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Each sample variance is weighted by its degrees of freedom, the weighted variances are averaged, and the square root returns the original measurement units. This is the conventional equal-variance pooled estimator used in Cohen’s d. Both groups require more than one observation for the displayed sample-variance calculation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| s_p | Pooled standard deviation |
| n_1 | First sample size |
| n_2 | Second sample size |
| s_1 | First sample standard deviation |
| s_2 | Second sample standard deviation |
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Original context
Read the surrounding source passage
\textbf{Cohen's $d$ Calculation:}
\begin{equation}
d = \frac{\bar{x}_2 - \bar{x}_1}{s_p}
\end{equation}
where $s_p = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}$.
For our data:
\begin{align}
\bar{x}_1 &= 0.2499, \quad s_1 = 0.0001, \quad n_1 = 1000 \\
\bar{x}_2 &= 0.9115, \quad s_2 = 0.0600, \quad n_2 = 1000
\end{align}Exact original notation
s_p = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}