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.
