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

 From Marta García-Granero To statalist@hsphsun2.harvard.edu Subject st: Wrong results for Wilcoxon signed ranks test when data have decimal places (even using double) Date Thu, 14 Feb 2013 17:02:36 +0100

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).
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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.
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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.
```
Thanks,
Prof. Marta Garcia-Granero, PhD
Department of Biochemistry and Genetics
University of Navarra
SPAIN.

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```