Question

A researcher conducted an ANOVA (alpha = .05) between 4 groups (G1, G2, G3, G4), with 11 people in each group. The MSBetween was 5.62 and the MSWithin was 2, leading to an F test statistic of 2.81.

Answer the following:

1) What were the hypotheses in statistical notation (2 points)?

2) What is the critical value (1 point)?

3) Make a decision regarding whether to reject H0 and what that means with regard to the group means (3 points).

4) What specifically do the MSBetween and MSWithin represent when the null hypothesis is true and when the null hypothesis is false (2 points)?

Answer 1

(1) The Hypothesis:

H0: The means of all 4 groups are equal

Ha: Them means of all 4 groups are not equal.

(2) k = 4. Therefore df1 = 4 - 1 = 3

N = 11 * 4 = 44. Therefore df2 = N - k = 44 - 4 = 40

The Critical value at = 0.05, df = 3,40 is 2.8387

(3) Since F test (2.81) is < Fcritical (2.8387), We Fail to reject H0. It means that there is no significant difference between any of the group means.

(4) If the null hypothesis is true, it means we have failed to reject the null hypothesis, and hence F stat must be very small. This means that MS between, the between group variances is small and within sample variance is large or almost numerically same as MS between.

If the Null Hypothesis is False, it means that Fstat is very large, and this means that the Between group variances are very large (which leads to the fact that the means are not equal) and the Within group variances (MS between) is small.