Chi-Square Tests for Association (Lesson 11.4)
Chapter 11 - Day 5
Learning Targets
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Check conditions for a test about the relationship between two categorical variables.
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Calculate the P-value for a test about the relationship between two categorical variables.
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Use the four-step process to perform a chi-square test for association.
Experience First
For this lesson, we will be using the same context and data from the previous lesson to determine if there is an association between taco tongue and evil eyebrow for all high school students. Students will use the 4-step process to perform a chi-square test for association (also called a chi-square test for independence).
Most of the hard work for this significance test was done in the previous lesson. In this lesson we add in the conditions for inference, the P-value, and the conclusion.
Students will use the Chi-square independence applet (part of the Traditional Inference applets at www.statsmedic.com/applets to find the P-value.
Even though students are using the applet to find the P-value, we still require them to show the work for the chi-square test statistic (they did this in the previous lesson!).
Formalize Later
Almost everything about this 4-step significance test is the same as the chi-square goodness of fit test from Lesson 11.2, so students should feel very comfortable.
If you are also an AP Stats teacher, you know that sometimes there is a distinction made between a chi-square test of association (1 random sample measuring two categorical variables) and a chi-square test of homogeneity (2+ random samples measuring one categorical variable or random assignment in an experiment). Here in Intro Stats we will not make this distinction. Luckily the mechanics of the calculations are the same for both tests.
Because the results are statistically significant, you may want to have students do a follow-up analysis. Here, we look at the contributions table at the bottom of the applet. These are the components that add up to give the chi-square test statistic. Find the largest component and explain it in the context of the problem.
"The largest component of the chi-square test statistic is for Yes Evil Eyebrow, No Taco Tongue, because the observed count (20) was much less than the expected count (40)."
