Interpreting ANOVA summary tables

For each of the following problems, identify the design (e.g., 2x4 factorial, or one-way) and the statistical significance of the main effect(s) and interaction(s) (if one). Answers are at the bottom of the page.

1. ANOVA of number of pecks.

Source
df
SS
MS
F Ratio
P-value
shape
1
7840.8
7840.8
81.24
< .0001
size
1
23931.7
23931.7
248.0
< .0001
shape*size
1
7926.8
7926.8
82.14
< .0001
error
2864
276395.8
96.5

2. ANOVA of causal rating.

Source
df
SS
MS
F Ratio
P-value
condition
3
17.15
5.72
1.07
.3621
stim type
3
14.13
4.71
.88
.4512
condition*stim-type
9
199.0
22.11
4.13
< .0001
error
541
2896
5.35

3. ANOVA of protein content of cereal.

Source
df
SS
MS
F Ratio
P-value
fiber
2
32.16
16.08
20.19
< .0001
error
74
58.93
.7964

4. ANOVA of ranking of similarity to target.

Source
df
SS
MS
F Ratio
P-value
Object
3
0
0
0
1.00
Transformation
2
2217
1108
1541
< .0001
Object*Transformation
6
77.9
13.0
18.0
< .0001
Rotated
1
965.8
965.8
1342
< .0001
 Object*Rotated
3
27.8
9.3
12.9
< .0001
Transformation*Rotated
2
86.7
43.4
60.3
< .0001
Object*Transformation*Rotated
6
16.3
2.72
3.77
.001
Error
1512
1088
.72

 

 

 

 

 

 

Answers

1. Design: 2 x 2 factorial.
Main effect for shape, main effect for size, significant interaction.

2. Design: 4 x 4 factorial.
No main effects. Significant interaction.

3. Design: one-way (3 levels of single IV: low, medium, high - just FYI).
Main effect for fiber content.

4. Design: 4 x 3 x 2 factorial.
No main effect for object, main effect for transformation, main effect for rotated. Three significant 2-way interactions (i.e., all of them), significant 3-way interaction.

Note: The value of "0" for SS and MS for Object is an indication that we are using the wrong statistical model for this data. This table was actually generated from data for a between-within design, although I analyzed it as if it were a strictly between-subject design for the purposes of this tutorial.