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sible to detect. More important, the presence of a significant interaction
may render the concept of a single “main effect” meaningless. For
example, suppose we decide to test the effect of fertilizer and sunlight on
plant growth. With too little sunlight, a fertilizer would be completely
ineffective. Its effects only appear when sufficient sunlight is present.
Aspirin and warfarin can both reduce the likelihood of repeated heart
attacks when used alone; you don't want to mix them!
Gunter Hartel offers the following example: Using five observations
per cell and random normals as indicated in Cornfield and Tukey's
diagram, a two-way ANOVA without interaction yields the following
results:
Source
df
Sum of Squares
F Ratio
Prob
>
F
Row
1
0.15590273
0.0594
0.8104
Col
1
0.10862944
0.0414
0.8412
Error
17
44.639303
Adding the interaction term yields
Source
df
Sum of Squares
F Ratio
Prob
>
F
Row
1
0.155903
0.1012
0.7545
Col
1
0.108629
0.0705
0.7940
Row*col
1
19.986020
12.9709
0.0024
Error
16
24.653283
Expanding the first row of the experiment to have 80 observations
rather than 10, the main effects only table becomes
Source
df
Sum of Squares
F Ratio
Prob
>
F
Row
1
0.080246
0.0510
0.8218
Col
1
57.028458
36.2522
<
.0001
Error
88
138.43327
But with the interaction term it is:
Source
df
Sum of Squares
F Ratio
Prob
>
F
Row
1
0.075881
0.0627
0.8029
Col
1
0.053909
0.0445
0.8333
row*col
1
33.145790
27.3887
<
.0001
Error
87
105.28747
