Transcript Document
Statistical Techniques 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.
The MEANS statement in SAS calculates a
simple mean of all available observations in the
treatment cells.
The LSMeans statement will calculate the mean
of the treatment cell means.
LSMeans calculation (continued)
Example:
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.
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.
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(S`Y)
The treatment mean can be obtained from a
means (or LSMeans) statement, but the
standard deviation provided is not the correct
standard error for the interval.
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.
The degrees of freedom for the tabular t value i
the d.f. from the MSE used to calculate the
standard error.
Confidence Intervals on Treatments
(continued)
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
Be aware of similarities and differences with the
t-test.
HOV tests and tests of normality will be include
Factorial treatment arrangement (two-way) with
interpretation interactions will be covered
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.
Be able to interpret and discuss Post-ANOVA
tests
contrasts
range tests
Exam Coverage (continued)
Be able to place a confidence interval on a
treatment mean.
Recognize designs and treatment arrangement
from a described problem.
be able to determine the experimental unit,
sampling unit, and get the d.f. error.
Answers to questions will be on the net.
Good Luck.