Paired sample sign Test
Paired samples sign test is applied to a situation where two sample are taken from two population which have continuous symmetrical distributions and known to be non normal such that the probability of having the first sample value less than the corresponding second value as well as the probability of having the first sample value more than the corresponding second sample (p) is ½.
The observations of the samples are modified as follows
This sing test has very important application in problems involving paired data such as data relating to the collection of an accounts receivable before and after a new collection policy responses of mother and daughter towards ideal family size etc, in these problems each pair of sample values can be replaced with a plus sign if first value is greater than the second a minus sign if the first value is smaller than the second or be discarded it the two value are equal.
The we proceed in the same manner as in one sample sign test.
The sign test in most often employed for observation that have been randomly selected in pairs using a paired difference experiment. The sign test is one of the few tests that can be employed when the only information available is A observation exceeds a B observation ( or vice versa). However the sign test can also be used to compare two population distributions where samples of equal size new been randomly and independently selected from the two populations. Then the pairs are formed by randomly matching each observation in samples A with an observation in samples B.