Why I am getting Same p-value, h and stats while using Wilcoxon Rank test for 7 different data set?

Question

Meghraj Kc 2022-6-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1739585-why-i-am-getting-same-p-value-h-and-stats-while-using-wilcoxon-rank-test-for-7-different-data-set

编辑： the cyclist 2022-6-13

I am trying to find the significant realtion between the az_solar and Mean_Surface_REF of seven different bands using Wilcoxon rank test. But I am geeting same p-value and statistics for every bands. However, each band contains different value.

Would some one please help me regrading these issue?

%% This is the code i am using

[p1,h1,stats1] = ranksum(az_solar,Mean_Surface_REF(:,1));

[p2,h2,stats2] = ranksum(az_solar,Mean_Surface_REF(:,2));

[p3,h3,stats3] = ranksum(az_solar,Mean_Surface_REF(:,3));

[p4,h4,stats4] = ranksum(az_solar,Mean_Surface_REF(:,4));

[p5,h5,stats5] = ranksum(az_solar,Mean_Surface_REF(:,5));

[p6,h6,stats6] = ranksum(az_solar,Mean_Surface_REF(:,5));

[p7,h7,stats7] = ranksum(az_solar,Mean_Surface_REF(:,7));

Results:

8.1275311e-44

Also, I have attached my dataset.

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Answer 1

dpb 2022-6-13

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https://ww2.mathworks.cn/matlabcentral/answers/1739585-why-i-am-getting-same-p-value-h-and-stats-while-using-wilcoxon-rank-test-for-7-different-data-set#answer_984945

在 MATLAB Online 中打开

taz=readmatrix('az_solar.xlsx').';
>> [mean(taz) std(taz)]
ans =
  138.9109     16.7621
>>
>> mnref=readmatrix('Mean_Surface_REF.xlsx');
>> [mean(mnref); std(mnref)]
ans =
    0.0030    0.0065    0.0166    0.0093    0.0013    0.0045    0.0049
    0.0034    0.0023    0.0043    0.0034    0.0039    0.0053    0.0052
>> 

pretty-much explains it -- the means are some 4-5 orders of magnitude between the one vector and any of the vectors in the array. You've just totally saturated the value of the test statistic to the point the p-value returned is essentially zero.

You'd have been able to determine this yourself if you had simply looked at your data before blindly throwing it at some test statistic.

>> [p,h,stats]=ranksum(taz,mnref(:,1))
p =
   8.0633e-44
h =
  logical
   1
stats = 
  struct with fields:
       zval: 13.8827
    ranksum: 25026
>> format long, format compact
>> 1-normcdf(stats.zval)
ans =
     0
>> normcdf(stats.zval)
ans =
     1
>> normcdf(stats.zval)
ans =
     1
>> 

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Answer 2

the cyclist 2022-6-13

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https://ww2.mathworks.cn/matlabcentral/answers/1739585-why-i-am-getting-same-p-value-h-and-stats-while-using-wilcoxon-rank-test-for-7-different-data-set#answer_984970

编辑：the cyclist 2022-6-13

在 MATLAB Online 中打开

That test statistic only depends on the count and relative ordering of the respective set elements. In your case, it looks like the counts are always the same, and (as @dpb points out), your 7 cases are always completely offset from the comparator set.

Here is a small example showing the same thing:

x = 1:5;
y1 = 101:105; % 5 elements, fully offset from x
y2 = 1001:1005; % Also 5 elements, fully offset from x [same result]
y3 = 101:103; % 3 elements, still fully offset [different result due to different count]
ranksum(x,y1)
ans = 0.0079
ranksum(x,y2)
ans = 0.0079
ranksum(x,y3)
ans = 0.0357