16. Non-parametric Tests

# 16.3 Paired Sample Sign Test

Here we have two measurements from each subject, typically before and after. If the difference between measurements is , assign a , if , assign a , if 0 assign a 0. (Be sure to keep the direction of subtraction consistent with the hypothesis.) We again have 2 cases, for small ( ) and large ( ) samples, as with the median sign test. The critical and test statistics are the same as the median sign test. We’ll work through an example with a small sample.

Example 16.5 : We have the following data on number of ear infections on swimmers before and after taking a medication that is hypothesized to prevent infections :

 Swimmer Infections before, Infections after, Difference ( ) A 3 2 + B 0 1 – C 5 4 + D 4 0 + E 2 1 + F 4 3 + G 3 1 + H 5 3 + I 2 2 0 J 1 3 –

In the last column, we have assigned when , when and when . We are interested in reduced infections so is “good” for this situation. Test if the reduction in infections is significant.

1. Hypothesis. : MD difference 0 : MD difference 0

2. Critical statistic.

Use the Sign Test Critical Values Table with = (no. of ) + (no. of ) = 7 + 2 = 9 and with a one-tailed test to find 3. Test statistic. 4. Decide. so do not reject .

5. Interpretation.

There is not enough evidence to say that there is a reduction in the number of infections. 