Rounded before-and-after sample summaries

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This block records the manuscript’s rounded means, standard deviations, and equal sample sizes. The before mean is near 0.25 and the after mean near 0.912. These numbers summarize recorded samples; they do not reconcile the mismatch between the proposed reciprocal-variance score and the low baseline.

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Original context

\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}

\begin{equation}
s_p = \sqrt{\frac{999 \cdot 0.0001^2 + 999 \cdot 0.0600^2}{1998}} = 0.0300
\end{equation}

\begin{equation}
d = \frac{0.9115 - 0.2499}{0.0300} = 22.06

\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

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