect size could be Cohen h', or the Alternative Ratio.
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