STAT 350 Lab #6 – Oneway ANOVA 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
146.97
12.50
B
140.89
14.81
C
154.65
12.60
D
160.95
10.63
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
Sum of Squares
Mean Square
F
Value
Fertilizer
3
3458.56000
1152.85333
7.12
Error
56
9066.67333
161.90488
Total
59
12525.23333
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 0.0004.
The null hypothesis is
μ
A
=
μ
B
=
μ
C
=
μ
D
.
(where
μ
A
= the mean yield for fertilizer A,
etc.).
Another way to state the null hypothesis is that the mean yield is the same for all
fertilizers.
Based on this
p
value, we reject the null hypothesis and conclude that not all the means
are the same (there is a difference in yields among the fertilizers).
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If appropriate, present the results of the multiple comparison test in a manner 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).
There are a couple ways to present these results, one with lines and one with letters.
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 Spring '08
 Staff
 Statistics, Standard Deviation, Null hypothesis, Multiple comparisons, ANOVA procedure

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