Question

Power and sample size determination for one-way ANOVA 1. If µ1 = 12, µ2 = 13, µ3 = 18 and µ4 = 21 with s e = 5, what is the power of the test when n1 = 2, n2 = 3, n3 = 3 and n4 = 2 and a = .05? 2. If µ1 = 12, µ2 = 13, µ3 = 18 and µ4 = 21 with s e = 5, what is the power of the test when n1 = n2 = n3 = n4 = 5 and a = .01? 3. In a one-way ANOVA k = 5, a = .01, b =.10 and and equal sample sizes are desired. a). What are the required samples sizes if D = 10, 15, 20 and 30? What generalization is suggested by your results? b) What are the required sample sizes for the same values of as in part 1 if ? How do these sample sizes compare to the ones in part 1? 4. In a one-way ANOVA k = 4, a = .05, b =.10 and D = 50; and equal sample sizes are desired. a) What are the required samples sizes if se = 50, 25,and 20? What generalization is suggested by your results? b). What are the required sample sizes for the same values of se as in part 1 if k = 5? How do these sample sizes compare to the ones in part 1? 5. In a oneway ANOVA with 3 treatment levels, a reasonable estimate of the standard deviation is 3.0. a) What would be the required sample size if: (1) the desired power is .90 or greater when the range of treatment means is 4.5 and (2) a = .05? b) If the sample size determined in part 1 is used what would be the minimum power of the test (using a = .05) when the range of the treatment means is 6.0?

Answer 1