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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
RANGE Range is the difference between the highest and the lowest value is series. This is the simplest absolute measure of dispersion. Symbolically : R= L- S
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