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

 Title Comparing p-values between a paired t-test and a signrank Author Bill Sribney, StataCorp

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

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