1. Chapter 13 Section 2

2. Chi-Square Test 1.Null hypothesis – written in words 2.Alternative hypothesis – written in words – always “different” 3.Alpha level 4.appropriate bar graph 5.Find Counts and Expected Counts 6.Assumptions 7.Find Chi-Square Test statistic 8.Find P-value 9.Write Conclusion 10.If in the conclusion, the null hypothesis is rejected – follow up analysis

3. Chi-square test of independence An overall test to see if there is good evidence of ANY differences among the parameters compared.

4. A 3-year study compared an antidepressant with Lithium (a standard treatment for cocaine addiction) and a placebo. The subjects were 72 chronic users of cocaine who wanted to break their drug habit. 24 of the subjects were randomly assigned to each treatment.

5. GroupTreatmentSubjectsNo relapseProportion 1 antidepressant 2414.583 2Lithium246.250 3Placebo244.167 Is this data good evidence that the proportions of successes for the three groups differ in the population of all cocaine users?

6. A 3-year study compared an antidepressant with lithium (a standard treatment for cocaine addiction) and a placebo. The 72 subjects were chronic users of cocaine who wanted to break their drug habit. 24 of the subjects were randomly assigned to each treatment.

7. NOYes Relapse 1. Anti- Depressant 1410 2. Lithium618 3. Placebo420 This is called a 3 X 2 table. (r X c) The explanatory variable is the treatment (one of the three drugs) and the response variable is success (no relapse) or failure (relapse).

8. Expected Counts Expected Counts 1. Anti- Depressant 816 2. Lithium816 3. Placebo816 Run the Chi-square test in your calculator and it will find the expected counts in the next matrix.

9. There are no differences among the proportions of successes for addicts given the three treatments. There are differences among the proportions of successes for addicts given the three treatments. Degrees of Freedom: (r-1)(c-1) = (3 -1)(2 – 1) = 2 Assumptions: 1.All individual expected counts are more than 1 2.No more than 20% of the expected counts are less than 5 3.If the table is a 2 X 2, all four expected counts should be 5 or greater

10. Given that there are no differences among the treatments for cocaine addiction the differences between the observed and expected would occur approx. 5 out of every 1000 times just by chance. Therefore this evidence rejects that there is no difference among the three treatments for cocaine addiction.

11. Follow-up Analysis: From looking at the proportions of success among the three treatments, comparing the specific observed and expected, and looking at the contribution to the overall chi-square statistic by the antidepressant component it appears that the antidepressant treatment has a much higher success rate than the Lithium or placebo.