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Chi square

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Transcript

  • 1. Chi-Square Jacob John Panicker MBA., SMS@CHMMC
  • 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. Phase 1
  • 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. 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. 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. Phase 2
  • 8. Equation ‘O’ Observed value  ‘E’ Expected value 
  • 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. 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. 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. 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. Thanks…