Chi square test - hypothesis testing, Operation Research

Chi Square Test ( X2)

Chi Square Test Defined  the chi square test is one  simplest  and most  commonly  used non parametric tests in statistical work. The Greek letter X2 is used  to denote this test. The quantity X2 describes the  magnitude of  discrepancy between  the observed and expected frequencies. The value of  X2 is calculated as,

X2 = [ ( O i -E i)2/ E i]  =  ( O-E1)2/E1  +  ( O2-E2)2/E2

+ ( O3-E3)2/E3  +  ( O4-E4)2/E4......... ( O-En)2/En

Here  O1, O2, O3,..........On are observed frequencies as E1, E2, E3, ......En are the corresponding expected or  theoretical  frequencies  obtained under some  theory  or hypothesis.

To determine  the  value of X2 and to draw conclusion the  following steps  are required.

a.Calculate the  expected frequencies E1, E2, E3,......En corresponding to observed frequencies  O1, O2, O3, ..On under some theory of hypothesis.

b.Compute the deviations ( O-E) for each frequency and then square these deviations to oblation ( O-E)2

( O-E)2 / E

c.Divide the  square deviation i ,e ( O-E)2  by the  corresponding expected frequency to obtain

d.Obtain  the sum  of all values computed in the step  (iii) to compute.

X2= ∑ [ (O-E)2/E]

This  gives the value of X2 if it s  zero  it multiples  that  there is not discrepancy  between the  observed and  expected frequencies. They coincide completely. The  greater the  value of X2 the greater will be discrepancy  between  the observed and expected frequencies.

e.Under the  nu..  hypothesis theory  fits  table value. If it is less than the  table  value the difference  between  theory  and observation is not  considered as significant. Such difference is regarded on  account  of sampling  fluctuations and is ignored. On  the other hand. If  calculated value  of X2 exceeds the table value  the different  between theory and observation is  considered significant. In other  words the discrepancy between  theory and observation cannot be attributed to chance and we  reject the  null hypothesis and conclude that experiment does not  support the theory.

Posted Date: 2/26/2013 11:23:58 PM | Location : United States

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