16.3 Paired Sample Sign Test

Gordon E. Sarty

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 $< 0$ , assign a $-$ , if $>0$ , 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 ( $N < 26$ ) and large ( $n \geq 26$ ) 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, $x_{b}$	Infections after, $x_{a}$	Difference ( $x_{b} - x_{a}$ )
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 $x_{b} - x_{a} > 0$ , $-$ when $x_{b} - x_{a} < 0$ and $0$ when $x_{b} - x_{a} = 0$ . We are interested in reduced infections so $+$ is “good” for this situation. Test if the reduction in infections is significant.