EXAMPLE 9.16

The sign test as a goodness-of-fit test. A study of the effect of the full moon on aggressive behaviors of dementia patients included 15 patients, 14 of whom exhibited a greater number of aggressive behaviors on moon days than on other days. The sign test (page 472) tests the null hypothesis that patients are equally likely to exhibit more aggressive behaviors on moon days than on other days. Because the sample proportion is and the null hypothesis is

To look at these data from the viewpoint of goodness of fit, we think of the data as two counts: patients who had a greater number of aggressive behaviors on moon days and patients who had a greater number of aggressive behaviors on other days.

550

If the two outcomes are equally likely, the expected counts are both 7.5 (). The expected counts are both greater than 5, so we can proceed with the significance test.

The test statistic is

We have so the degrees of freedom are 1. From Table F, we conclude that