Techniques Statistical I
EXST7005
Miscellaneous ANOVA Topics & Summary
LSMeans calculation
The calculations of LSMeans is different. For a
balanced design, the results will be the same.
However, for unbalanced designs the results wi
often differ.
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The MEANS statement in SAS calculates a
simple mean of all available observations in the
treatment cells.
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The LSMeans statement will calculate the mean
of the treatment cell means.
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LSMeans calculation (continued)
Example:
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The MEAN of 4 treatments, where the
observations are 3,4,8 for a1, 3,5,6,7,9 for a2,
7,8,6,7 for a3 and 3,5,7 for a4 is 5.8667.
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The individual cells means are 5, 6, 7 and 5 for
a1, a2, a3 and a4 respectively. The mean of
these 4 values is 5.75. This would be the
LSMean.
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Raw means
Treatments
a1
b1
b2
Means
a2
5
7
a3
6
8
4
5
7
9
7 5.75
Means
9
6.5
5
7
7
6.6
LSMeans means
Treatments
a1
b1
b2
Means
Treatments
a1
b1
b2
Means
a2
6
8
7
a3
6
5
5.5
a2
7 5.75
9
6
7.5
a3
Means
7
6.33
Means
6.5
6.6
7
Confidence Intervals on Treatments
Like all confidence intervals on normally
distributed estimates, this will employ a t value
and will be of the form Mean ta/2(SY)
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The treatment mean can be obtained from a
means (or LSMeans) statement, but the
standard deviation provided is not the correct
standard for error the interval.
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Confidence Intervals on Treatments
(continued)
The standard error is the square root of MSE/n,
where n is the number of observations used in
calculating the mean.
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The degrees of freedom for the tabular t value i
the d.f. from the MSE used to calculate the
standard error.
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Confidence Intervals on Treatments
(continued)
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If there are several error terms (e.g.
experimental error and sampling error) use the
one that is appropriate for testing the treatment
Exam Coverage
ANOVA (one-way and two-way) will be covered
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Be aware of similarities and differences with the
t-test.
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HOV tests and tests of normality will be include
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Factorial treatment arrangement (two-way) with
interpretation interactions will be covered
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Exam Coverage (continued)
RBD will be covered only as the concepts. How
is the linear model different, why do we block,
what is a block, etc. No SAS output on RBD.
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Be able to interpret and discuss Post-ANOVA
tests
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contrasts
range tests
Exam Coverage (continued)
Be able to place a confidence interval on a
treatment mean.
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Recognize designs and treatment arrangement
from a described problem.
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be able to determine the experimental unit,
sampling unit, and get the d.f. error.
Answers to questions will be on the net.
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Good Luck.
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