Reported effect size based on the incorrect pooled deviation

Read the equation

Dividing the rounded mean difference 0.6616 by the source’s incorrect 0.0300 yields the reported value near 22.06. Using the correctly pooled standard deviation changes the standardized effect substantially. The recovered CSV audit gives d≈15.5983482 from the unrounded sample summaries.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

• The larger printed value inherits the preceding pooled-standard-deviation error.

Original context

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
\end{equation}

\textbf{t-statistic Calculation:}
\begin{equation}
t = \frac{\bar{x}_2 - \bar{x}_1}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} = \frac{0.6616}{\sqrt{\frac{0.0001^2}{1000} + \frac{0.0600^2}{1000}}} = 348.79
\end{equation}

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

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