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Lectures
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Summer
Lectures
Lecture #9
1. 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
 =
 =
2. 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:
3. 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.
4. Assignments:
(1) Review Sections 9.8, and 5.6 in Kirk.
(2) Do questions 5(c), 5(d), 6(c), 6(d), 7(c), and
7(d) in Chapter 9 of Kirk.
(3) Preview Sections 5.8, 9.4, and 9.10 in Kirk.
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Last updated: November 24, 1998
URL:
http://www.indiana.edu/~jopeng/Y603/summer/sum9.html
Comments: jopeng@indiana.edu
Copyright
1998, The Trustees of Indiana
University
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