Chi -Square

CHI-SQUARE TEST AND ITS IMPLEMENTATION

The chi-square test of independence is a very useful statistical tool that helps in identifying if two variables are related to each other. In a functional sense it is very similar to a correlation co-efficient of determination R^2, however the key difference is that chi-square test was developed to work with nominal or categorical data, where as standard R^2 works only with numerical data.
It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution. The events considered must be mutually exclusive and have total probability 1. A common case for this is where the events each cover an outcome of a categorical variable. A simple example is the hypothesis that an ordinary six-sided die is "fair", i.e., all six outcomes are equally likely to occur.
                                 
                                      STEPS OF CHI-SQUARE TEST

To determine the value of   x2 following steps are required:
1-calculate the xpected frequencies E1,E2,......En corresponding to observed frequencies O1,O2,.........On.
2-compute the deviations(O-E) for each frequency and then square these deviations to obtain (O-E)2:
3-divide the square deviations by corresponding expected frequencies:
                                                    (O-E)2/E
4-obtain the s=sum of all values computed in step 3 to compute:
                                    The value of the test-statistic is
                                        x2=sigma[   (O-E)2/E]
where
Χ2 = Pearson's cumulative test statistic, which asymptotically approaches a χ2 distribution.
Oi = an observed frequency;
Ei = an expected (theoretical) frequency, asserted by the null hypothesis;
n = the number of cells in the table.
                   
                       

                        CHI-SUQARE TEST IN CORPORATE STRATEGIES

Any business situation where... [continues]

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