Wilcoxon Signed Rank Test Results: Variations in p-values and z-values Compared to SPSS

Hi, I am using the signrank() function from the Matlab library.

1) To verify the p-value, h and z-value. I have compared the results with the Wilcoxon signed rank test in SPSS. I found out that in some cases the Matlab p-value is different and z-value sometimes can't be found in Matlab. May I know what the reasons that lead to these differences? I have attached the result of SPSS for references and codes for three types of cases. Only the 3rd case get the similar p-value and z-value when compared to SPSS.

2) In addition, I found out that in case 1, the result of hypothesis test (h1) gets (0 in double mode)... isn't it should get in the logical mode?

3) Is there anything I should edit in the Matlab code to get more reliable answer?

Thanks in advance.

% Perform Wilcoxon Signed Rank Test

clear
clc


load Workspace_Data_WilcoxonSignedRank

% Compare dataset for Pair1 (1st Case)
[p1,h1,stats1] = signrank(Pair1_A,Pair1_B,'tail','both','alpha',0.05,'method','approximate')    

p1 = 1

h1 = 0

stats1 = struct with fields:
    signedrank: 0

% When I perform the wilcoxon signed Rank test to Pair 1, why does h1 get (0 in double mode?) 
% supposely it should get in logical mode like Pair 2 and Pair 3. 
% Is p1 is the correct value?


% Compare dataset for Pair2 (2nd Case)
[p2,h2,stats2] = signrank(Pair2_A,Pair2_B,'tail','both','alpha',0.05,'method','approximate')    

p2 = 0.0588

h2 = logical
   0

stats2 = struct with fields:
          zval: -1.8898
    signedrank: 0

% Correct compared to 

% Compare dataset for Pair3 (3rd Case)
[p3,h3,stats3] = signrank(Pair3_A,Pair3_B,'tail','both','alpha',0.05,'method','approximate')    

p3 = 1.7344e-06

h3 = logical
   1

stats3 = struct with fields:
          zval: 4.7821
    signedrank: 465

Answer 1

[Suraj Kumar]

Hi Wei,

Based on my understanding, you are facing issues in getting the z-value in MATLAB for some cases. To resolve this issue, you can refer the following steps:

The ‘zval’ is not generated in the first case as the values are all identical. Hence, this is a degenerate case of all ties.

Now to generate the ‘zval’ in such cases , we can create a default value for ‘zval’ and generate it like this:

[p1,h1,stats1] = signrank(Pair1_A,Pair1_B,'tail','both','alpha',0.05,'method','approximate')  ;   
if ~isfield(stats1, 'zval')  
    stats1.zval = nan;  
end 
[p,h,statsrnd1] = signrank(Pair1_A,Pair1_B+randn(size(Pair1_B))); 
statsvector1 = [stats1;statsrnd1] 

Additionally, the type of the hypothesis result being returned as double instead of logical is also due to the values being treated as ties.

‘signrank’ function uses a tolerance defined as ‘epsdiff = eps(x) + eps(y)’. It calculates the absolute differences and considers values with ‘abs(d(i)) < epsdiff’ as ties.

To know more about this, you can refer to the following documentation link:

https://www.mathworks.com/help/stats/signrank.html#:~:text=For%20the%20two%2Dsample%20case%2C%20signrank%20uses%20a,d(i))%20%3C%20epsdiff(i))%20are%20treated%20as%20ties.

Hope this answers your query!