How many tails do you have, if you’ll forgive the expression?

Q: I have been told that my distribution is “single tailed”. What does it mean? Is this something I should feel guilty about?

A: Not at all. In fact it has nothing to do with your anatomy. Here is the explanation of its meaning:
Generally speaking, when you are testing a hypothesis you want to know if there is any difference between two treatments.
If there is no difference, we call it “null hypothesis”, (“nullus” meaning “not any” in Latin), and statisticians always make this a priori assumption. If, after the statistical test, they find no difference between treatments, they assume the NULL HYPOTHESIS. If, on the contrary they find a difference, they REJECT the null hypothesis, and therefore accept the ALTERNATIVE HYPOTHESIS. That is how it works. 

Now, pay attention: If you are comparing A against PLACEBO, there is only ONE possible alternative hypothesis (The null hypothesis is A is equal to placebo, i.e. there is no difference between them):
A is better than placebo
(…but you would not even consider the possibility that placebo is better than A, because that would mean that A, instead of a treatment, is a risk factor).


But if you are comparing drug A against drug B, then we have TWO possible alternative hypotheses:
A is better than B
B is better than B

In the first case (A against placebo) we call it a SINGLE-TAILED distribution. In the second (A against B) we call it DOUBLE-TAILED a distribution.

And, to answer a message from a male reader of the blog (in case some others share the same doubt): no, double tailed distributions will not enhance your sexual life. You have a terrible misconception. 

Thanks for reading