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This statistic divides the difference between the two sample means by a pooled within-group standard deviation. It expresses the size of a difference in standard-deviation units rather than the probability that a hypothesis is true. For serially correlated time samples from one intervention, its descriptive arithmetic can be computed while the independent-group interpretation needs additional care.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| d | Standardized mean difference |
| x_bar_1 | First sample mean |
| x_bar_2 | Second sample mean |
| s_p | Pooled standard deviation |
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Original context
Read the surrounding source passage
\textbf{Consciousness Jump Analysis:}
\begin{itemize}
\item Test: Welch's two-sample t-test (unequal variances)
\item Effect size: Cohen's $d = (\mu_2 - \mu_1) / s_{pooled}$
\item Significance threshold: $\alpha = 0.05$ (two-tailed)
\end{itemize}
\textbf{Stability Analysis:}
\begin{itemize}
\item Descriptive statistics: mean, SD, min, max, range
\item Trend test: Mann-Kendall for monotonic trendExact original notation
d = (\mu_2 - \mu_1) / s_{pooled}