Microsoft Office Tutorials and References

In Depth Information

The answer to this question is analogous to the decision rule used in this topic for

both the one-group t-test and the two-group t-test
. You will recall that this rule (See

Sect. 4.1.6 and Sect. 5.1.8) was:

If the absolute value of t is less than the critical t, you accept the null hypothesis.

or

If the absolute value of t is greater than the critical t, you reject the null hypothesis,

and accept the research hypothesis.

Now, here is the decision rule for ANOVA:

Objective
: To learn the decision rule for the ANOVA F-test

The decision rule for the ANOVA F-test is the following:

If the value for F is less than the critical F-value, accept the null hypothesis.

or

If the value of F is greater than the critical F-value, reject the null hypothesis, and

accept the research hypothesis.

Note that Excel tells you the critical F-value in cell G31: 3.32

Therefore, our decision rule for the honey bees AVOVA test is this:

Since the value of F of 8.19 is greater than the critical F-value of 3.32, we reject the

null hypothesis and accept the research hypothesis.

Therefore, our conclusion, in plain English, is:

There is a signiﬁcant difference between the average number of sound bursts per

cycle between the three subspecies of honey bees.

Note that it is not necessary to take the absolute value of F of 8.19. The F-value

can never be less than one, and so it can never be a negative value which requires us

to take its absolute value in order to treat it as a positive value.

It is important to note that ANOVA tells us that there was a signiﬁcant difference

between the population means of the three groups,
but it does not tell us which pairs

of groups were signiﬁcantly different from each other
.

8.4 Testing the Difference Between Two Groups

using the ANOVA t-test

To answer that question, we need to do a different test called the ANOVA t-test.

Objective
: To test the difference between the means of two

groups using an ANOVA t-test when the ANOVA

results indicate a signiﬁcant difference between

the population means.

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