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

[Marta García-Granero <mgarciagranero@gmail.com>]

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.

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









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