>>>>> "MM" == Martin Maechler <[EMAIL PROTECTED]>
>>>>> on Wed, 16 Jul 2008 18:02:47 +0200 writes:
>>>>> "MC" == Mark Cowley <[EMAIL PROTECTED]>
>>>>> on Wed, 16 Jul 2008 15:32:30 +1000 writes:
MC> Dear list,
MC> I am analysing a set of quantitative proteomics data
MC> from 16 patients which has a large numbers of missing
MC> data, thus some proteins are only detected once, upto a
MC> maximum of 16. I want to test each protein for
MC> normality by the Shapiro Wilk test (function
MC> shapiro.test in package stats), which can only be
MC> applied to data with at least 3 measurements, which is
MC> fine. In the case where I have only 3 observations, and
MC> two of those observations are identical, then the
MC> shapiro.test produces negative P-values, which should
MC> never happen. This occurs for all of the situations
MC> that I have tried for 3 values, where 2 are the same.
MM> Yes. Since all such tests are location- and scale-invariant, you
MM> can reproduce it with
MM> shapiro.test(c(0,0,1))
MM> The irony is that the original papers by Roydon and the R help
MM> page all assert that the P-value for n = 3 is exact !
MM> OTOH, the paper [Roydon (1982), Appl.Stat 31, p115-124]
MM> clearly states that
MM> X(1) < X(2) < X(3) ... < X(n)
MM> i.e., does not allow "ties" (two equal values).
MM> If the exact formula in the paper were evaluated exactly
MM> (instead with a rounded value of about 6 digits),
MM> the "exact P-value" would be exactly 0.
I have now slightly increased the precision in some of the
calculations involved, and also make sure that P-value >= 0
for n == 3.
This is now in both R-patched and R-devel.
Thank you, Marc, for the report!
But really, back to your data analysis question :
I cannot imagine that the P-value of a Shapiro-Wilks test with
n=3 (non-NA) observations is a good tool to help you draw valid
conclusions about your data ....
We have had several threads (on R-help) about the (non)sense of
normality testing...
MM> Now that would count as a bug in the paper I think.
The bug is not in Roydon's math-stat paper, but arguably in the
Fortran code that was published in the accompanying paper...
MM> More about this tomorrow or so.
Martin Maechler, ETH Zurich
MC> Reproducible code below:
MC> # these are the data points that raised the problem
>>> shapiro.test(c(-0.644, 0.0566, 0.0566))
MC> Shapiro-Wilk normality test
MC> data: c(-0.644, 0.0566, 0.0566)
MC> W = 0.75, p-value < 2.2e-16
>>> shapiro.test(c(-0.644, 0.0566, 0.0566))$p.value
MC> [1] -7.69e-07
MC> # note the verbose output shows a small, but positive P-value, but
MC> when you extract that P using $p.value, it becomes negative
MC> # various other tests
>>> shapiro.test(c(1,1,2))$p.value
MC> [1] -8.35e-07
>>> shapiro.test(c(-1,-1,2))$p.value
MC> [1] -1.03e-06
MC> cheers,
MC> Mark
>>> sessionInfo()
MC> R version 2.6.1 (2007-11-26)
MC> i386-apple-darwin8.10.1
MC> locale:
MC> en_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8
MC> attached base packages:
MC> [1] tcltk graphics grDevices datasets utils stats
MC> methods base
MC> other attached packages:
MC> [1] qvalue_1.12.0 Cairo_1.3-5 RSvgDevice_0.6.3
MC> SparseM_0.74 pwbc_0.1
MC> [6] mjcdev_0.1 tigrmev_0.1 slfa_0.1
MC> sage_0.1 qtlreaper_0.1
MC> [11] pajek_0.1 mjcstats_0.1 mjcspot_0.1
MC> mjcgraphics_0.1 mjcaffy_0.1
MC> [16] haselst_0.1 geomi_0.1 geo_0.1
MC> genomics_0.1 cor_0.1
MC> [21] bootstrap_0.1 blat_0.1 bitops_1.0-4
MC> mjcbase_0.1 gdata_2.3.1
MC> [26] gtools_2.4.0
MC> -----------------------------------------------------
MC> Mark Cowley, BSc (Bioinformatics)(Hons)
MC> Peter Wills Bioinformatics Centre
MC> Garvan Institute of Medical Research, Sydney, Australia
MC> ______________________________________________
MC> R-help@r-project.org mailing list
MC> https://stat.ethz.ch/mailman/listinfo/r-help
MC> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
MC> and provide commented, minimal, self-contained, reproducible code.
MM> ______________________________________________
MM> R-help@r-project.org mailing list
MM> https://stat.ethz.ch/mailman/listinfo/r-help
MM> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
MM> and provide commented, minimal, self-contained, reproducible code.
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