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Kim, in principle, in the hypothesis testing paradigm, the argument that 
p-values need adjustment for multiplicity of comparisons applies exactly 
the same for parametric and non-parametric analyses - though the user 
needs to be aware that, in contrast to the parametric case, for a given 
sample size the p-value can take only a finite set of possible values, 
which can be quite small for small sample sizes.

BUT - we always need to consider very carefully whether the p-value is 
really the most helpfully informative measure of strength of effect or 
strength of evidence. Arguably, it is a flawed measure of strength of 
evidence (as it only relates to the weight of evidence against H0, not the 
weight of evidence favouring H1), and a quite useless measure of strength 
of effect - for instance, it cannot be interpreted meaningfully except in 
relation to the sample size. There is a growing emphasis on use of 
interpretable effect size measures, with CIs, rather than p-values as the 
main basis for inferences. Both absolute and relative effect size measures 
are available, for comparisons of means, comparisons of proportions, and 
relative measures such as U/mn = AUROC as a better expression of the 
outcome of a Mann-Whitney comparison. Effect size measures relate 
primarily to measurement, not to coincidence, so there is not such a 
compelling reason to adjust for multiple comparisons - only if you are 
really using the CI to see whether it includes the H0 value, i.e. 
significance testing by the back door. No, these effect size measures are 
interpretable in their own right. Some of them are of course already very 
well known and widely used - e.g. for two independent proportions, their 
difference, ratio and odds ratio. The ones relating to non-parametrics are 
less well known, but also potentially extremely useful. 

For a general introduction to effect sizes, see RJ Grissom & JJ Kim, 
Effect Sizes for Research, 2nd edition, Routledge, and my book - link 
below. At my website there is an Excel spreadsheet to calculate a CI for 
the U/mn measure, which also points to my 2006 articles that describe this 
measure and how to calculate a CI for it. 

Hope this helps.

Robert G. Newcombe PhD CStat FFPH HonMRCR
Professor of Biostatistics
Cochrane Institute of Primary Care and Public Health
School of Medicine
Cardiff University
4th floor, Neuadd Meirionnydd
Heath Park, Cardiff CF14 4YS

Tel: (+44) 29 2068 7260

My book Confidence Intervals for Proportions and Related Measures of 
Effect Size is now published.

Available at http://www.crcpress.com/product/isbn/9781439812785

See http://www.facebook.com/confidenceintervals

Home page http://medicine.cf.ac.uk/person/prof-robert-gordon-newcombe/






From:   Kim Pearce <[log in to unmask]>
To:     [log in to unmask], 
Date:   26/11/2013 12:20
Subject:        Multiple comparisons correction - non parametric tests
Sent by:        A UK-based worldwide e-mail broadcast system mailing list 
<[log in to unmask]>

Hello everyone,

This is just a very quick question.  When applying 'multiple comparisons' 
adjustments  to p values from a table of statistical tests, all of the 
papers/texts I have ever encountered have dealt with p values derived from 
parametric statistics (Pearson's correlation coefficient, ANOVA etc).  Am 
I correct in thinking that such multiple comparisons corrections e.g. 
sequential Bonferroni can also be applied to p values from non parametric 
tests?

Many thanks for your advice on this matter,

Kind Regards,

Dr Kim Pearce PhD, CStat
Senior Statistician
Haematological Sciences
Institute of Cellular Medicine
William Leech Building
Medical School
Newcastle University
Framlington Place
Newcastle upon Tyne
NE2 4HH

Tel: (0044) (0)191 282 0451

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