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 = -0.0333 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!