# LEARNING PROGRAMME Hypothesis testing Part 2: Categorical variables Intermediate Training in Quantitative Analysis Bangkok 19-23 November 2007.

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LEARNING PROGRAMME Hypothesis testing Part 2: Categorical variables Intermediate Training in Quantitative Analysis Bangkok 19-23 November 2007

LEARNING PROGRAMME - 2 Topics to be covered in this presentation  Pearson’s chi square

LEARNING PROGRAMME - 3 Learning objectives By the end of this session, the participant should be able to:  Conduct chi square

LEARNING PROGRAMME - 4 Hypothesis testing for categorical variables… We sometimes want to determine… Whether the proportion of people with some particular outcome differ by another variable Ex. Does the proportion of food insecure households differ in male and female headed households??

LEARNING PROGRAMME - 5 What if we we want to test whether there is a relationship between two categorical variables ? Pearson Chi-Square

LEARNING PROGRAMME - 6 Pearson’s chi-square test  Pearson’s chi-squared test (X²) is an omnibus test that is used to test the hypothesis that the row and the column variables of a contingency table are independent  It’s a comparison of the frequencies you observe in certain categories to the frequency you might expect to get in those categories by chance.

LEARNING PROGRAMME - 7 Assumptions of the chi-square test Two assumptions: 1.For the test to be meaningful it is imperative that each unit contributes to only one cell of the contingency table. 2.The expected frequencies should be greater than 5 in each cell (or the test may fail to detect a genuine effect)

LEARNING PROGRAMME - 8 Chi square formula…

LEARNING PROGRAMME - 9 Chi square example Child Gender * underweight Crosstabulation underweightTotal noyes Child GenderMaleCount20865872673 Expected Count2144.6528.42673 FemaleCount22042532674 Expected Count2145.6528.62674 TotalCount429010575347 Expected Count429010575347

LEARNING PROGRAMME - 10 Chi Square example…  X 2 = [(2086-2144.6) 2 /2144.6] + [(587- 528.4) 2 /528.4] + [(2204-2145.4) 2 /2145.4] + [(470-528.6) 2 /528.6]  X 2 = 1.60 + 6.50 + 1.60 + 6.50  X 2 = 16.2 (then check x 2 distribution…)

LEARNING PROGRAMME - 11 Chi Square example…  If we do it by spss, we get the same answer

LEARNING PROGRAMME - 12

LEARNING PROGRAMME - 13 To calculate chi-squares in SPSS In SPSS, chi-square tests are run using the following steps: 1.Click on “Analyze” drop down menu 2.Click on “Descriptive Statistics” 3.Click on “Crosstabs…” 4.Move the variables into proper boxes 5.Click on “Statistics…” 6.Check box beside “Chi-square” 7.Click “Continue” 8.Click “OK”

LEARNING PROGRAMME - 14 Reading the Chi-square test  However, it is difficult to get an idea about the strength of that relationship

LEARNING PROGRAMME - 15 Important Note:  If you compare two categorical variables and at least one has multiple categories, you can determine which categories are different from one another by running a Z-test under “Custom Tables”  This is rather complicated so we will not discuss in detail

LEARNING PROGRAMME - 16 Now…..exercise!!!!

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