Is my boss correct in saying that the p-value given with a paired t-test
should 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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Date
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January 1999; updated July 2005
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Your boss is wrong, but it’s not surprising that she/he would think
this. 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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