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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.

Since we have three groups of data (one group for each of the three subspecies

of bees), we would have to perform three separate ANOVA t-tests to determine

which pairs of groups were signiﬁcantly different. This requires that we would

have to perform a separate ANOVA t-test for the following pairs of groups:

1. SUBSPECIES A vs. SUBSPECIES B

2. SUBSPECIES A vs. SUBSPECIES C

3. SUBSPECIES B vs. SUBSPECIES C

We will do just one of these pairs of tests, SUBSPECIES B vs. SUBSPECIES C,to

illustrate the way to perform an ANOVA t-test comparing these two subspecies. The

ANOVA t-test for the other two pairs of groups would be done in the same way.

8.4.1 Comparing Subspecies B vs. Subspecies C in the Number

of Sound Bursts Per Cycle Using the ANOVA t-Test

Objective: To compare Subspecies B vs. Subspecies C in number of sound

bursts per cycle using the ANOVA t-test.

The ﬁrst step is to write the null hypothesis and the research hypothesis for

these two subspecies of bees.

For the ANOVA t-test, the null hypothesis is that the population means of the

two groups are equal, while the research hypothesis is that the population means of

the two groups are not equal (i.e., there is a signiﬁcant difference between these

two means). Since we are comparing SUBSPECIES B (Group 2) vs.

SUBSPECIES C (Group 3), these hypotheses would be:

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