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

Outline Application areas Illustration with example Limitations Conclusion and QA April 14, 2019 Chi-squared Test

Application Areas Application 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? April 14, 2019 Chi-squared Test

Example1 An Example:* Observed Frequencies Application Areas Illustration with Example Limitations Conclusion and QA 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. April 14, 2019 Chi-squared Test

Computing Expected Frequencies Example2 Application Areas Illustration with Example Limitations Conclusion and QA 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. April 14, 2019 Chi-squared Test

Computing Expected Frequencies 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. April 14, 2019 Chi-squared Test

Example4 Expected Frequencies Application Areas Illustration with Example Limitations Conclusion and QA 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. April 14, 2019 Chi-squared Test

Example5 Null Hypothesis 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. April 14, 2019 Chi-squared Test

Example6 Computing Chi-square Application Areas Illustration with Example Limitations Conclusion and QA 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. April 14, 2019 Chi-squared Test

Consulting Chi-square Table 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. April 14, 2019 Chi-squared Test

Limitations Limitations of Chi-square Test 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 April 14, 2019 Chi-squared Test

Conclusion Conclusion 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. April 14, 2019 Chi-squared Test

Questions Question Any Question? Application Areas Illustration with Example Limitations Conclusion and QA Question Any Question? Questions April 14, 2019 Chi-squared Test