Chi-squared Test Minhaz Fahim Zibran 31st October 2007

Chi-squared Test Minhaz Fahim Zibran 31st October 2007

Outline July 30, 2023 Application areas Illustration with example Limitations Conclusion and QA Chi-squared Test 2

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? July 30, 2023 Chi-squared Test 3

Application Areas Illustration with Example Limitations Conclusion and QA An Example:* Example1 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. July 30, 2023 Chi-squared Test 4

Application Areas Illustration with Example Limitations Conclusion and QA Computing Expected Example2 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. July 30, 2023 Chi-squared Test 5

Application Areas Illustration with Example Limitations Conclusion and QA Computing Expected Example3 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. July 30, 2023 Chi-squared Test 6

Application Areas Illustration with Example Limitations Conclusion and QA Expected Frequencies Example4 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. July 30, 2023 Chi-squared Test 7

Application Areas Illustration with Example Limitations Conclusion and QA Null Hypothesis Example5 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 tuberculosi respiratory system and other types of tuberculosis is independe *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. July 30, 2023 Chi-squared Test 8

Application Areas Illustration with Example Limitations Conclusion and QA Computing Chi-square Example6 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. July 30, 2023 Chi-squared Test 9

Application Areas Illustration with Example Limitations Conclusion and QA Consulting Chi-square Example7 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. July 30, 2023 Chi-squared Test 10

Application Areas Illustration with Example Limitations Conclusion and QA Limitations of Limitations 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 July 30, 2023 Chi-squared Test 11

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. July 30, 2023 Chi-squared Test 12

Application Areas Illustration with Example Limitations Conclusion and QA Any Question? Question Questions July 30, 2023 Chi-squared Test 13