# What is the difference between a two-tailed and a one-tailed test?

2015-09-17

A statistical test is based on two competing hypotheses: the null hypothesis H0 and the alternative hypothesis Ha.

The type of alternative hypothesis Ha defines if a test is one-tailed or two-tailed.

## Two-tailed tests

A Two-tailed test is associated to an alternative hypotheses for which the sign of the potential difference is unknown. For example, suppose we wish to compare the averages of two samples A and B. Before setting up the experiment and running the test, we expect that if a difference between the two averages is highlighted, we do not really know whether A would be higher than B or the opposite. This drives us to choose a two-tailed test, associated to the following alternative hypothesis: Ha: average(A) ≠ average(B). Two-tailed tests are by far the most commonly used tests.

## One-tailed tests

A One-tailed test is associated to an alternative hypothesis for which the sign of the potential difference is known before running the experiment and the test. In the example described above, the alternative hypothesis related to a one-tailed test could be written as follows: average(A) < average(B) or average(A) > average(B), depending on the expected direction of the difference.

In all of the XLSTAT statistical test dialog boxes, the user is able to choose between two-tailed or one-tailed tests (Options tab, usually).

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