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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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