Assume that $y_{i j}$ are i.i.d and follow a normal distribution with variance $sigma^{2}$. Under the null
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Assume that $y_{i j}$ are i.i.d and follow a normal distribution with variance $\sigma^{2}$. Under the null hypothesis that a factorial effect 0 ,
a. Show that
\[\frac{\bar{y}_{+}-\bar{y}_{-}}{s / 2} \sim t_{2^{k}(m-1)}\]
in a $2^{k}$ design with $m$ replications.
b. Suppose that $y_{i j}$ are not normal. Why is it still reasonable to assume that the ratio of the factorial effect to its standard error follows a normal distribution?
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Design And Analysis Of Experiments And Observational Studies Using R
ISBN: 9780367456856
1st Edition
Authors: Nathan Taback
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