Tom McWilliams, Decision Sciences Dept., Drexel U., wrote:
A colleague had a reviewer suggest that he use a Fisher-Hayter multiple
comparisons procedure (he'd used Scheffe in his article) so he asked me about it
and I replied "huh"? (Haven't heard of it.) I'm trying to point him in the right
direction without actually going to the office (It's summer, after all.) A quick
search of the CIS database generated the following relevant-sounding reference:
~~~
Hi, Tom --
Yes, that's the correct citation. Here's the full reference:
Hayter, A.J. (1986). The maximum familywise error rate of Fisher's least
significant difference test. Journal of the American Statistical Association, 81,
1000-1004.
An explanation of the procedure:
"Whereas the Tukey HSD is well known, the Fisher-Hayter MCP is relatively new
(Hayter, 1986). Like the Tuckey MCP, it controls alpha familywise at .05 for all
the pairwise comparisons in an experiment. Unlike the Tukey, the Fisher-Hayter
method needs the overall F test to be significant in order to maintain control of
alpha familywise. Because most researchers use the overall F test before doing
MCPs, it is easy to use the FIsher-Hayter. The advantage of Fisher-Hayter over
Tukey is that it gives a slight gain in power. The Fisher-Hayter method is done in
the following steps:
1. If the overall F test is significant, do steps 2-5; if not, retain all null
hypotheses of no differences between all possible pairs of population means.
2. Obtain all possible differences between pairs of group means.
3. Compute the t-statistics for all possible differences [NOTE: t=the mean
diff/sqrt((MSw/n)*2), where MSw is from the overall ANOVA and n=the size of each
group].
4. Compare the absolute values of the t-statistics to the critical value
q/sqrt(2), where q is the alpha-percent critical value from the Studentized range
distribution with parameters J-1 and df-within ... Note that this differs from the
Tukey MCP (which uses J) by using J-1 as the number-of-means parameter to get the
correct [critical value].
5. Reject a null hypothesis of equal population means for any absolute value of t
that equals or exceeds the critical value."
Quoted from:
Toothaker, L. E., & Miller, L. (1996). Introductory Statistics for the Behavioral
Sciences, 2nd Ed. Pacific Grove, CA: Brooks/Cole.
(If you have unequal sample sizes, you'd need to use the Games-Howell procedure.)
Cheers.
Lise DeShea (used to be L. Miller)
~~~
Lise DeShea, Ph.D.
Assistant Professor
Educational and Counseling Psychology
University of Kentucky
245 Dickey Hall
Lexington KY 40506-0017
[EMAIL PROTECTED]
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