Interpretation of ttest command and p value

[Maeve Khaa]

Hello Statalist,

My question is about the 'ttest' command. The data includes the returns of a stock (see dataex example below). I want to test whether the returns are > 0 with significance level of 0.05. My question is whether this can be done by using the following command:

ttest returnBUYSELLMA8_0p5_2_0 == 0


The results:

Then I will have to look at the Pr(T > t) = 0.0000 value. What is the reason it is exactly 0.0000? Coincidence or does Stata not give more values after four zero's?

Thank you a lot in advance.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float returnMA8_0p5_2_0
    .3430868
           0
   .18330643
-.0006944396
  -.09748733
     .157546
    .3222847
   -.6935745
  -.20959064
    1.287822
    .3004651
  .020013265
  -.04793998
   .16305614
   -.1613806
    .6232174
   .00817757
 .0004640102
    .8821417
           0
   .06751802
 .0004664179
 -.064593524
   .02559367
   -.4879828
  -.27945906
    .0517562
  -.33261395
  -.07048872
    .1826529
    .4290987
   -.4988926
   .19883224
    .5680488
     .485252
     .255064
   .25186157
 -.003727866
 .0002330003
   .16162603
    .4853477
    .6341666
    .8092486
     .456621
     .491038
    .0912823
    .7490073
   .02282486
    .5351283
    .3565111
.00022624434
   -.6785083
   .24813333
   .29475766
     .487984
    .4525862
    .4377828
    .8644269
    .1849917
    .7047205
    .5621571
   .17880316
   .24886924
    .6587124
   1.0664852
    .1548311
    .4454558
    .5343285
  -.08766777
    .2689541
   -.8963893
    -.664264
   -.0450633
  -.09366927
 .0004545423
  .023793284
    .0896731
  -.08135593
  -.04443387
    .4749024
   .41462195
 -.035368133
    .2261495
      -.3225
    .1685291
   .22739518
    .4570766
   .25022635
    .7950564
   .05629966
    .2616592
   .02434031
  .003409075
    .3001591
   -.0120399
  -.02431818
   -.6375854
 .0004587156
   .22791554
   .12557077
end

[Nick Cox]

The test is of whether the mean is zero. As the mean is more than 5 times its standard error, the null is overwhelmingly rejected. Stata uses 4 decimal places here for P-values and 0.0000 indicates less than 0.00005. If you want to see more decimal places just go

return list 
display r(p)

afterwards.

Whether the test is what you need or want is a different question and -- in any case -- note that this t-test with returns, or any other time series, ignores serial dependence completely. But you're mixing in an approach using a fixed significance level of 0.05 and with that ritual it's sufficient to know that P << 0.05.

Again, whether that has substantive or even statistical meaning is a bigger question. The main point about a significance test is, or used to be, to stop researchers making fools of themselves by over-interpreting results from very small samples, which is not your situation.