An analysis of variance is used to evaluate the mean differences for a research

Question

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 5 in each treatment. If the data produce an F-ratio of F = 3.15, then which of the following is the correct statistical decision?

Reject the null hypothesis with ? = .05 but not with ? = .01. Reject the null hypothesis with either ? = .05 or ? = .01. Fail to reject the null hypothesis with either ? = .05 or ? = .01. There is not enough information to make a statistical decision.

Explanation / Answer

Here,

df1 = number of groups - 1 = 4 -1 = 3
df2 = number of participants - number of groups = 4*5 - 4 = 16

Thus, the critical F at 0.05 and 0.01 is

Fcrit(0.05) = 3.238871517
Fcrit(0.01) = 5.292214046

Thus, since at both levels, Fcrit > F, then

OPTION C: Fail to reject the null with either ? = .05 or ? = .01

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