Would using two one-tailed tests rather than one two-tailed test increase the significance of a hypothesis test, all else equal?

Question

Since a smaller sample is needed to reach a given level of significance for a one-tailed test than a two-tailed test, why not just run two one tailed-tests on both sides?

I understand that taking a one-tailed test, in many cases, makes unjustified assumptions about the direction of the effect under question, but why can't this simply be mitigated by taking the opposite one-tailed test as well?

It seems this way combines the best of one-tailed tests (increased significance) and two-tailed tests (avoiding bias).

Answer 1

The "advantage" of one-sided tests that you refer to is that - by using the same significance level as for a two-sided test - you are essentially willing to make twice as many false rejections in your preferred direction under the null hypothesis.

It is a misconception that this is really an advantage, it is a particular choice by the researcher that favors a particular outcome. In most fields where one-sided and two-sided tests are done, it is standard to use twice the significance level for two-sided tests. At that point the "advantage" of one - sided tests goes away.

Doing two one-sided tests does indeed result in a two-sided test, but one with a type one error rate that is the sum of those of the one-sided tests.