> I collected data for five neighbourhoods (using five point scale
> questions) and have been told that my data should be treated as
> non-parametric. A key research question is to determine if the
> differences amongst the five neighbourhoods are significant with
> respect to the five point scaled questions. Incidently I conducted 575
> surveys (with each survey containing 45 closed-ended questions).
> Based on the non-parametric structure of the data, I conducted the
> Kruskal-Wallis H test (using SPSS 11) to determine if the five
> neighbourhoods differed but this test did not clearly tell me which
> neighbourhoods differed! Would it be valid for me to conduct a
> Mann-Whitney U test amongst the various pairs of neighbourhoods to
> determine which differed significantly (seems like a lot of work as
> compared to a traditional post-hoc analysis following an ANOVA test?
> Anyway can these two tests then be reported as being used?
> Thanks and I apologize if this question is too basic for the group but
> I am a stressed "qualitative" geography grad student trying to
> complete a long thesis period!
> Any help would be appreciated!
The primary (but not sole) reasons for using the non-parameteric
methods in general are (1) that the measures depart so much from
having interval level characteristics that you can't trust indices
like means and standard deviations and/or (2) that the distributional
assumptions of the more traditional tests are violated to the point
where you can't trust the significance tests. If this is the case,
then you need to use analytic methods that can accomodate deal with
the questions you want answered, and non-parametric methods are one
such approach. There are other approaches that may be better
depending on which of the above has led you to not trust the
traditional tests. But the traditional non-parametric methods are not
an unreasonable way to proceed. The Mann-Whitney U is just one of
many non-paramteric appraoches you can apply. For a somewhat
technical discussion of other approaches, see the recent books by
Norman Cliff. Note that when you apply a Mann-Whitney U or Kruskal
test, you are not testing for group differences in central tendency.
Rather you are testing for differences in entrie distribtuions of
scores and you reject the null hypothesis if the two distributions
differ in any way, not just in terms of central tendency.
You can do the Mann-Whitney U test on all possible pairs of groups.
It is cumbersome, but do-able. The logic underlying this has been
developed by Dunn (1964) in an article in Technometrics titled
"Multiple comparisons using rank sums" (Volume 6, pages 241-252). The
main thing you need to concern yourself with is that by doing multiple
contrasts, you may want to control for inflated Type I errors across
the contrasts (much like you do with Tukey tests in traditional ANOVA
paradigms). Dunn recommended the traditional Bonferroni method for
controlling for multiple contrasts, but this is overly conservative.
More powerful modifications of the Bonferroni method have been
proposed since Dunn's article and you should consider using these. My
favorite is the Holm modified Bonferroni method. You can find a fairly
simple description of how to use this method in the appendix of an
article I published in the Journal of Child and Adolescent Psychology.
If you e mail me directly, I will send you a copy of the article on a
pdf file. The method also is implemented in a set of add-on programs
for SPSS at www.zumastat.com.
I should also note that in doing the above, there is no reason to do
the overall H test first. Rather, you can move directly to doing the
pairwise comparisons with the U test. The Holm procedure, like so
many other experimentwise error control procedues (such as the Tukey
hsd test), was not developed with the idea that there would be an
overall "screening" test applied before it. This is a common
misperception for a wide range of tests that control experimentwise
errors. Indeed, using an omnibus screening test first often
undermines these tests by changing the sampling distribution of the
underlying statistic. But this is a technical point that is a whole