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# Chi square

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### Chi square

1. 1. Chi-Square Jacob John Panicker MBA., SMS@CHMMC
2. 2. The actual agenda of this presentation is to discus… Phase-1 (Theory) ◦ X2 ◦ Characteristics of X2 ◦ Use (Application) of X2 Phase-2 (Problems) ◦ ◦ ◦ ◦ Equation Level of Significant Degree of Freedom Steps for the X2 test
3. 3. Phase 1
4. 4. Chi-Square-X2  The statistical test in which the test statistic follows a X2 –distribution, is called the X2 test.  X2 test is one of the simplest and most and most widely used non-parametric tests in statistical work.
5. 5. Characteristics of X2 test    It is a non-parametric test It’s a distribution free test It is easy to calculate X2 test statistic
6. 6. Uses (Application) of X2 test Useful for the test of goodness of fit.  Useful for the test of independence of attributes  Useful for testing homogeneity  Useful for testing given population variance 
7. 7. Phase 2
8. 8. Equation ‘O’ Observed value  ‘E’ Expected value 
9. 9. Level of Significance Confidence with which a null hypothesis is accepted or rejected depends on what is called significant level. The probability with which we may reject a null hypothesis, is called the level of significance.
10. 10. Degree of freedom ◦ Degree of freedom is defined as the number of independent observations which is obtained by subtracting the number of constrains from the total number of observations.
11. 11. Steps for the X2 test. H0 and H1 between observed & expected frequencies.  Compute the test statistics, Observed frequencies are available in a given problem. But expected frequencies are to be computed.  Degree of freedom: where than one attribute D.F=(r-1)(c-1) where ‘r’ is the number of independent constraints to be satisfied by the frequencies. 
12. 12. Contineued…. Obtain the table value of X2 for the degree of freedom & for the desired level of significance  If the calculated value of X2 is less than the table value we conclude that there is goodness of fit  Source: Quantitative Methods- L. R. Potti
13. 13. Thanks…