Should the p-value given with a paired t-test always be lower than the signrank?

Usually, the ttest p-value is smaller than the signrank p-value, but it’s easy to see that this is not always true. Here is an example:

. list



     
      x 


     
 


  1. 
      1 


  2. 
      2 


  3. 
      3 


  4. 
      4 


  5. 
      5 


     
 


  6. 
      6 


  7. 
      7 


  8. 
      8 


  9. 
  10000 


 10. 
 -10036 





. ttest x=0

One-sample t test



Variable 
 
     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]

 
 
 

       x 
 
      10           0    1493.398    4722.541   -3378.302    3378.302


    mean = mean(x)                                                t =   0.0000
Ho: mean = 0                                     degrees of freedom =        9

    Ha: mean < 0                 Ha: mean != 0                 Ha: mean > 0
 Pr(T < t) = 0.5000         Pr(|T| > |t|) = 1.0000          Pr(T > t) = 0.5000

 
. signrank x = 0
 
Wilcoxon signed-rank test


    sign 
 
      obs   sum ranks    expected

 
 
 

positive 
 
        9          45        27.5

negative 
 
        1          10        27.5

    zero 
 
        0           0           0

 
 
 

     all 
 
       10          55          55


unadjusted variance  
     96.25

adjustment for ties  
      0.00

adjustment for zeros 
      0.00

                     
 

adjusted variance    
     96.25

Ho: x = 0
             z =   1.784
 Prob > |z| =   0.0745