Nonparametric test for repeated measures with two groups

[Maynard Williams]

Hi,

Can anyone tell me if there is a nonparametric equivalent of a repeated
measures ANOVA involving two groups? I have a pre-post treatment design
involving both a control and intervention group and wish to test whether
changes from pre-treatment to post-treatment differ significantly for the
two groups. Is use of a Mann-Whitney U test on the change scores for the
two groups appropriate? If not, are there any other nonparametric methods
suitable?

Thanks in anticipation.

Maynard

[Anonysus]

Hi Maynard,

the Mann-Whitney-U-test is suitable for non-paired groups, as control
and intervention group are.
For paired groups, such as intervention group pre compared to
int. group post (OR control pre compared to control post) you could use
Wilcoxon-test.

Hope this helps a bit,

(-:

Susann.
--
Direct access to this group with http://web2news.com
http://web2news.com/?comp.soft-sys.stat.spss

[Bruce Weaver]

Just out of curiousity, why can you not use ANOVA (or perhaps ANCOVA with
pre-test as coveriate) on your data? ANOVA is often more robust than you
might think. What kind of sample sizes do you have?

If you definitely are not happy with ANOVA/ANCOVA on the raw data, you
might consider using ANOVA/ANCOVA on the rank-transformed data. Conover's
book on "nonparametric statistics" is a good source of information about
this approach.

Finally, I used to advise people to use an approach I learned from Rolfe
Morrison, who taught me stats in grad school. You can see a description
of that approach here:

http://www.angelfire.com/wv/bwhomedir/notes/alternative_to_anova.txt

These days, I am less inclined to recommend that approach, because it is a
lot easier, and often just as good, to use parametric tests on
rank-tranformed data (see Conover).

By the way, I should give credit to Mike Fuller (from Univ of Kent,
Canterbury), who came up with the same approach independently of Morrison.

Cheers,
Bruce
--
Bruce Weaver
E-mail: wea...@mcmaster.ca
Homepage: http://www.angelfire.com/wv/bwhomedir/

[Maynard Williams]

Hi Bruce

Thanks very much for your response.

Let me describe things a bit more. I actually have an exptal. and control
group with a pre-treatment measure and 3 post-treatment measures. There are
four outcomes of interest, two from one psychological instrument and two
from
another closely related one.

I am, in fact, using a repeated measures ANCOVA to analyse the data, using
the pre-test as a covariate and one other covariate on which the groups
differ at baseline and which is prognostic of outcome. Unfortunately the
sample size is very small (n=10 per group) and the data distributions depart
markedly from those assumed by parametric tests. I have settled on log
tranformations but have tried assorted others including reciprocal
transformations to assorted powers. Yes, I know that ANOVA/ANCOVA are
robust but, given the small sample size, thought I'd also like to try some
nonparametric tests as well.

I will look at the Morrison reference but am particularly interested in the
Conover approach. Unfortunately we don't have the text at our university
library, even though I know it is frequently cited. I will get hold of it
however. In the meantime, does Conover simply suggest ranking the data and
performing standard parametric ANOVA/ANCOVAS, just as the Spearman
correlation is exactly equivalent to a Pearson correlation on ranked scores.
If so, that would be really simple, but I suspect it isn't that easy.

Thanks again for you help. Its much appreciated.

Maynard

"Bruce Weaver" <wea...@mcmail.cis.mcmaster.ca> wrote in message
news:Pine.SOL.4.33.030507...@mcmail.cis.mcmaster.ca...

[Maynard Williams]

Thanks for the reply Susan. Yes, I realise that the Mann-Whitney can be used
to compare independent groups and that the Wilcoxen test can be used to
compare the pre and post test results for each of the groups separately.
However, I wish to assess whether any observed change for the intervention
group differs significantly from that found for the control group. Using
the Wilcoxen test for each group separately does not really address this
issue, i.e. it does not directly compare the changes, only whether the
changes for each group separately are significant.

Regards
Maynard

"Anonysus" <information....@web2news.net> wrote in message
news:2915...@web2news.com...

