The Chi-square Independence Test
- Evaluating the relationship between two categorical variables, at least 1 categorical variable with more than 2 levels
Chi-Square Test of Independence
Expected Counts in Two-way Tables
Evaluating the hypothesis
- Quantify how different the observed counts are from the expected counts
- Large deviation from what would be expected based on sampling variation(chance) alone provide strong evidence for the alternative hypothesis
- Called an independence test since we’re evaluating the relationship between two categorical variables
INSTRUCTIONS
- Define the query: Does there appear to be relationship between COL1 and COL2?
- Set the hypothesis
- H0: nothing going on(independent)
- H1: something going on(dependent)
- Check conditions
- Calculate the expected counts
- Calculate test statistic, find p-value
- Make a decision, and interpret it in context of the research question
(Example)
[Obesity and Marital Status]
A study reported in the medical journal Obesity in 2009 analyzed data from the National Longitudinal Study of Adolescent Health. Obesity was defined as having a BMI of 30 or more. The research subjects were followed from adolescence to adulthood, and all the people in the sample were categorized in terms of whether they were obese and whether they were dating, cohabiting, or married.Study results
1. Define the query
Does there appear to be a relationship between weight and relationship status?
2. Set the hypothesis
- H0: Weight and relationship status are independent. Obesity rates do not vary by relationship status.
- H1: Weight and relationship status are dependent. Obesity rates do vary by relationship status.
- Check conditions
- Calculate the expected counts
- Calculate test statistic, find p-value
- Make a decision, and interpret it in context of the research question
Can we conclude from these data that living with someone is making some people obese, and that marrying someone is making people even more obese? NO!
