Section 7-2: Testing for an Association

Between Two Categorical Variables

Example 1: Painkillers and Miscarriage

Is there an association between the use of painkillers during pregnancy and the likelihood of miscarriage? Scientists interviewed 1009 pregnant women soon after they got positive results from pregnancy tests about their use of painkillers around the time of conception or in the early weeks of pregnancy. The scientists then recorded which of the pregnancies were successfully carried to term. The results are shown in the table below. (NSAIDS are a class of painkiller that includes aspirin and ibuprofen.) Does there appear to be an association between having a miscarriage and using painkillers?

	Miscarriage	No miscarriage	Total
NSAIDs	18	57	75
Acetaminophen	24	148	172
No painkiller	103	659	762
Total	145	864	1009

(a) What is the expected count for the cell with NSAID use and Miscarriage?

(b) Find all expected counts and add them to the table above.

(c) What is the contribution to the chi-square statistic for the cell with NSAID use and Miscarriage?

(d) Find all six contributions.

(e) What is the value of the chi-square test statistic for these data?

(f) What are the degrees of freedom for the test? What is the p-value?

(g) Using a 5% significance level, what is the conclusion of the test? Be specific. If there is an association between having a miscarriage and using painkillers, describe how the two variables are related.

Quick Self-Quiz:Chi-square Test for Association

478 middle school students in Michigan were asked whether grades, athletic ability, or popularity was most important to them. The results are shown below, broken down by gender. Do the data provide evidence of an association between the two variables? Show all details and be sure to state your conclusion clearly.

	Grades	Sports	Popular
Boy	117	60	50
Girl	130	30	91