Re: st: Nemenyi test

[David Hoaglin <dchoaglin@gmail.com>]

Celia,

It is helpful to have the more-detailed information about your data.

Peter Nemenyi (a gentle and dedicated man, whom I miss) proposed
several tests, but he wrote his thesis 50 years ago.  Later work found
shortcomings with some of them, and I suspect that none of his tests
are used much now (I have not searched the literature).

The sizes of the groups are not necessarily a reason to prefer
Kruskal-Wallis. I would also have considered -oneway-.  Since you got
different results, you should examine the data (graphically) to see
what features might be responsible.  I have recently analyzed some
data on antibodies, titers obtained by two-fold serial dilution; the
appropriate scale for the analysis was logarithmic (logs base 2).  In
any scale the data would have many ties.  The choice of scale would
not affect the results of a rank-based procedure such as KW, but it
would have a major impact on the results of -oneway-.  One common
problem arises when the variability (e.g., standard deviation) within
the group is systematically related to the level (e.g., mean) of the
group.  A suitable transformation (such as the logarithm) can reduce
or remove that pattern.  -oneway- expects the variability to be the
same in all the groups.

If I read your message correctly, you used KW on the full set of five
groups, but -oneway- on only the 2 by 2 (i.e., omitting the negative
control).  Could the four groups in the 2 by 2 differ from the control
group, but not from one another?  If, as an exploratory step, you make
pairwise comparisons among those four groups, what are the results?

For assessing differences among groups, -oneway- has a number of
options.  It does not, however, take full account of the structure of
your groups (primigravid/multigravid crossed with not
infected/infected).  If you want to estimate the main effects and the
interaction of those two factors, you can replace the one-way ANOVA
with a regression that has four non constant predictors (all indicator
variables):
primagravid and not infected
multigravid and not infected
primagravid and infected
multigravid and infected .
Then you can use -lincom- to estimate the difference between
multigravid and primagravid (averaging over not infected/infected),
the difference between infected and not infected (averaging over
primagravid and multigravid), and the double difference.

I hope this discussion helps.

David Hoaglin

On Fri, Aug 30, 2013 at 3:26 AM, Célia Dechavanne <celia_dv@yahoo.fr> wrote:
> Dear all,
>
> Thank you for your answers. As I said I'm not a statistician.
> I have just one quantitative variable (specific antibody measures) for 5
> groups (women primigravid/multigravid that are not infected/infected and a
> negative control). I just want to know if there is a difference of the
> antibody rate between the groups. As the number of women by group is small,
> I choose a KW to test if there is a difference between the 5 groups. The p
> was <0.001. Now, I would like to know what is the group "responsible" for
> the difference, that's why I would like to perform a test 2 by 2. I thought
> that the Nemenyi test was the good one (advise from a statistician) but I
> didn't find anything to perform this test with Stata. Thus I perform a
> oneway, but there was no significant difference between the groups (2 by 2).
> This appears as illogical, so I guess that I realized a mistake choosing
> oneway. Am I wrong?
> Thanks for your help and your patience
>
> Celia

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