SIGN TEST

Earlier we discussed the binomial test. You used the binomial distribution to test different hypotheses. Now we are going to study the sign test, which is based on the binomial distribution. When the sample size in our experiment is 25 or smaller, we can evaluate the results by using the binomial distribution as the sampling distribution.

The sign test measures the significance of the difference between two treatment conditions. It is used with two groups that are matched. You choose this test when you are concerned with the direction of differences, which you indicate by a plus or a minus sign. When using the sign test you analyze every matched pair's scores, recording whether the sign of the difference between a pair is negative or positive. If the scores of a pair are the same, you disregard that pair. The pertinent requirement for this test is that each pair is matched on the important variable that you are studying . The actual test of significance is based on the chi-square table (if fewer than 25 samples) and the z statistic if the sample is larger than 25. The requirements for the sign test are as follows :

1. Ordinal data

2. Two- group test

3. Related groups

4. When a pair of observations are tied, neither is used

5. Plus and minus signs are used to indicate differences

What we are trying to find out is whether the number of plus signs exceeds the number of minus signs. If the two are the same, then there is no difference. The symbols used are: x = the number of pluses or the number of minuses, whichever is less, and N = total number of pluses and minuses in the group.

The frequency of occurrence of a particular plus or minus sign can be determined by looking at the probabilities table for the binomial distribution, when p and q both are equal to 1/2 _.