Suppose that we have a oneway ANOVA with equal numbers of observations on each treatment, that is, ni n, i 1, , k In this case the F test can be considered an average t test (a) Show that a t test of H0 Icirc cedil i Icirc cedil i sup2 versus H1 Icirc cedil i Icirc cedil i sup2 can be based on the statistic (b) Show that where F is the usual ANOVA F statistic (Y Y,)2

Question: Suppose that we have a oneway ANOVA with equal numbers of observations on each treatment, that is, ni = n, i = 1,..., k. In

Suppose that we have a oneway ANOVA with equal numbers of observations on each treatment, that is, ni = n, i = 1,..., k. In this case the F test can be considered an average t test.
(a) Show that a t test of H0: Î¸i = Î¸i€² versus H1: Î¸i ‰ Î¸i€² can be based on the statistic

(b) Show that

where F is the usual ANOVA F statistic.

(Y - Y,)2

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