Question

1. Open the Corn Yield dataset. There you see data recorded from an experiment to test 4 organic pesticide methods (wasps, nematodes, pepper spray, and bacteria) to see if they eradicate corn weevils better than a standard chemical pesticide (control). For each method, effectiveness is determined by the average weight in grams of corn that is yielded from a randomly selected ear of corn.

1. Use Minitab to do an Anderson-Darling test on the Yields to determine if the normality assumption for a valid ANOVA can be considered to be met. What is your conclusion?
2. Use Minitab to compute the sample standard deviations for the five groups. What is your conclusion about the ANOVA constant standard deviation assumption?
3. Use Minitab to carry out a 1-way ANOVA for this data, with Tukey Comparisons. Based on this test (and assuming it to be valid), state your conclusions about these pesticide methods.

Method	Yield
Control	86.19
Control	102.77
Control	88.37
Control	75.28
Control	89.3
Control	102
Control	105.17
Control	88.24
Control	83.39
Control	89.42
Control	100.13
Control	110.1
Wasps	103.12
Wasps	110.71
Wasps	95.2
Wasps	94.29
Wasps	87.58
Wasps	119.14
Wasps	102.52
Wasps	93.54
Wasps	86.95
Wasps	98.31
Wasps	105.37
Wasps	117.17
Nematodes	106.19
Nematodes	109.82
Nematodes	114.99
Nematodes	112.27
Nematodes	99.57
Nematodes	114.35
Nematodes	103.11
Nematodes	106.01
Nematodes	97.19
Nematodes	95.55
Nematodes	115.06
Nematodes	98.91
Bacteria	93.3
Bacteria	90.45
Bacteria	97.31
Bacteria	100.4
Bacteria	106.2
Bacteria	110.56
Bacteria	111.3
Bacteria	109.52
Bacteria	101.65
Bacteria	94.42
Bacteria	110.1
Bacteria	93.94
Pepper Spray	92.80936
Pepper Spray	86.69
Pepper Spray	101.1568
Pepper Spray	96.04139
Pepper Spray	100.2126
Pepper Spray	99.53069
Pepper Spray	104.079
Pepper Spray	97.14578
Pepper Spray	111.48
Pepper Spray	104.5611
Pepper Spray	94.44477
Pepper Spray	91.83284

Answer 1

a) The Result for Anderson Darling test is given in the Graph below

Here P.Value=0.875 which is greater then 0.05 level of significance hence we conclude that the data is normal.

b) The standard deviation of groups are as follow

Groups	StDev
Bacteria	7.71
Control	10.4
Nematodes	7.22
Pepper	98.33
Wasps	10.57

we can use residual plot to check the constant variation assumption

Since the residuals are randomly distributed in the above residual plot. therefore we can conclude that the assumption of normality is met.

c) F test results are as follow

Source	DF	SS	MS	F	P
Method	4	1052.2	263.1	3.5	0.013
Error	55	4133.8	75.2
Total	59	5186

Since p.value is less then 0.05 at 5% level of significance hence we conclude that pesticide methods are significant different.

Turkey test out put

Grouping Information Using Tukey Method

Method N Mean Grouping
Nematodes 12 106.085 A
Bacteria 12 101.596 A B
Wasps 12 101.158 A B
Pepper Spray 12 98.332 A B
Control 12 93.363 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Method

Individual confidence level = 99.34%

Method = Bacteria subtracted from:

Method Lower Center Upper ---------+---------+---------+---------+
Control -18.218 -8.232 1.753 (-------*-------)
Nematodes -5.496 4.489 14.475 (--------*-------)
Pepper Spray -13.249 -3.264 6.722 (-------*--------)
Wasps -10.423 -0.437 9.548 (--------*-------)
---------+---------+---------+---------+
-12 0 12 24

Method = Control subtracted from:

Method Lower Center Upper ---------+---------+---------+---------+
Nematodes 2.736 12.722 22.707 (--------*-------)
Pepper Spray -5.017 4.969 14.954 (-------*-------)
Wasps -2.191 7.795 17.781 (-------*--------)
---------+---------+---------+---------+
-12 0 12 24

Method = Nematodes subtracted from:

Method Lower Center Upper ---------+---------+---------+---------+
Pepper Spray -17.739 -7.753 2.233 (--------*-------)
Wasps -14.912 -4.927 5.059 (-------*-------)
---------+---------+---------+---------+
-12 0 12 24

Method = Pepper Spray subtracted from:

Method Lower Center Upper ---------+---------+---------+---------+
Wasps -7.159 2.826 12.812 (-------*--------)
---------+---------+---------+---------+
-12 0 12 24