Question

In most research situations, we use a two-tailed test instead of a one-tailed test (even in the case of a directional hypothesis). Why?

Answer 1

One - tailed test :

A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both.  One- tailed test is only justified if you have a specific prediction about the direction of the difference and you are completely uninterested in the possibility that the opposite outcome could be true.

For example, we may wish to compare the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. A one - tailed test will test if the mean is significantly greater than x or significantly less than x, not both simultaneously.

Two- tailed test:

Whereas ,a two - tailed test will test both the greater than & less than scenarios simultaneously. A two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction.

For example, we may wish to compare the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.

In most cases, Two - tailed test is preferred over One - tailed test because of its ability to test the significance in both the directions.

Hope, I answered your query.