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Y603 Lectures
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Lecture #14
1. Intraclass Correlation
Coefficient
Intraclass correlation
coefficient: It is usually written as 
which is comparable to the notion of  .
equals the ratio of a variance component due to Factor A (or B or
A*B interaction) over the sum of all variance components.
Conceptually it means the same thing as the
but is computed for random effects only.
2. Pooling strategies in random-effects
model and SAS programming
Pooling strategies used in
two-way random-effects ANOVA: Three positions concerning
whether to pool the SS interaction with SS error: (A) Never pool,
(B) always pool, and (C) pool only if it makes statistical and
conceptual sense after conducting a preliminary test on the
interaction first. Kirk recommends the first and the third
positions.
The advantage of conducting the
preliminary test and then decide if pooling is necessary is that
the reduced model often is more powerful than the full model in
detecting a significant main-effect, if there is any. The reason
is because the pooled MS error (or MS residual) is always
associated with a few more degrees of freedom than the MS error
based on the full model. Hence, the F test of main effects, formed
from the pooled MS error requires a slightly smaller critical
value than does the original F-ratio.
The disadvantages of pooling after the
preliminary test are several fold: first, we will be unable to
statistically evaluate the contingencies (such as Paullís
criterion) under which pooling takes place. Second, the F-ratio
based on the pooled MS error is no long a ratio of two independent
chi-square variables; therefore, the sampling distribution is
unknown. Third, subsequent tests based on the reduced model are
carried out as if there was no preliminary test preceding them;
hence, a slight, positive bias is built into the subsequent test.
Finally, the pooled MS error may be numerically larger, compared
with the original MS error. As a result, the advantage of having a
few more degrees of freedom in pooled MS error is offset by the
larger pooled MS error itself.
3. Assignments:
(1) Review Sections 9.11 and 9.9 in
Kirk.
(2) Finish all problems attached here
with the random-effects model.
(3) Preview Sections 7.1, 7.2, and 7.4,
in Kirk.
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