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
1) Provide an overall description of the business and the competitive environment in which it operates.  You should describe: a) what type of business it  is (e.g. retail, manuf

Disadvantage  of standard Deviation It is not  easy  to understand  and calculate. It gives  more  weight  to the extremes  and less  to the items   nearer to mean. Since

significance and scope of operation resarch in morden management?

Operation research is only a Tool of Analysis and Not the Complete Decision making Process: It should always be kept in mind that O. R alone cannot make the final decision . it

CONSTRUCTION PROCEDURE The construction of an interview schedule or questionnaire is a time consuming task requiring considerable attention to all the details. The investig

Application of the chi Square Test   The  chi square distribution  has a number of applications are given  below: a.Chi Square test of goodness of fit. b.Chi square te

35mm Slider  35 mm Slider like OHP transparencies casts  an images but they  have different  uses and  properties. They are used  to show an actual photographic  images in the


Demerits  of Range a.It gives  importance  to the  two  extreme  values and is very much affected by the extreme items. b.The range  provides  no information  about the  st

Name the feature which is not normally associated with a Non-Governmental Organisation (NGO)?  Government funded is the organisation.