Wilcoxon Signed Rank Test (one tail)

[Gabe Gladstein]

Hi,
I'm conducting a Wilcoxon Signed Rank Test for non-normally distributed data taken before and after a treatment is applied. My research hypothesis is that the treatment should lead to an increase, but the Wilcoxon test is two-tailed and thus only measures a significant difference in medians but provides no directionality, that I know of. Is there a way to make the Wilcoxon test indicate directional significance (like a one-tailed t test would)?

[Marcos Almeida]

For this, you may wish to use - signtest - instead.

[Bruce Weaver]

Hi Gabe. I'll start with a disclaimer. Use of a one-tailed test implies that one is perfectly happy--and it is perfectly sensible--to treat a huge difference in the "wrong" direction equivalently to a zero difference. There may be some circumstances where that is sensible and justifiable; but given that those circumstances are fairly rare, most authors recommend using two-tailed tests (virtually) always. (The concern is that the decision to use a one-tailed test may be post hoc, after the effect is confirmed to be in the "right" direction.)

What is your sample size? If it is large enough to justify using the z-test you get from signrank, you can just compute the one-tailed p-values yourself via the normal() function. E.g.,

clear
webuse fuel
signrank mpg1 = mpg2
display "Prob < z = " normal(r(z)) "     Prob > z = " 1-normal(r(z))

Output:

. clear

. webuse fuel

. signrank mpg1 = mpg2

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        3        13.5        38.5
    negative |        8        63.5        38.5
        zero |        1           1           1
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -1.63
adjustment for zeros      -0.25
                     ----------
adjusted variance        160.63

Ho: mpg1 = mpg2
             z =  -1.973
    Prob > |z| =   0.0485

. display "Prob < z = " normal(r(z)) "     Prob > z = " 1-normal(r(z))   
Prob < z = .02427202     Prob > z = .97572798