Conflicting unilateral and bilateral tests. How to proceed?

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?

• stats.stackexchange.com/questions/407009/… – An old man in the sea. May 7 at 17:08
• 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. – Robert Israel May 7 at 18:46
• @RobertIsrael Thanks for your comment ;) – An old man in the sea. May 8 at 21:56