Comparison of directional hypotheses and nondirectional hypotheses

A nondirectional alternative hypothesis states that the null hypothesis is wrong. A nondirectional alternative hypothesis does not predict whether the parameter of interest is larger or smaller than the reference value specified in the null hypothesis.

A directional alternative hypothesis states that the null hypothesis is wrong, and also specifies whether the true value of the parameter is greater than or less than the reference value specified in null hypothesis.

The advantage of using a directional hypothesis is increased power to detect the specific effect you are interested in. The disadvantage is that there is no power to detect an effect in the opposite direction.

Example of directional and nondirectional hypotheses

Nondirectional
A researcher has results for a sample of students who took a national exam at a high school. The researcher wants to know if the scores at that school differ from the national average of 850. A nondirectional alternative hypothesis is appropriate because the researcher is interested in determining whether the scores are either less than or greater than the national average. (H0: μ = 850 vs. H1: μ≠ 850)
Directional
A researcher has exam results for a sample of students who took a training course for a national exam. The researcher wants to know if trained students score above the national average of 850. A directional alternative hypothesis can be used because the researcher is specifically hypothesizing that scores for trained students are greater than the national average. (H0: μ = 850 vs. H1: μ > 850)
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