Suppose I have $H_0: \beta = 0$ vs $H_1: \beta \neq 0$. My data tells me that I don't reject the null, with a p-value of approximately 0.06.

Then out of curiosity, since by the scientific theory one would expect $\beta<0$, I test $H_0: \beta \geq 0$ vs $H_1: \beta < 0$, and the data says that we should reject the null, with a p-value of 0.03...

I get the reason why we're having these two different conclusions has to do with the different quantiles we're using.

However, how should I conclude in this situation?

  • $\begingroup$ stats.stackexchange.com/questions/407009/… $\endgroup$ – An old man in the sea. May 7 at 17:08
  • $\begingroup$ Ideally, you should choose a test before you do your experiment, and stick with it, rather than going "test-shopping". Given any data set and a sufficiently rich collection of different possible tests, it s almost certain that you can find one that lets you reject the null hypothesis, even if the null hypothesis happens to be true. $\endgroup$ – Robert Israel May 7 at 18:46
  • $\begingroup$ @RobertIsrael Thanks for your comment ;) $\endgroup$ – An old man in the sea. May 8 at 21:56

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