Should the p-value given with a paired t-test
always be lower than the signrank?
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Title
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Comparing p-values between a paired t-test and a signrank
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Author
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Bill Sribney, StataCorp
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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
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| Variable | | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] |
| | | |
| x | | 10 0 1493.398 4722.541 -3378.302 3378.302 |
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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
