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2 x 3 factorial Analysis of Variance ANOVA- formula and example

2 x 3 factorial Analysis of Variance ANOVA- formula and example

The layout of a 2x3 factorial ANOVA

B1B2 B3

A1
A1B1
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
A1B2
Subject 6
Subject 7
Subject 8
Subject 9
Subject 10
A1B3
Subject 11
Subject 12
Subject 13
Subject 14
Subject 15

A2
A2B1
Subject 16
Subject 17
Subject 18
Subject 19
Subject 20
A2B2
Subject 21
Subject 22
Subject 23
Subject 24
Subject 25
A2B3
Subject 26
Subject 27
Subject 28
Subject 29
Subject 30

In this example of a factorial design, we have a 2x3 (we read this as "a two by three") factorial. Two by three, meaning two factors: A and B. "two" meaning two levels for factor A. "three" meaning three levels for B. In another case of a 3x2 factorial design we have two factors, A and B, factor A three levels, factor B two levels.

FORMAT OF 2x3 FACTORIAL ANOVA SUMMARY TABLE

Source SS df MS F p
Berween A
Between B
AxB (interaction)
Within
Total

Interaction -factorial designs

Note the term "Interaction" in the ANOVA summary table of the factorial design What is interaction? The best way to grasp the concept of interaction is to graph it.

ANOVA 2x3 factorial -practice example

An experimenter wanted to test the effect of two drugs on emotionality of male and female teenagers. He randomly selected 15 male and 15 female teenagers and randomly assigned them to 6 groups: Group 1, Group 2, Group 3, Group 4, Group 5, Group 6. five subjects in each group as shown in the following table.

Drug 1
B1
Drug 2,
B2
Drug 3,
B3

Male
A1
A1B1 Group1

Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
A1B2 Group2

Subject 6
Subject 7
Subject 8
Subject 9
Subject 10
A1B3 Group3

Subject 11
Subject 12
Subject 13
Subject 14
Subject 15

Female
A2
A2B1 Group3

Subject 16
Subject 17
Subject 18
Subject 19
Subject 20
A2B2 Group4

Subject 21
Subject 22
Subject 23
Subject 24
Subject 25
A2B3 Group2

Subject 26
Subject 27
Subject 28
Subject 29
Subject 30

The data are presented on the table below. The scores are the values recorded on a device measuring galvanic skin response, a measure of emotionality. Higher values indicate stronger emotion.

B1B2 B3

A1
A1B1
11
11
13
12
10
A1B2
17
18
17
16
17
A1B3
27
25
24
26
27

A2
A2B1
15
14
14
16
15
A2B2
20
19
18
20
18
A2B3
30
29
29
28
31
.

2x3 FACTORIAL ANOVA SUMMARY TABLE
Source SS df MS F p
Berween A 67.5 1 67.5 62.31 <.0001
Between B 1088.07 2 544.04 502.19 <.0001
AxB (interaction) 3.8 2 1.9 1.75 0.1952
Within 26 24 1.08
Total 1185.37 29

After we calculate the F, we go to .........Next
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What does p mean?

What does p mean?

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