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# Re: st: Wrong results for Wilcoxon signed ranks test when data have decimal places (even using double)

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Wrong results for Wilcoxon signed ranks test when data have decimal places (even using double) Date Thu, 14 Feb 2013 16:32:04 +0000

```Surprising though it may seem in the face of this carefully presented
evidence, I wouldn't call this a bug, at least not one that is
fixable.

It's an anomaly and it's awkward, but it's not a bug

First off, a look at the code for -signrank- suggests that Stata uses
-double- precision where possible, and that's as far as ado code goes.

It's an anomaly and it's awkward, but if it were a bug there would be
a solution and Marta's suggestion that there be "some rounding",
whatever that means precisely, does not sound like a good solution,
because how is StataCorp supposed to justify what rounding it does,
and how does that fit in with anybody else's idea of what the correct
procedure is, exactly and reproducibly? For example, which
authoritative accounts say you should apply some rounding first to get
reproducible results?

Also, Marta has a solid argument that when you have a rank procedure,
and data that come all presented to 2 decimal places, that you should
get exactly the same result when data are multiplied by 100 and become
integers. That's totally sound logic: the results of ranking are
invariant under multiplication of the originals by a positive
constant. But that's not only the only consideration. The other
consideration is that people reasonably expect this test to be
applicable to non-integer data and so Stata's code has to work within
the constraints that implies.

The underlying fact, often rehearsed on this list, is that Stata does
not do, and does not claim to do, exact decimal arithmetic unless
there is an exact binary equivalent of that decimal calculation. So
the heart of the matter is that Stata will very occasionally give what
look wrong answers to decimal problems, as in the case of

. di %21x  0.70 - 0.65
+1.9999999999990X-005

. di %21x  0.65 - 0.6
+1.99999999999a0X-005

Every smart child knows that the answers to these problems should be
same, but they aren't when mapped to the nearest equivalent problems
in binary.

I can't comment on exactly what SPSS does; that's clearly pertinent too.

Nick

On Thu, Feb 14, 2013 at 4:02 PM, Marta García-Granero
<mgarciagranero@gmail.com> wrote:
> Apologies for sending this twice, but yesterday I tried to piggyback into
> another thread ("Rounding Errors Stata 12"), although closely related to
> this question, and I think my question got lost. Besides, I'm going to
> explain the problem a bit more (and better).
>
> I'm converting some class notes (basic statistics) from SPSS to Stata, and I
> have found that the way Stata handles ranking tied data in Wilcoxon test can
> be sometimes wrong, when data have decimal places, even using -double-
> everywhere.
>
> The sample dataset comes from the on-line e-book Statistics at Square One
> (exercise at the end of chapter 1). I am using Stata 12.1 64 bits (last
> update installed) on W7, but I found the same problem with Stata 12.1 32
> bits on Windows XP. The results I get using Stata doesn't match the ones, I
> got either with my hand calculations, or with SPSS.
>
> set type double
> input copper
> 0.70
> 0.45
> 0.72
> 0.30
> 1.16
> 0.69
> 0.83
> 0.74
> 1.24
> 0.77
> 0.65
> 0.76
> 0.42
> 0.94
> 0.36
> 0.98
> 0.64
> 0.90
> 0.63
> 0.55
> 0.78
> 0.10
> 0.52
> 0.42
> 0.58
> 0.62
> 1.12
> 0.86
> 0.74
> 1.04
> 0.65
> 0.66
> 0.81
> 0.48
> 0.85
> 0.75
> 0.73
> 0.50
> 0.34
> 0.88
> end
>
> * One sample Wilcoxon's test (against population median = 0.6)
>
> signrank copper = 0.6
>
> * Multiply data by 100 to get rid of decimal places and running the test
> again (pop. median = 60)
> * this time all the output (positive&negative sum of ranks, Z stat&p value)
> is correct
>
> generate copper100 = round(copper*100)
> signrank copper100 = 60
>
> * Generating the ranks for absolute differences between copper & pop median
> for both variables (copper&copper100)
> * Ranks should have been the same in both cases, but they are not
> * Notice the difference for cases 5/6/7, 18/19, 22/23/24, 29/30, 32/33
> * "ranks2" is correct (recognizes all tied data), and leads to the right
> Wilcoxon's p-value
>
> egen double ranks1 = rank(abs(copper-0.6))
> egen double ranks2 = rank(abs(copper100-60))
> generate absdiff = abs(copper-0.6)
> sort absdiff
> list absdiff ranks1 ranks2
>
> I would label that as a Stata bug. Tied absolute differences are not
> recognized as so because there is a difference at the 15th decimal place.
> Maybe some rounding should be performed before assigning ranks.
>

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