Sign Test

Posted in Statistics, Total Reads: 777
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Definition: Sign Test

The sign test is used to test the hypothesis that there is no difference in medians between two continuous distributions of random variables. This does not require the assumption that the population is normally distributed.


Data:

The data consists of n observations, x1, x2, . . . , xn, drawn from a population with unknown median h.


Assumptions:

The sample is selected randomly from a continuous probability distribution.


Hypothesis:

(A) Right-tailed Test

H0: h = h0

Ha: h > h0


(B) Left-tailed Test

H0: h = h0

Ha: h < h0


(C) Two-tailed Test

H0: h = h0

Ha: h ¹ h0


Test Statistics:

(A) Right-tailed Test

S+ = Number of sample measurements greater than h0.


(B) Left-tailed Test

S- = Number of sample measurements less than h0.


(C) Two-tailed Test

S = maximum of S+ and S-


A significance level of 95% is generally used. This test is commonly used for non- normally distributed data and when the number of data points in the sample is low.

 

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