Data for a classical experiment of the effects of nitrogen f

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

Solution

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