Stat 301 – Day 22 Relative Risk

Announcements HW 5  Learn by Doing Lab 2-3  Evening Office hours  Friday: 10-11, 12-1

Last Time – Two Sample Z test When the sample sizes are large we can approximate the hypergeometric distribution with the Normal distribution  Continuity correction Advantages?  Test statistic along with p-value  Confidence interval for  1 –  2 Also see Wilson Adjustment (1S/1F to each sample)

Formulas Test statistic Confidence interval Larger difference between the two sample proportions => larger test statistic => smaller p-value Larger sample sizes => larger test statistic => smaller p-value What if both sample size and difference change?

Theory-Based Inference

PP 2.8: Delivery of instructions

PP 2.8: Combined studies

Study Conclusions Significance  With a p-value of.09, the difference in the sample proportions is significant at the.10 level but not the.05 level  Though were significantly more likely to be able finish delivering the instructions Estimation  Are 90% confident that the survival rate with CC alone is up to 8.5 percentage points higher than the survival rate with CPR (or 1 percentage point less)

Student Conclusions, cont. Causation  We can potentially draw cause-and-effect conclusions from this study because of the random assignment Generalizability  Can probably generalize to heart attack victims/ bystanders in the Seattle area but maybe not more? (because not a random sample)

Investigation 2.9 Statistic: 62/2584 – 148/2584 = Let X represent the number developing the flu in the control group  P(X > 148) where N = 5168, M = 210, n = 2584 Extremely strong evidence that the observed difference in the sample proportions did not arise from the random assignment process alone

Relative risk Definition: Relative risk is the ratio of the conditional proportions  Often set up to be larger than one  RR = (Unvaccincated Influenza)/(Vacc Influenza) =.057/.024  2.39  Interpretation: Those without the vaccine were 2.39 times more likely to develop influenza Or the risk of influenza was about 140% higher if not vaccinated

Our usual questions How do I decide whether my observed relative risk of 2.39 is surprising under the null hypothesis of no difference between the two treatments?? 1. Simulate the shuffling of 210 influenza and 4958 healthy people to two groups 2. Calculate the relative risk for each shuffle 3. Where does 2.39 fall in this distribution? How do I estimate the size of the rel. risk?

To Do Finish Inv 2.9 PP 2.9 Start reviewing for Exam 2! Have a great weekend!