Microsoft Office Tutorials and References

In Depth Information

H
0
: l
2
¼
l
3

H
1
: l
2
6¼
l
3

For Group 2 vs. Group 3, the formula for the ANOVA t-test is:

ANOVA t
¼
X
1
X
2

s
:
e
:
ANOVA

ð
8
:
2
Þ

where

s

1

n
1

þ
1

n
2

s
:
e
:
ANOVA
¼

MS
w

ð
8
:
3
Þ

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 =-2.09).

2. Find 1/n
2
? 1/n
3
(since both groups have a different number of bees in them,

this becomes: 1/10 ? 1/12 = 0.10 ? 0.08 = 0.18

3. Multiply MS
w
times the answer for step 2 (1.67 9 0.18 = 0.31)

4. Take the square root of step 3 (SQRT (0.31) = 0.55

5. Divide Step 1 by Step 4 to ﬁnd ANOVA t (-2.09/0.55 =-3.80)

Note:

Since Excel computes all calculations to 16 decimal places, when you use

Excel for the above computations, your answer will be -3.78 in two

decimal places, but Excel’s answer will be much more accurate because it

is always in 16 decimal places.

Now, what do we do with this ANOVA t-test result of -3.80? In order to

interpret this value of -3.80 correctly, we need to determine the critical value of t

for the ANOVA t-test. To do that, we need to ﬁnd the degrees of freedom for the

ANOVA t-test as follows:

8.4.1.1 Finding the Degrees of Freedom for the ANOVA t-Test

Objective: To ﬁnd the degrees of freedom for the ANOVA t-test.

The degrees of freedom (df) for the ANOVA t-test is found as follows:

df
¼
take the total sample size of all of the groups and subtract the

number of groups in your study
ð
n
TOTAL
k where k
¼
the

number of groups
Þ

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