1. Section 8.5 - Inference for Experiments Objectives: 1.To understand how randomization differs in surveys and experiments when comparing two populations 2.To construct and interpret a confidence interval for the difference of two proportions in an experiment 3.To use a test of significance to decide whether one treatment gives results that are different from the results of another treatment 4.To learn how to apply inference procedures in an observational study

2. Introduction Recall that one of the conditions for using the methods for comparing two proportions was that the data came from independently selected random samples from two populations. In this section we will investigate the situation where the data come from two groups split by random assignment (treatment and control). We will see that the methods of Sections 8.3 and 8.4 carry over to this new situation. The only difference will be in the way the hypotheses and conclusions are stated. Section 8.5 - Inference for Experiments

3. Confidence Interval for a Difference in Proportions from an Experiment The form of the confidence interval and all the computations remain the same, as do the conditions on sample size. The interpretation of the confidence interval is a little different. We are estimating the difference in the proportion of successes Section 8.5 - Inference for Experiments

4. Confidence Interval for a Difference in Proportions from an Experiment Section 8.5 - Inference for Experiments

5. E76. A randomized clinical trial on Linus Pauling’s claim that vitamin C helps prevent the common cold was carried out in Canada among 818 volunteers, with results reported in 1972. The data showed that 335 of the 411 in the placebo group got colds over the winter in which the study was conducted, while 302 of the 407 in the vitamin C group got colds. a.Find and interpret a 95% confidence interval for the difference of two proportions. b.Find a 99% confidence interval for the difference of proportions. Does your conclusion change from your interpretation in part a? Section 8.5 - Inference for Experiments

6. E76. A randomized clinical trial on Linus Pauling’s claim. Section 8.5 - Inference for Experiments

7. E76. A randomized clinical trial on Linus Pauling’s claim. Section 8.5 - Inference for Experiments

8. E76. A randomized clinical trial on Linus Pauling’s claim. Section 8.5 - Inference for Experiments

9. Significance Tests for a Difference in Proportions from an Experiment The sampling distribution of the difference between two proportions will be approximately normal under the typical randomization scheme used in experiments. The formula for the estimated standard error remains the same. The difference between the two testing scenarios is in the stating of the hypotheses and conclusions. Section 8.5 - Inference for Experiments

10. Components of a Significance Test for the Difference of Two Proportions from an Experiment. (1) Check Conditions: Section 8.5 - Inference for Experiments

11. Components of a Significance Test for the Difference of Two Proportions from an Experiment. (2) Write a null and alternative hypothesis. The null hypothesis is that the two treatments would have resulted in the same proportion of successes if each treatment could have been given to all subjects. The alternative hypothesis for a two-sided test is that the two treatments would not have resulted in the same proportion of successes if each treatment could have been given to all subjects. The alternative hypothesis for a one-sided test is that one of the specific treatments would have resulted in a higher proportion of successes than the other if each treatment could have been given to all subjects. Section 8.5 - Inference for Experiments

12. Components of a Significance Test for the Difference of Two Proportions from an Experiment. (3) Compute a test statistic and a P-value (or critical values) Section 8.5 - Inference for Experiments

13. Components of a Significance Test for the Difference of Two Proportions from an Experiment. (4) Write a conclusion State whether you reject or do not reject the null hypothesis. Link this conclusion to your computations by comparing the test statistic z to the critical value z *, or by comparing the P-value to the significance level . You reject H 0 if z is more extreme than z *, or if the P-value is smaller than . Write a sentence giving your conclusion in the context of the situation. Section 8.5 - Inference for Experiments

14. E79. The Physicians’ Health Study conducted a famous experiment on the effect of low-dose aspirin on heart attacks. This was a randomized, double-blind, placebo-controlled clinical trial. Male Physician volunteers with no previous important health problems were randomly assigned to an experimental group (n 1 = 11,037) or a control group (n 2 = 11,034). Those in the experimental group were asked to take a pill containing 325 mg of aspirin every second day. After about 5 years, there were 139 heart attacks in the aspirin group and 239 in the placebo group. Is there significant evidence that aspirin use reduces the rate of heart attacks in this group? Test at the 1% level. Section 8.5 - Inference for Experiments

15. E79. The Physicians’ Health Study experiment on the effect of low-dose aspirin on heart attacks. (1) Give the name of the test and check conditions. Section 8.5 - Inference for Experiments

16. E79. The Physicians’ Health Study experiment on the effect of low-dose aspirin on heart attacks. (2) State the hypotheses and define symbols. Section 8.5 - Inference for Experiments

17. E79. The Physicians’ Health Study experiment on the effect of low-dose aspirin on heart attacks. (3) Compute the test statistic, z, and find the critical values, z *, and the P-value. Include a sketch. Section 8.5 - Inference for Experiments

18. E79. The Physicians’ Health Study experiment on the effect of low-dose aspirin on heart attacks. (3) Compute the test statistic, z, and find the critical values, z *, and the P-value. Include a sketch. Section 8.5 - Inference for Experiments

19. E79. The Physicians’ Health Study experiment on the effect of low-dose aspirin on heart attacks. (4) Write a conclusion Section 8.5 - Inference for Experiments