A one-way ANOVA uses ni observations from group i, i = 1,…, c.

a. Verify the noncentrality parameter for the scaled between-groups sum of squares.

b. Suppose c = 3, with ????1 − ????2 = ????2 − ????3 = ????∕2. Evaluate the noncentrality, and use it to find the power of a F test with size ???? = 0.05 for a common sample size n, when (i) n = 10, (ii) n = 30, (iii) n = 50.

c. Now suppose ????1 − ????2 = ????2 − ????3 = Δ????. Evaluate the noncentrality when each ni = 10, and use it to find the power of a F test with size ???? = 0.05 when Δ = 0, 0.5, 1.0.