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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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