Hi
@dtammerz Those are
solutions to the maximum difference (hopefully the "⇒" is not throwing you off; "⇒" signifies "implies")
The denominator (i.e., the square root) is the
standard deviation (aka, standard error) of the difference between correlated means and is equal to sqrt[to 4 + 1 - 2*0.3*sqrt(4)*sqrt(1)] = 0.398 (shown in exhibit).
So we really just have
T = |D|/ σ(diff); i.e., the test-statistic T is the raw difference standardized by dividing by σ(diff). Just like we standardize the raw difference between the observed sample mean and the null hypothesized mean, X - μ, by dividing it by the SE, (X - μ)/SE, to retrieve the test statistic for a (univariate) sample mean.
Given T = |D|/ σ(diff), the max distance |D| = T*σ(diff); in this case, |D|= T*0.398. If we seek two-sided 95.0%, then |D| = 1.96*0.398 = 0.78, and if we seek two-sided 99.0% confidence, then |D| = 2.58*0.398 = 1.02. I hope that's helpful!
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