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One sided vs Two sided test


There are two kinds of hypothesis tests in statistics – one sided tests and two sided tests. The tests for which the critical region is divided into two equal parts are called two sided tests. The tests for which the critical region is a single region are called one sided tests. They are also called as one tailed and two tailed tests respectively.

The critical region (also called the rejection region) is the region where the null hypothesis is rejected if the value of the test statistic happens to lie in it. The critical regions for two tailed and one tailed tests at 95% level of significance look like as shown in the image below.

one sided vs two sided test
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How to decide whether to apply one sided or two sided test?

We generally decide whether to apply one tailed or two tailed test depending on the form in which the alternative hypothesis is stated.

If the alternative hypothesis is stated in the form of an inequality then we usually use a two sided test. For example, suppose we have the null hypothesis that the mean life of bulbs produced by a manufacturer is 5 months. If the alternative hypothesis is that the mean life is not equal to 5 months then we would apply a two sided test.

If the alternative hypothesis involves statements of the form that a parameter is greater or lesser than a given value then we use a one tailed test. For example, if the alternative hypothesis in the above example was that mean life of bulbs was less than 5 months we would use a one sided test.

One sided tests are called as directional tests since we suspect that the parameter value points towards a certain direction. Two sided tests are called non-directional tests because we are not making any claims about which direction the parameter value tends towards.

It is important to note that the critical table value for the test statistic is different depending on whether the test is one tailed or two tailed. Hence it is important to decide whether we want to do a one tailed test or a two tailed test.

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