Glass Delta
Explanation
Glass Delta is an effect size measure that is commonly used when comparing a mean of a 'control group' vs. 'treatment group' situation. Hedges improved on this for other situations. Glass delta, unlike Cohen d, does not assume the variances to be equal.
Obtaining the Measure
with Excel
Excel file: ES - Glass Delta (E).xlsm
with stikpetE
To Be Made
without stikpetE
To Be Made
with Python
Jupyter Notebook: ES - Glass Delta (P).ipynb
with stikpetP
To Be Made
without stikpetP
To Be Made
with R (Studio)
Jupyter Notebook: ES - Glass Delta (R).ipynb
with stikpetR
To Be Made
without stikpetR
To Be Made
manually (formulas)
The formula is (Glass, 1976, p. 6):
\(\delta = \frac{\bar{x}_1 - \bar{x}_2}{s_2}\)
With:
\(s_2 = \sqrt{\frac{\sum_{i=1}^{n_2} \left(x_{2,i} - \bar{x}_2\right)^2}{n_2 - 1}}\)
\(\bar{x}_i = \frac{\sum_{j=1}^{n_i} x_{i,j}}{n_i}\)
*Symbols used:*
- \(x_{i,j}\), the j-th score in category i
- \(n_i\), the number of scores in category i
Interpretation
Unfortunately, I've been unable to find any rule-of-thumb specifically for Glass Delta, but most likely the ones from Cohen d should be a decent alternative.
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