Suppose that we are testing whether five population means ar

Suppose that we are testing whether five population means are equal to each other. We would normally use ANOVA for that, but suppose that we carry out separate hypothesis tests in which we compare the four means to each other, two at a time. Using a level of significance of 0.01, what is the probability of a Type 1 error in one or more of the pair-wise hypothesis tests?

0.01

0.05

0.096

0.99

Solution

Suppose that we are testing whether five population means are equal to each other. We would normally use ANOVA for that, but suppose that we carry out separate hypothesis tests in which we compare the four means to each other, two at a time. Using a level of significance of 0.01, what is the probability of a Type 1 error in one or more of the pair-wise hypothesis tests?

0.01

0.05

0.096

0.99

For 4 groups, number of comparisons are n(n-1)/2 = 4*3/2 =6

Type 1 error for 6 comparisons = 1-0.99⁶ =0.0585

The answer = 0.05