One Way ANOVA

1
Logic of Two Way ANOVA
One Way ANOVA
2
Logic of Two Way ANOVA
Two Way ANOVA
3
Logic of Two Way ANOVA
4
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 1 Get the cell means, row means, column
means, and grand mean
5
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 1 Get the SStotal
56
6
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 2 Get the SSwithin
14
7
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 3 Get the SStime
18
8
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 4 Get the SStemp
12
9
Steps for Two Way ANOVA
70o
50o
90o


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Step 5 Get the SSinteraction
12
10
Steps for Two Way ANOVA
70o
50o
90o
Step 6 Finish the table


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
11
Steps for Two Way ANOVA
70o
50o
90o
Step 6 Finish the table


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Source SS df s2 F
Between
SStime 18
SStemp 12
SStimXtemp 12
Within 14
Total 56
12
Steps for Two Way ANOVA
70o
50o
90o
Step 6 Finish the table


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Source SS df s2 F
Between
SStime 18 1
SStemp 12 2
SStimXtemp 12 2
Within 14 12
Total 56 17
13
Steps for Two Way ANOVA
70o
50o
90o
Step 6 Finish the table


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Source SS df s2 F
Between
SStime 18 1 18
SStemp 12 2 6
SStimXtemp 12 2 6
Within 14 12 1.17
Total 56 17
14
Steps for Two Way ANOVA
70o
50o
90o
Step 6 Finish the table


1 2 3
4 5 6
3 1 2
Morning
1 4 1
0 1 2
0 0 0
Afternoon
Source SS df s2 F
Between
SStime 18 1 18 15.38
SStemp 12 2 6 5.12
SStimXtemp 12 2 6 5.12
Within 14 12 1.17
Total 56 17
15
Steps for Two Way ANOVA
Since there are only two levels of time, you know
they are significantly different from one another
Since there are three levels of temp, you will
need to use post-hoc multiple comparisons (e.g.
Tukeys HSD) to determine which levels differ
from one another.
16
Steps for Two Way ANOVA
To understand the interaction more fully, you
might want to look at the simple effects
You could compute the effect of temp just in the
morning, for example.
You would simply compute SStemp at AM
17
Assumptions for the Two Factor ANOVA

• Observations within each sample are independent.
• Populations are normally distributed.
• Populations from which the samples are selected
  must have equal variances (homogeneity of
  variance).
• Equal cell Ns (if calculating by hand)