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

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

3. 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

4. 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
April 14, 2019
Chi-squared Test

5. 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
April 14, 2019
Chi-squared Test

6. 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
April 14, 2019
Chi-squared Test

7. 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
April 14, 2019
Chi-squared Test

8. 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
April 14, 2019
Chi-squared Test

9. 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
April 14, 2019
Chi-squared Test

10. 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 =
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.
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Chi-squared Test

11. 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

12. 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

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