Chapter 8

Random Error and the Role of Statistics
1. Why should confidence intervals and P values have a different interpretation in a case-control study or a cohort study than a randomized experiment? What is the effect of the difference on the interpretation?

2. Which has more interpretive value, a confidence interval, a P value, or a statement about statistical significance? Explain.

3. In what way is a P value inherently confounded?

4. What are the two main messages that should come with a statistical estimate? How are these two messages conveyed by a P-value function?

5. Suppose that a study showed that former professional football players experienced a rate ratio for coronary heart disease of 3.0 compared with science teachers of the same age and sex, with a 90% confidence interval of 1.0 to 9.0. Sketch the P-value function. What is your interpretation of this finding, presuming that there is no confounding or other obvious bias that distorts the results?

6. One argument sometimes offered in favor of statistical significance testing is that it is oft en necessary to come to a yes-or-no decision about the effect of a given exposure or therapy. Significance testing has the apparent benefit of providing a dichotomous interpretation that could be used to make a yes-or-no decision. Comment on the validity of the argument that a decision is sometimes needed based on a research study. What would be the pros and cons of using statistical significance to judge whether an exposure or a therapy has an effect?

7. Are confidence intervals always symmetric around the point estimate? Why or why not?

8. What is the problem with using a confidence interval to determine whether or not the null value lies within the interval?

9. Consider two study designs, A and B, that are identical apart from the study size. Study A is planned to be much larger than study B. If both studies are conducted, which of the following statements is correct? (1) The 90% confidence interval for the rate ratio from study A has a greater probability of including the true rate ratio value than the 90% confidence interval from study B. (2) The 90% confidence interval for the rate ratio from study A has a smaller probability of including the true rate ratio value than the 90% confidence interval from study B. (3) The 90% confidence intervals for the rates ratio from study A and study B have equal probabilities of including the true rate ratio value. Before answering, be sure to take into account the fact that no study is without some bias.