Three different varieties of tomatoes (Hunester (H), Pusa (P) and Ife No. 1 (If1
ID: 3250205 • Letter: T
Question
Three different varieties of tomatoes (Hunester (H), Pusa (P) and Ife No. 1 (If1)) and four different planting densities (10, 20, 30 and 40 thousand plants per hectare) are being considered to be Planted in a certain region. To see if the variety or density of plants affect the product, each combination of variety and density is used in three different plots, resulting in the production data below. (A = 0.01). Test the hypothesis Test Tukey if the interaction hypothesis is not rejected and at least one of the main effects in terms of the null is rejected.Explanation / Answer
Answer:
Two factor ANOVA
Factor 2
Means:
P10
P20
P30
P40
H
9.20
12.43
12.90
10.80
11.33
Factor 1
IF1
8.93
12.63
14.50
12.77
12.21
P
16.30
18.10
19.93
18.20
18.13
11.48
14.39
15.78
13.92
13.89
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 variety
328.445
2
164.2225
104.12
1.48E-12
Factor 2 density
86.692
3
28.8973
18.32
2.12E-06
Interaction
8.037
6
1.3395
0.85
.5451
Error
37.853
24
1.5772
Total
461.028
35
To test the main effect variety, calculated F=104.12, P=0.000 which is < 0.01 level. Main effect variety is significant.
To test the main effect density, calculated F=18.32, P=0.000 which is < 0.01 level. Main effect density is significant.
To test the interaction effect variety, calculated F=0.85, P=0.5451 which is > 0.01 level. Interaction effect variety is not significant.
Tukey simultaneous comparison t-values (d.f. = 24)
H
IF1
P
11.33
12.21
18.13
H
11.33
IF1
12.21
1.71
P
18.13
13.26
11.56
critical values for experimentwise error rate:
0.05
2.50
0.01
3.21
Tukey simultaneous comparison t-values (d.f. = 24)
P10
P40
P20
P30
11.48
13.92
14.39
15.78
P10
11.48
P40
13.92
4.13
P20
14.39
4.92
0.79
P30
15.78
7.26
3.13
2.35
critical values for experimentwise error rate:
0.05
2.76
0.01
3.47
Tukey simultaneous comparison shows the variety P is significant with H and IF1.
Tukey simultaneous comparison shows the density P10000 is significant with P20000,P30000,P40000.
Two factor ANOVA
Factor 2
Means:
P10
P20
P30
P40
H
9.20
12.43
12.90
10.80
11.33
Factor 1
IF1
8.93
12.63
14.50
12.77
12.21
P
16.30
18.10
19.93
18.20
18.13
11.48
14.39
15.78
13.92
13.89
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 variety
328.445
2
164.2225
104.12
1.48E-12
Factor 2 density
86.692
3
28.8973
18.32
2.12E-06
Interaction
8.037
6
1.3395
0.85
.5451
Error
37.853
24
1.5772
Total
461.028
35
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