The sign test is the simplest of the parametric tests. Its name comes from the fact that it is based on the direction ( or sings for pluses or minuses ) of a part of observation and not on their numerical magnitude.
In any problem in which sign test is used we count:
Number of + sings
Number of - sings
Number of 0 s ( i, e, which cannot be included either as positive or negative)
We take H0 p= 0.5( Null hypothesis)
If the difference is due to chance effects the probability of a +sing for any particular pair is 1/2as is the probability of a -sing. If s is the number of times the less frequent sign occurs then S has the binomial distribution with p= ½.
The critical value for a two sided alternative at α= 0.05 can be conveniently found by the expression.
K = (n -1)/ 2 -( 0.98)√n
Ho is rejected if S ≤ K for the sign tests.
The sign test can be of two types:
a.The one sample sign test
b. The paired sample sign test