Data for a classical experiment of the effects of nitrogen fertilizer on plant y
ID: 3394634 • Letter: D
Question
Data for a classical experiment of the effects of nitrogen fertilizer on plant yield are provided below. The experiment consists of measuring the yield of six separate plots divided into four sub-plots where nitrogen fertilizer was applied or withheld. Construct a test to determine if mean plant yield varies by plot and nitrogen application. In addition, you must also evaluate their interaction. Your answer must include an ANOVA table AND your conclusions. All numeric values must be rounded to the nearest hundredth, with the exception of degrees of freedom. See example below. There is no need for hand calculation if you use Excel’s analysis ToolPak.
Application of nitrogen
Plot
No
Yes
1
49.5
62.8
46.8
57.0
2
55.5
59.8
56.0
58.5
3
62.8
55.8
55.0
69.5
4
45.5
62.0
44.2
48.8
5
51.5
52.0
48.8
49.8
6
53.2
57.2
56.0
59.0
DELETE THE EXAMPLE AND PASTE YOUR ANOVA TABLE DIRECTLY BELOW.
ANOVA EXAMPLE
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
3411.65
3
1137.22
2.57
0.06
2.80
Columns
8782.90
2
4391.45
9.93
0.00
3.19
Interaction
6225.90
6
1037.65
2.35
0.05
2.29
Within
21220.40
48
442.09
Total
39640.85
59
Summary: CLICK IN THIS BOX TO WRITE YOUR SUMMARY
Application of nitrogen
Plot
No
Yes
1
49.5
62.8
46.8
57.0
2
55.5
59.8
56.0
58.5
3
62.8
55.8
55.0
69.5
4
45.5
62.0
44.2
48.8
5
51.5
52.0
48.8
49.8
6
53.2
57.2
56.0
59.0
Explanation / Answer
Data for a classical experiment of the effects of nitrogen fertilizer on plant yield are provided below. The experiment consists of measuring the yield of six separate plots divided into four sub-plots where nitrogen fertilizer was applied or withheld. Construct a test to determine if mean plant yield varies by plot and nitrogen application. In addition, you must also evaluate their interaction. Your answer must include an ANOVA table AND your conclusions. All numeric values must be rounded to the nearest hundredth, with the exception of degrees of freedom.
Two factor ANOVA
Nitrogen
Means:
No
Yes
p1
48.15
59.90
54.03
p2
55.75
59.15
57.45
p3
58.90
62.65
60.78
plot
p4
44.85
55.40
50.13
p5
50.15
50.90
50.53
p6
54.60
58.10
56.35
52.07
57.68
54.88
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
F critical
plot
343.30
5
68.66
3.36
.04
3.12
nitrogen
189.28
1
189.28
9.26
.01
4.75
Interaction
98.52
5
19.70
0.96
.48
Error
245.27
12
20.44
Total
876.37
23
Interaction between plot and nitrogen is not significant F(5,12)=0.96, P =0.48.
The main effect plot is significant, F(5,12)=3.36, P=0.04.
The main effect Nitrogen is significant F(1,12)=9.26, P=0.01.
Two factor ANOVA
Nitrogen
Means:
No
Yes
p1
48.15
59.90
54.03
p2
55.75
59.15
57.45
p3
58.90
62.65
60.78
plot
p4
44.85
55.40
50.13
p5
50.15
50.90
50.53
p6
54.60
58.10
56.35
52.07
57.68
54.88
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
F critical
plot
343.30
5
68.66
3.36
.04
3.12
nitrogen
189.28
1
189.28
9.26
.01
4.75
Interaction
98.52
5
19.70
0.96
.48
Error
245.27
12
20.44
Total
876.37
23
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