p val > 1 in ExactMannWhitneyUTest

[nw11]

A = [ 1.34937, 1.75722,0.276514, 1.04546 , 1.69085 , 0.738085, 2.36313 ]
B = [ 2.62325 , 1.16533 , 1.1327  ,  0.728714]

julia>ExactMannWhitneyUTest(A,B)
Exact Mann-Whitney U test
-------------------------
Population details:
    parameter of interest:   Location parameter (pseudomedian)
    value under h_0:         0
    point estimate:          0.20035500000000006

Test summary:
    outcome with 95% confidence: fail to reject h_0
    two-sided p-value:           1.0727272727272728

Details:
    number of observations in each group: [7, 4]
    Mann-Whitney-U statistic:             14.0
    rank sums:                            [41.0, 25.0]
    adjustment for ties:                  0.0

[ararslan]

Wow, that's extraordinarily probable.

[andreasnoack]

I'm not sure this is really a bug. It is a standard issue with two-sided p-values. I've previously made this comment although the issue here isn't that the distribution is asymmetric but that the test statistic happens to be the middle outcome of the discrete distribution. Hence, the middle observation is counted twice. I don't think it is big deal. Asymptotically, it won't be larger than one.

[ararslan]

It's pretty jarring as a user. Perhaps we could just add a clamp(pval, 0, 1) when showing the value?

[nalimilan]

I guess we should do whatever other software do.

[ararslan]

I don't recall ever having seen a value outside of [0, 1] for p-values in R or SAS.

[bjarthur]

glad i'm not the only one who came across this!

[rpgowers]

I also found this for a case where U1 = U2, e.g.

a = [12,10,7,6,3,1]
b = [11,9,8,5,4,2]

Where

MannWhitneyUTest(a,b)

yields an error:

Exact Mann-Whitney U test
-------------------------
Population details:
    parameter of interest:   Location parameter (pseudomedian)
    value under h_0:         0
    point estimate:          0.0

Error showing value of type ExactMannWhitneyUTest{Float64}:
ERROR: p-values must be in [0; 1]

whilst
pvalue(MannWhitneyUTest(a,b))
simply gives 1.0627705627705626 without any kind of warning.

[pdeffebach]

R clamps at 1

r$> a = c(12, 10, 7, 6, 3, 1)                                              

r$> b = c(11, 9, 8, 5, 4, 2)                                               

r$> m = wilcox.test(a, b)                                                  

r$> m$p.value                                                              
[1] 1