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







Related Discussions:- Chi square test - hypothesis testing, Assignment Help, Ask Question on Chi square test - hypothesis testing, Get Answer, Expert's Help, Chi square test - hypothesis testing Discussions

Write discussion on Chi square test - hypothesis testing
Your posts are moderated
Related Questions
Small Sample The central limit  theorem does not work well  with small  samples  even if  the  population  in non Gaussian. So  we cannot  rely on the central limit theorem

SOLVE THE FOLLOWING LP USING SIMPLE METHOD MAXIMIZE Z=3X1+2X2 SUBJECT TO CONSTRAINT X1+X2 X1-X2 X1,X2>=0

can u send me some assigment problems

NON PARAMETRIC TESTS All  practical  data follow normal distribution under  such situations can estimate the  parameters such  as mean  variance etc ,,, and use the  standard

A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn, wheat, and soybeans. Each acre of corn costs $100 for preparation, requires 7 worker-days of la

Question 1 A) Differentiate among descriptive and inferential analysis of data B) Describe with examples various measures of Central Tendency Question 2 The chi-square

Scope of operation research?

Consider the closed network of the following figure. The number at the arrows give the transition probabilities for a customer leaving the queue to route to a subsequent queue. Eve

In large sized linear programming problems, the solution cannot be obtained by the graphical method and hence a more systematic method has to be developed to find

how do you calculate using this method where the least cost appears twice