# Are one-sided tests inferior to two-sided tests?

I recently did a one-sided test for a homework question. This ended up being graded as correct. However, one of my group mates is a stat major and he said that most professional statisticians use only two-sided tests because using a one-sided test halves the p-value and therefore makes reporting results less accurate or misleading.

Are one-sided tests somehow inferior to two-sided tests? Is it improper to use one-sided tests in practice?

I don't understand what the point is in teaching them if we aren't supposed to use them for actual statistical work.

• No, they are both fair; it depends on your null hypothesis. – Jon Oct 12 '16 at 3:12
• It depends on circumstances. In some application areas they're seen as anathema (perhaps due to people applying them post hoc - but pretending they didn't, to get significance). But there are any number of situations where one tailed tests make complete sense. – Glen_b Oct 12 '16 at 3:28
• If you have a one sided problem then you should use a one sided test. In some way they are (sometimes better) because some one sided tests can be shown to be uniformly most piwerful. – user83346 Oct 12 '16 at 4:41
• which one-sided test did you use and why ,? How do you define one-sided test ? – Subhash C. Davar Apr 7 '18 at 9:30

Your group mate doesn't know what he's talking about. It depends on what you're interested in. For example, if you were a pharmaceutical company trying to determine whether a new drug lowers blood pressure, you'd want $H_0 : \theta \geq 0$ and $H_A : \theta < 0$ where $\theta$ is, say, the difference in before and after blood pressure.

Regarding "halving the p-value" what that refers to is that for your garden-variety t-test for a mean, at the same value of $\bar{x}$, your sample mean, the p-value is doubled because under the null hypothesis you are computing $P(|\frac{\bar{x}}{s/\sqrt{n}}| > Z)$ or $P(-|\frac{\bar{x}}{s/\sqrt{n}}| < Z)$ where $Z$ is a standard normal random variable. This is because we only care about the magnitude of the difference.

On the other hand, for a one-sided test you only care about one direction. So we could compute just $P(\frac{\bar{x}}{s/\sqrt{n}} > Z)$ for example. This is related to the idea of statistical power. Yes, the p-value is lower for the same value of the sample mean, but this could be good or bad. If you're only going to be going forward with a drug trial if it reduces the symptoms, it could make things worse for all you care and that could be just as much a reason not to continue as if it does nothing.

• So if the drug company finds it makes you worse they are obliged to suppress that result? – mdewey Oct 12 '16 at 8:54
• I wouldn't say that at all. But this does highlight a quirk, if you want to call it that, in classical hypothesis testing which is that you have to state what you're looking for before you look for it. Otherwise you could end up in the trap of testing hypotheses suggested by the data, no? Your comment also highlights the need for solid reasoning to accompany statistics. A p-value alone is meaningless, so even a "non-significant" result could be cause for further investigation and using p-value thresholds to determine releasing or not can be tricky and wrong. – Josh Magarick Oct 12 '16 at 23:27

However, one of my group mates is a stat major and he said that most professional statisticians use only two-sided tests because using a one-sided test halves the p-value and therefore makes reporting results less accurate or misleading.

This is silly. I would say that's an inaccurate statement.

Even if true, there are far worse things that could increase you False Discovery Rate (FDR) such as data that does not follow a nice Normal distribution, or for nonparametric tests, data that does not follow assumptions. Another item often ignored is large sample sizes, which can also affect FDR.

One sided tests are valid if the research question is concerned with a single side of the distribution.