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Y603 Lectures
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Lecture #12
1. 
in a fixed-effects two-way ANOVA design
There are three types of omega
squared in a two-way factorial design: one due to Factor A,
another due to Factor B, and the third due to the interaction of A
and B:
Partial 
Or,
Partial 
Or,
Partial 
Or,
2. Effect size in a factorial
design
Effect size for Factor A= ,
where the omega square index is in its partial form.
Likewise, we may define the effect size
for Factor B or A*B interaction as
 =
 =
3. Power of an F-test
To determine power and desirable
sample size, we need to compute a third parameter for the
noncentral F distribution which is the distribution under the
alternative hypothesis:
 =
Take this value, the df for Factor A, df
for MS error, and alpha (say, .05) to Tang's Chart (in Table E.12
starting on page 816) in order to determine power.
Turn to p. 400 Kirk (1994) for an
estimation of the f
parameter for Factor B and A*B interaction:
4. Sample size determination for testing
the main effect of A
Method 1 Trial and
Error--Given a desirable  ,
you may try different values of n in the eq. above.
Method 2 Enter  into
Table E13 on p. 826 and return with a n=53 for the power of
.8
Method 3 Return to Tang's
chart ...
Reverse the process outlined in (2)
above, you will be able to determine a desirable sample size
needed in planning for the next (or future) study.
Step 1: Preset the power
to be .82 (say).
Step 2: Preset the alpha to be
.05 (say).
Step 3: Preset the DF for the
error term to infinity.
Step 4: Derive a 
value based on preset power (.82), alpha (.05), and DF for the
error term.
Step 5: Plug the 
value into the formula listed in (4) above and determine n per
cell.
Step 6: Use the n derived from
Step 5 to redetermine the DF for the error term.
Step 7: Repeat Steps 4-6 until
n converges.
5. Assignments:
(1) Review Sections 9.8, and 5.6 in
Kirk.
(2) Do questions 5(c), 5(d), 5(e), 6(c),
6(d), 6(f), 7(c), 7(d), and 7(e) in Chapter 9 of Kirk.
(3) Preview Sections 5.8, 9.4, and 9.10
in Kirk.
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