Question

The following statistics are computed by sampling from three normal populations whose variances are equal: (You may find it useful to reference the t table and the q table.) x−1 = 15.1, n1 = 8; x−2 = 20.9, n2 = 9; x−3 = 28.0, n3 = 6; MSE = 28.6

a. Calculate 99% confidence intervals for μ1 − μ2, μ1 − μ3, and μ2 − μ3 to test for mean differences with Fisher’s LSD approach. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

b. Repeat the analysis with Tukey’s HSD approach. (If the exact value for nT – c is not found in the table, then round down. Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

c. Which of these two approaches would you use to determine whether differences exist between the population means?

a. Tukey's HSD Method since it protects against an inflated risk of Type I Error.

b. Fisher's LSD Method since it protects against an inflated risk of Type I Error.

c. Tukey's HSD Method since it ensures that the means are not correlated.

d. Fisher's LSD Method since it ensures that the means are not correlated.

Answer 1

a)

Level of significance	0.01
no. of treatments,k	3
DF error =N-k=	20
MSE	28.600
t-critical value,t(α/2,df)	2.8453

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj))

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	-5.800	7.3939	-13.19	1.59	means are not different
µ1-µ3	-12.900	8.2179	-21.12	-4.68	means are different
µ2-µ3	-7.100	8.0198	-15.12	0.92	means are not different

b)

Level of significance	0.01
no. of treatments,k	3
DF error =N-k=	20
MSE	28.600
q-statistic value(α,k,N-k)	4.639

critical value = q*√(MSE/2*(1/ni+1/nj))

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	-5.80	8.52	-14.32	2.72	means are not different
µ1-µ3	-12.90	9.47	-22.37	-3.43	means are different
µ2-µ3	-7.10	9.25	-16.35	2.15	means are not different

c)

a. Tukey's HSD Method since it protects against an inflated risk of Type I Error.