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.