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Section 21.4 Summary of Procedures for Paired Differences
Test of \(H_0: \mu_d = 0\) .
Randomization test (randomizing the sign of the difference)
Paired t -test (Valid with
\(n > 30\) or normal population of differences)
Standardized (test) statistic:
\begin{equation*}
t_0 = \frac{\bar{x}_{diff} - \mu_0}{s_{diff}/\sqrt{n}}
\end{equation*}
Degrees of freedom =
\(n - 1\)
t -Confidence interval for \(\mu_d\) .
\begin{equation*}
\bar{x}_{diff} \pm t_{n-1}^* \times \frac{s_{diff}}{\sqrt{n}}
\end{equation*}
Valid with
\(n > 30\) or normal population of differences
Technology.
R: t.test(..., paired=TRUE)
JMP: Analyze > Specialized Modeling > Matched Pairs
The paired
t -test is equivalent to a one-sample
t -test on the differences. Also keep in mind that even if the original distributions are skewed, the differences could still be more normally distributed.
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