[Bruce Weaver]

On Thu, 8 May 2003, Maynard Williams wrote:

---------------------- >8 -----------------------

> I will look at the Morrison reference but am particularly interested in the
> Conover approach. Unfortunately we don't have the text at our university
> library, even though I know it is frequently cited. I will get hold of it
> however. In the meantime, does Conover simply suggest ranking the data and
> performing standard parametric ANOVA/ANCOVAS, just as the Spearman
> correlation is exactly equivalent to a Pearson correlation on ranked scores.
> If so, that would be really simple, but I suspect it isn't that easy.
>
> Thanks again for you help. Its much appreciated.
>
> Maynard

Here is Conover's advice in a nutshell (from "Practical Nonparametric
Statistics", 1999, 3rd Ed., p. 419):

"The recommended procedure in experimental designs for which no
nonparametric test exists is to use the usual analysis of variance
on the data and then to use the same procedure on the rank transformed
data. If the two procedures give nearly identical results the assumptions
underlying the usual analysis of variance are likely to be reasonable and
the regular parametric analysis valid. When the two procedures
give substantially different results, the experimenter may want to take
a closer look at the data and to lok especially for outliers...or
very nonsymmetric distributions."

HTH.

[Rich Ulrich]

On Thu, 8 May 2003 21:47:12 +1200, "Maynard Williams"
<maynard....@xtra.co.nz> wrote:

> Hi Bruce
>
> Thanks very much for your response.
>
> Let me describe things a bit more. I actually have an exptal. and control
> group with a pre-treatment measure and 3 post-treatment measures. There are
> four outcomes of interest, two from one psychological instrument and two
> from
> another closely related one.
>
> I am, in fact, using a repeated measures ANCOVA to analyse the data, using
> the pre-test as a covariate and one other covariate on which the groups
> differ at baseline and which is prognostic of outcome. Unfortunately the
> sample size is very small (n=10 per group) and the data distributions depart
> markedly from those assumed by parametric tests. I have settled on log

If I have this right:

You have at least 3 outcome variables where
the metrics (scalings) are
(a) not similar, and (b) not well behaved.
And yet you want to combine them
in a 'repeated measures' paradigm.
That could be a really bad situation, where the
best recovery might be the arbitrary ranking of scores....

- I suggest that spending a little time on scale development,
early, might save a lot of time. Or save an experiment.

> tranformations but have tried assorted others including reciprocal
> transformations to assorted powers. Yes, I know that ANOVA/ANCOVA are
> robust but, given the small sample size, thought I'd also like to try some
> nonparametric tests as well.

Okay, you have absolutely no confidence in the meaning
of the natural scoring of any of your data. Right?

>
> I will look at the Morrison reference but am particularly interested in the
> Conover approach. Unfortunately we don't have the text at our university
> library, even though I know it is frequently cited. I will get hold of it
> however. In the meantime, does Conover simply suggest ranking the data and
> performing standard parametric ANOVA/ANCOVAS, just as the Spearman
> correlation is exactly equivalent to a Pearson correlation on ranked scores.
> If so, that would be really simple, but I suspect it isn't that easy.
>

Yes, it is that easy.

However, one place where ranking are not-so-good
is when the R-squared is quite large, and the design
has more than one variable. That is because the
extreme scores might not be well represented; ranks
are not actually equally spaced linear, if you press the case.

I mention this, in particular, because you say that
you have N of 10; and an experiment *has* to
have large effects to be 'significant' when the Ns are that small.

--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html

[Maynard Williams]

Hi Rich

Thanks for your response. I should have made it clear that the
pre-treatment and 3 post-treatment measures are not different measures but
the same variable measured repeatedly. Further, I have four such outcomes,
two from one psyhological instrument and two from another. Thus there are
four outcomes measured repeatedly (4 times). I will be using four ANCOVAs,
one for each measure. Each of the outcomes is "badly behaved" in terms of
parametric test assumptions. I am reasonably happy with the log
transformations for each of the outcomes but just wanted to cross-check the
results against analogous nonparametric procedures.

Thanks to you and the other group members for the interest and helpful
replies.

Maynard
"Rich Ulrich" <wpi...@pitt.edu> wrote in message
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