Consider the following sample data for a two-factor ANOVA analysis. There are tw
ID: 3309524 • Letter: C
Question
Consider the following sample data for a two-factor ANOVA analysis. There are two levels (heavy and light) of factor A (weight), and three levels (small, medium, and large) of factor B (size). For each combination of size and weight, there are three observations.
Size
Small
Medium
Large
23
20
11
Heavy
21
32
20
25
26
20
Weight
13
20
11
Light
32
17
23
17
15
8
use the .05 significance level to answer the following questions.
a. Complete the ANOVA table (round your SS, MS, and P values to 3 decimal place and F to 2 decimal places)
Source
SS
DF
MS
F
P
Size
Weight
Interaction
Error
Total
b. Compute the P-value of Sizes
c. Compute the P-value of Weight
d. Compute the P-value of Interaction
Size
Small
Medium
Large
23
20
11
Heavy
21
32
20
25
26
20
Weight
13
20
11
Light
32
17
23
17
15
8
Explanation / Answer
1. From the given data
Two-way ANOVA: Data versus Weight, Size
Source DF SS MS F P
Weight 1 98.000 98.0000 2.48 0.141
Size 2 156.333 78.1667 1.98 0.180
Interaction 2 36.333 18.1667 0.46 0.642
Error 12 473.333 39.4444
Total 17 764.000
b) P-value of Size = 0.180 > alpha 0.05, so we accept H0
Thus we conclude that there is no significance difference among the levels of size
c) P-value of Weight = 0.141 > alpha 0.05, so we accept H0
Thus we conclude that there is no significance difference among the levels of weight
d)
P-value of Weight = 0.642 > alpha 0.05, so we accept H0
Thus we conclude that there is no interaction between weight and size