with a test of interaction the tukey\'s if there is an interaction Factorial des
ID: 3150408 • Letter: W
Question
with a test of interaction the tukey's if there is an interaction
Factorial designs have been used in forestry to assess the effects of various factors on the growth behavior of trees. In one such experiment, researchers thought that healthy spruce seedlings should bud sooner than diseased spruce seedlings ("Practical Analysis of Factorial Experiments in Forestry," Canadian J. of Forestry, 1995: 446-461). Inaddition. before planting, seedlings were also exposed to three levels of pH to see whether this factor has an effect on virus uptake into the squareroot system. The following table shows data from a 2 times 3 experiment to study both factors:Explanation / Answer
Two factor ANOVA
Factor 2
Means:
pH3
Ph5.5
pH7
Diseased
1.24
0.80
1.16
1.07
Factor 1
Healthy
1.52
1.24
1.28
1.35
1.38
1.02
1.22
1.21
5
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1
0.588
1
0.5880
27.56
2.21E-05
Factor 2
0.651
2
0.3253
15.25
.0001
Interaction
0.128
2
0.0640
3.00
.0687
Error
0.512
24
0.0213
Total
1.879
29
Post hoc analysis
p-values for pairwise t-tests for Factor 2
Ph5.5
pH7
pH3
1.02
1.22
1.38
Ph5.5
1.02
pH7
1.22
.0054
pH3
1.38
1.15E-05
.0220
Tukey simultaneous comparison t-values (d.f. = 24)
Ph5.5
pH7
pH3
1.02
1.22
1.38
Ph5.5
1.02
pH7
1.22
3.06
pH3
1.38
5.51
2.45
critical values for experimentwise error rate:
0.05
2.50
0.01
3.21
There is no significant interaction between pH and health, F=3.0, P=0.0687.
There is significant difference between 3 pH groups, F=15.25, P=0.0001
Tukey simultaneous comparison shows that Ph 5.5 group significant from pH 3 and pH7 groups.
There is significant difference between 2 Health groups, F=27.56, P=0.0000
Two factor ANOVA
Factor 2
Means:
pH3
Ph5.5
pH7
Diseased
1.24
0.80
1.16
1.07
Factor 1
Healthy
1.52
1.24
1.28
1.35
1.38
1.02
1.22
1.21
5
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1
0.588
1
0.5880
27.56
2.21E-05
Factor 2
0.651
2
0.3253
15.25
.0001
Interaction
0.128
2
0.0640
3.00
.0687
Error
0.512
24
0.0213
Total
1.879
29
Post hoc analysis
p-values for pairwise t-tests for Factor 2
Ph5.5
pH7
pH3
1.02
1.22
1.38
Ph5.5
1.02
pH7
1.22
.0054
pH3
1.38
1.15E-05
.0220
Tukey simultaneous comparison t-values (d.f. = 24)
Ph5.5
pH7
pH3
1.02
1.22
1.38
Ph5.5
1.02
pH7
1.22
3.06
pH3
1.38
5.51
2.45
critical values for experimentwise error rate:
0.05
2.50
0.01
3.21
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