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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:
H 0 :
m 2 m 3
H 1 :
m 2 6¼ m 3
For Group 2 vs. Group 3, the formula for the ANOVA t-test is:
X 1
X 2
ANOVA t
¼
(8.2)
s
:
e
: ANOVA
where
s
1
n 1 þ
1
n 2
s
:
e
: ANOVA ¼
MS w
(8.3)
The steps involved in computing this ANOVA t-test are:
1. Find the difference of the sample means for the two groups (14.66 – 16.75
¼
2.09).
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