1. Section 13.2 Chi-square Test of Association / Independence
AP Statistics
March 19, 2013

2. Example
Chronic users of cocaine need the drug to feel pleasure. Perhaps giving them a medication that fights depression will help them stay off cocaine. A three-year study compared an antidepressant called desipramine with lithium (a standard treatment for cocaine addiction) and a placebo.
The subjects were 72 chronic users of cocaine who wanted to break their addiction.
AP Statistics, Section 13.1

3. Observed No Relapse Yes Relapse Desipramine 14 10 24 Lithium 6 18
Placebo 4 20 48 72
AP Statistics, Section 13.1

4. Expected (assuming independence)
No Relapse
Yes Relapse
Desipramine 24
Lithium
Placebo 48 72
AP Statistics, Section 13.1

5. Formula for expected counts
AP Statistics, Section 13.1

6. Observed No Relapse Yes Relapse Desipramine 14 10 24 Lithium 6 18
Placebo 4 20 48 72
Expected
No Relapse
Yes Relapse
Desipramine 8 16 24
Lithium
Placebo 48 72
AP Statistics, Section 13.1

7. AP Statistics, Section 13.1

8. What's new for Chi-squared Test for independence?
H0: the categories are independent.
Ha: the categories are not independent.
You can safely use the chi-square test with critical values from the chi-square distribution when no more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater. In particular, all four expected counts in a 2X2 table should be 5 or greater.
AP Statistics, Section 13.1