Chi square test and its types
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This document discusses the chi-square test and its applications. It begins by listing the learning objectives, which are to describe the conditions and assumptions of the chi-square test, and how to calculate and interpret the results. It then provides an introduction to the chi-square test and discusses its applications for goodness of fit, homogeneity, and independence tests. Examples of each application are given. The document also outlines the assumptions of the chi-square test and the steps to perform it, including defining the null hypothesis, calculating expected and observed frequencies, the test statistic, and interpreting results. It concludes by emphasizing the importance of understanding when to correctly apply chi-square tests.
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