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Chi-squared Test

Chi-squared Test. Minhaz Fahim Zibran 31 st October 2007. Outline. Application areas Illustration with example Limitations Conclusion and QA. Application Areas Illustration with Example Limitations Conclusion and QA. Application. Application Areas.

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Chi-squared Test

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  1. Chi-squared Test Minhaz Fahim Zibran 31st October 2007

  2. Outline • Application areas • Illustration with example • Limitations • Conclusion and QA Chi-squared Test

  3. Application Areas Illustration with Example Limitations Conclusion and QA Application Application Areas • Qualitative data classified into discrete categories. Example: We have the number of men and women died from tuberculosis of respiratory system and other types of tuberculosis. Question: Is death caused by tuberculosis of respiratory system and other types of tuberculosis is dependent on gender? Chi-squared Test

  4. Application Areas Illustration with Example Limitations Conclusion and QA Example1 An Example:* Observed Frequencies Table 1*: Observed frequencies of deaths from tuberculosis in England and Wales in 1956 *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  5. Application Areas Illustration with Example Limitations Conclusion and QA Example2 Computing Expected Frequencies Table 2*: Table 1 with interior cells replaced by letters *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  6. Application Areas Illustration with Example Limitations Conclusion and QA Example3 Computing Expected Frequencies Table 2*: Table 1 with interior cells replaced by letters • Proportion of deaths (including males and females) due to tuberculosis of respiratory system and other types of tuberculosis: • The expected values E1 and E2 must be chosen in such a way that the following holds. *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  7. Application Areas Illustration with Example Limitations Conclusion and QA Example4 Expected Frequencies Table 3*: Expected frequencies on the assumption of independent classification *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  8. Application Areas Illustration with Example Limitations Conclusion and QA Example5 Null Hypothesis Table 1*: Observed frequencies of deaths from tuberculosis in England and Wales in 1956 Table 3*: Expected frequencies on the assumption of independent classification • Null Hypothesis: “The number of men and women died in 1956 due to tuberculosis of • respiratory system and other types of tuberculosis is independent of their sex.” *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  9. Application Areas Illustration with Example Limitations Conclusion and QA Example6 Computing Chi-square • Produce chi-square value using the formula *This example and data are taken from A. E. Maxwell. Analysing Qualitative Data. 4th Edition. Chapman and Hall Ltd., 1971.Library of Congress Catalog Card Number 75-10907. Chi-squared Test

  10. Application Areas Illustration with Example Limitations Conclusion and QA Example7 Consulting Chi-square Table • Determine degree of freedom (df) • df = (r - 1)(c - 1) • = (2 – 1) (2 - 1) = 1 • Chi-square Value • X2 = 101.35 Table 4*: Percentage of chi-square distribution • Result of Test: our null hypothesis is rejected *Part of the chi-square table is presented here. The table with more values may be found in books on statistics. The full table may be found in Table 8 of Biometrika Tables of Statisticians, vol. 1, Biometrika Trustees. Chi-squared Test

  11. Application Areas Illustration with Example Limitations Conclusion and QA Limitations Limitations of Chi-square Test • Limitations: Applicable to only qualitative data grouped into categories, or labeled using nominally scaled variables Restricted to be applied for large samples. Fits well when expected frequencies are higher than 5. • Remedy: • Correction of continuity known as ‘Yates Correction’ • Fisher’s Exact Test Chi-squared Test

  12. Application Areas Illustration with Example Limitations Conclusion and QA Conclusion Conclusion Chi-square test tells us whether the classifications are dependent or not. If it tells that the classifications are dependent, it does NOT necessarily imply any causal relationship. Chi-squared Test

  13. Application Areas Illustration with Example Limitations Conclusion and QA Question Any Question? Questions Chi-squared Test

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