Graphing Example: 2x2x3
Three factors: Sex [male, female]
Athletic Ability [athletic, non-athletic]
Task Difficulty [easy, medium, hard]
Data (mean percentage scores on test): [Note that the overall mean is 64.25]
Non-Athletic
Athletic
Male
60
63
75
Male
52
49
49
Female
80
82
78
Female
65
60
58
E
M
H
E
M
H
There are a total of 7 possible effects. Three main effects: Sex, Athletic ability, Task difficulty
Three two-factor interactions: SxA, SxT, AxT
One three-factor interaction: SxAxT
Graphing the main effects
1) Main effect of SEX: Need one mean for each level of this independent variable:
Male = (60+63+75+52+49+49)/6 = 58.00
Female = (80+82+78+65+60+58)/6 = 70.50
75
70
or
65
60
Mean Performance
Mean Performance
75
55
70
65
60
55
Male
Female
Male
Female
2) Main effect of ATHLETIC ABILITY: Need one mean for each level of this variable:
Athletic = (60+63+75+80+82+78)/6 = 73.00
Non-Athletic = (52+49+49+65+60+58)/6 = 55.50
75
70
or
65
60
55
50
Mean Performance
Mean Performance
75
70
65
60
55
50
Athletic
NonAthletic
Athletic
1
NonAthletic
3) Main effect of TASK DIFFICULTY: One mean for each level of this independent variable:
Easy = (60+80+52+65)/4 = 64.25
Medium = (63+82+49+60)/4 = 63.50
Hard = (75+78+49+58)/4 = 65.00
Mean Performance
66
65
64
63
Easy
Medium
Hard
Graphing the two-factor interactions
4) Interaction of SEX x ATHLETIC ABILITY: A mean for each level of these two variables:
[1] Athletic males = (60+63+75)/3 = 66
[2] Athletic females = (80+82+78)/3 = 80
Athletic Non-Athletic
[3] Non-athletic males = (52+49+49)/3 = 50
[4] Non-athletic females = (65+60+58)/3 = 61
66
50
Male
Female
85
Athletic
75
or
65
55
Non-athletic
61
Female
75
65
Male
55
45
45
Male
Mean Performance
Mean Performance
85
80
Athletic
Female
2
Nonathletic
5) Interaction of SEX x TASK DIFFICULTY
[1] Male-Easy = (60+52)/2 = 56.00
[2] Male-Medium = (63+49)/2 = 56.00
[3] Male-Hard = (75+49)/2 = 62.00
[4] Female-Easy = (80+65)/2 = 72.50
[5] Female-Medium = (82+60)/2 = 71.00
[6] Female-Hard = (78+58)/2 = 68.00
Mean Performance
Easy
Medium
70
Hard
65
or
60
Mean Performance
75
75
Male
Female
Easy
56.0
72.5
Medium
56.0
71.0
Hard
62.0
68.0
Female
70
65
60
Male
55
55
Male
Easy
Female
Medium
Hard
6) Interaction of ATHLETIC ABILITY x TASK DIFFICULTY
Athletic
[1] Athletic-Easy = (60+80)/2 = 70.00
70.0
Easy
[2] Athletic-Medium = (63+82)/2 = 72.50
[3] Athletic-Hard = (75+78)/2 = 76.50
Medium 72.5
[4] Non-athletic-Easy = (52+65)/2 = 58.50
[5] Non-athletic-Medium = (49+60)/2 = 54.50
Hard
76.5
[6] Non-athletic-Hard = (49+58)/2 = 53.50
Hard
Medium
Easy
or
60
50
Mean Performance
Mean Performance
58.5
54.5
53.5
80
80
70
Non-athletic
Athletic
70
60
Non-athletic
50
Athletic
Nonathletic
Easy
3
Medium
Hard
Graphing the three-factor interaction
7) Interaction of SEX x ATHLETIC ABILITY x TASK DIFFICULTY (Data are from page 1)
Non-Athletic
Athletic
75
65
60
63
75
Male
52
49
49
Female
80
82
78
Female
65
60
58
E
M
H
E
M
H
85
Athletic
Hard
Easy
Medium
or
Medium
Hard
Easy
55
Mean Performance
Mean Performance
85
Male
Non-athletic
Male
Female
75
Male
65
Female
55
45
45
Athletic
Male
Non-athletic
Easy
Female
Medium
Hard
or
Male
Female
85
75
Hard
65
Medium
Mean Performance
Mean Performance
85
Easy
55
Athletic
Medium
55
Hard
Athletic
Nonathletic
or
Non-athletic
85
Mean Performance
Mean Performance
Nonathletic
Athletic
85
Female
65
55
Easy
65
45
45
75
75
Male
45
75
65
Female
55
Male
45
Easy
Medium
Hard
Easy
Medium
Hard
or (etc.: There are four other possibilities...)
4
Etc.