Directional and nondirectional hypotheses

A nondirectional alternative hypothesis (H1) simply states that the null hypothesis (H0) is wrong. It does not predict whether the parameter of interest is larger or smaller than the reference value specified in H0.

A directional H1 states that H0 is wrong, and also specifies whether the true value of the parameter is greater than or less than the reference value specified in H0.

Examples:

·    Nondirectional - A researcher has results for a sample of students who took a national exam at a particular high school. The researcher wants to know if the scores at that school differ from the national average of 850. A nondirectional H1 is appropriate because the researcher is interested in determining if the scores are either less than or greater than the national average. (H0: m = 850 vs. H1: m does not equal 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 H1 may be used because the researcher is specifically hypothesizing that scores for trained students are greater than the national average. (H0: m = 850 vs. H1: m > 850)

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

For example, suppose a researcher predicts that trained students do better on an exam than the national average (H1: m > 850). With this directional hypothesis, the test is more likely to detect a positive effect of training on test scores. However, the test will not be able to detect a negative effect at all. If for some reason the training actually makes students do worse on the exam (that is, m is actually less than 850), the test will not be able to detect this.