Alternative hypothesis

The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test. The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect, such as zero. If your sample contains sufficient evidence, you can reject the null hypothesis and favor the alternative hypothesis. The alternative hypothesis is often denoted as H₁ or H_A.

If you are performing a two-tailed hypothesis test, the alternative hypothesis states that the population parameter does not equal the null hypothesis value. For example, when the alternative hypothesis is H_A: μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative hypothesis can test for a difference only in one direction. For example, H_A: μ > 0 can only test for differences that are greater than zero.