An overview of the chi square test and its types

1. Chi square test and its variations
Dr. S. A. Rizwan, M.D.
Public Health Specialist
SBCM, Joint Program – Riyadh
Ministry of Health, Kingdom of Saudi Arabia

2. Learning objectives
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Describe the conditions in which this test is used
• Describe the assumptions for this test
• Describe the steps involved in calculating this test
• Interpret the test result
• Describe the types of this test χ2

3. Introduction
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Chi square test, also called Pearson’s chi
square test
• First investigated by Karl Pearson in 1900

4. Applications of chi square test
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Goodness of fit - whether an observed frequency
distribution differs from a theoretical distribution.
• Homogeneity - compares the distribution of counts for
two or more groups using the same categorical variable
• Independence (most commonly used) - assesses
whether unpaired observations on two variables are
independent of each other
• Others

5. Applications – example 1
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• A 6-sided die is thrown 60 times. The
number of times it lands with 1, 2, 3,
4, 5 and 6 face up is 5, 8, 9, 8, 10 and
20, respectively. Is the die biased,
according to the Pearson's chi-squared
test at a significance level of 95%

6. Applications – example 2
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• A random sample of 100 people has
been drawn from a population in
which men and women are equal in
frequency, the observed number of
men and women would be compared
to the theoretical frequencies of 50
men and 50 women

7. Applications – example 2.1
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• A random sample of 100 persons
been drawn from men and 100
persons from among women. They
were asked about smoking habits.
Compare the percentage of smokers
among men and women.
Men Women Total
Smoker 40 20 60
Non-
smoker 60 80 140
Total 100 100 200

8. Applications – example 3
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• A city of 1 million residents with four
neighborhoods: A, B, C, and D. A random
sample of 650 residents of the city is taken
and their occupation is recorded as "white
collar", "blue collar", or "no collar". The null
hypothesis is that each person's
neighborhood of residence is independent of
the person's occupational classification

9. Types / variations
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Test for goodness of fit
• Test for Homogeneity
• Test of Independence
• Cochran–Mantel–Haenszel test
• Test for Trend
* Advanced learning: What is Yate’s correction?

10. Assumptions
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Simple random sample
• Data in the cells should be frequencies, or counts
of cases
• Categories of the variables are mutually exclusive
• Study groups must be independent
• Value of cell expecteds should be 5 or more in at
least 80% of the cells
• No cell should have an expected of less than one

11. Steps in Chi square test for independence
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Recall the general steps
1. Null hypothesis
2. Alternative hypothesis
3. Level of significance
4. Test statistic
5. Critical value
6. Decision & interpretation

12. Steps in Chi square test for independence
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Draw the contingency table

13. Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Calculate totals for each row and column
Steps in Chi square test for independence

14. Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Calculated expected frequencies for each cell
Steps in Chi square test for independence

15. Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Calculate Chi square value using the formula and degree of freedom
Steps in Chi square test for independence

16. Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Look at a chi-square table, for a 0.05 level of significance & 2 df, what is
the critical chi-square value and make the conclusion
Steps in Chi square test for independence

17. Summary
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
• With computers, these tests are performed easily
• There are many situations where chi square is
incorrectly applied
• It is important to know when to and when not to
use them

18. Take home messages
Demystifying statistics! – Lecture 8 SBCM, Joint Program – Riyadh
• Chi square is one of the most used statistical tests
• Remember the different types of tests and their
applications
• Remember the assumptions and always check for
violations before interpreting the results

19. Thank you!
Email your queries to sarizwan1986@outlook.com