Question

A researcher conducts two studies on child health. In Study 1, 30 children consume either a low-, moderate-, or high-fat meal (n = 10 per group). In Study 2, the researcher conducts the same study, except that a No Meal control group is added, with n = 10 in each group. If F= 3.11 in both studies, then in which study will the decision be to reject the null hypothesis at a .05 level of significance for a one-way between-subjects ANOVA?

Answer 1

In Study 1: k = number of groups = 3.

Therefore df 1 = k - 1 = 3 - 1 = 2

N = Total Number of observations = 30.

Therefore df 2 = N - k = 30 - 3 = 27

The Critical value at (0.05,2,27) = 3.354

The Decision Rule is that if F test is > F critical, Then Reject H0.

Here F test (3.11) is > F critical (3.354), therefore we fail to reject H0.

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In Study 2: k = number of groups = 4.

Therefore df 1 = k - 1 = 4 - 1 = 3

N = Total Number of observations = 30 + 10 = 40.

Therefore df 2 = N - k = 40 - 4 = 36

The Critical value at (0.05,3,36) = 2.866

The Decision Rule is that if F test is > F critical, Then Reject H0.

Here F test (3.11) is < F critical (2.866), therefore we reject H0.

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The decision to reject the null hypothesis will be in Study 2.