A non-parametric test for a hypothesis , according to which a random variable has a binomial distribution with parameters . If the hypothesis is true, then
and is the beta-function. According to the sign test with significance level , , the hypothesis is rejected if
where , the critical value of the test, is the integer solution of the inequalities
The sign test can be used to test a hypothesis according to which the unknown continuous distribution of independent identically-distributed random variables is symmetric about zero, i.e. for any real ,
In this case the sign test is based on the statistic
which is governed by a binomial law with parameters if the hypothesis is true.
Similarly, the sign test is used to test a hypothesis according to which the median of an unknown continuous distribution to which independent random variables are subject is ; to this end one simply replaces the given random variables by .
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|||E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986)|
|||B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)|
|||N.V. Smirnov, I.V. Dunin-Barkovskii, "Mathematische Statistik in der Technik" , Deutsch. Verlag Wissenschaft. (1969) (Translated from Russian)|
Sign test. M.S. Nikulin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sign_test&oldid=16925