SING TEST

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