## Area under a normal distribution curve–two tailed test.

The right tailed test and the left tailed test are examples of **one-tailed tests**. They are called “one tailed” tests because the (the area where you would ) is only in one tail. The two tailed test is called a two tailed test because the rejection region can be in *either * tail.

Note that, if we wanted to know if the test mean was *lower* than the accepted value (*μ* *μ*_{0}) then the representation would be reversed *i.e.* the white area representing 5% of possible values would be on the left-end of the value axis. It would still be a one–tailed test, however.

## Rejection Region for Two-Tailed Z Test (H1: μ ≠ μ 0 ) with α =0.05

**Sample question: **You are testing the hypothesis that the drop out rate is more than 75% (>75%). Is this a left-tailed test or a right-tailed test?

## One-Tailed Test: Definition & Examples - Video & …

If two means, for example, came from the *same* population, then we would expect them to both lie within the shaded blue area representing 90% of the possible values centred on the population mean (*i.e.* μ±45%). If, on the other hand, the means were from *different populations*, then we would expect one of them to fall in the either of the white areas each representing 5% of the possible values – one above, and one below, the population mean.

## The 20% Statistician: One-sided tests: Efficient and …

For example, you develop a drug which you think is just as effective as a drug already on the market (it also happens to be cheaper). You *could* run a two-tailed test (to test that it is more effective and to also check that it is less effective). But you don’t really care about it being **more** effective, just that it isn’t any less effective (after all, your drug is cheaper). You can run a one-tailed test to check that your drug is at least as effective as the existing drug.

## The results of a one-tailed test are shown in Figure 2

On the other hand, it would be inappropriate (and perhaps, unethical) to run a one-tailed test for this scenario in the opposite direction (i.e. to show the drug is more effective). This sounds reasonable until you consider there may be certain circumstances where the drug is less effective. If you fail to test for that, your research will be useless.

## One-tailed vs. two-tailed tests: Statistics Foundations: 2

In a , you have to decide if a claim is true or not. Before you can figure out if you have a left tailed test or right tailed test, you have to make sure you have a single tail to begin with. A **tail** in hypothesis testing refers to the tail at either end of a distribution curve.