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STAT 350 – Fall 2008
Lab #6
Solution
For the following problems, do the analysis using SAS.
Please put all SAS input (Editor
window) and all SAS output (Output window, NOT the Log window) as an appendix.
Nothing
pasted directly from SAS should be given as an answer to the questions below!
1.
Four formulations of fertilizer (called A, B, C, and D) were tested for their effect on corn
yield.
Each fertilizer was applied to 15 individual 1acre plots and corn yield (in bushels)
was measures.
The data is given in the associated Excel file on the "fertilizer" worksheet.
Conduct an analysis of variance on this data. If appropriate also conduct an appropriate
multiple comparison test to determine if any of the fertilizers result in significantly different
yields.
a.
Present a nice table summarizing the data:
the mean and standard deviation of the yields
for each fertilizer.
Fertilizer
Mean
Standard Deviation
A
140.800
14.145
B
153.085
15.483
C
159.295
11.816
D
146.750
12.085
b.
Give an ANOVA table to summarize the ANOVA results.
Make a nice table (as you
would do for a report/publication) – do NOT paste in anything from SAS directly!
Source
df
Sums of Squares
Mean Squares
F
p
Fertilizer
3
3822.31
1274.10
7.02
0.0003
Error
76
13784.49
181.37
Total
79
17606.80
c.
What is the
p
value for the ANOVA?
State the null hypothesis you are testing and state
what your conclusion about this hypothesis is.
The
p
value is 0.0003.
The null hypothesis is that the mean yield of corn is the same for all 4 fertilizers.
Clearly we will be rejecting that null hypothesis and concluding that at least one of the
fertilizers results in a yield that is significantly different from the others.
Lab #6  Solution
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If appropriate, present the results of the multiple comparison test using the linemethod
discussed in class.
In a few sentences, clearly explain what these results mean (assume
you are talking to a farmer/biologist who is not up on his statistical jargon).
In this case, Tukey's test is appropriate (we have no "control").
Fertilizer C
Fertilizer B
Fertilizer D
Fertilizer A
159.295
153.085
146.750
140.800
Fertilizer C resulted in the highest mean yield, but this was not significantly different
than Fertilizer B.
There was no statistically significant difference in the mean yields of
Fertilizer B and Fertilizer D.
Fertilizer A resulted in the lowest mean yield, but this was
not significantly different from Fertilizer D.
2.
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 Fall '08
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