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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
Date January 1999; updated July 2005; minor revisions July 2011

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
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