1.
Refer
to the following generated data from a hypothetical study of classroom
interventions, relating to whether the students passed ("yes") or
failed ("no") a particular assessment:

Pass 

Group 
Yes 
No 
Intervention 
168 
43 
Control 
359 
146 
a. What is the Risk of failing the assessment for those receiving the intervention?
b. What is the Risk of failing the assessment for those not receiving the intervention?
c. What is the Relative
Risk of failing for the Intervention
group versus the Control group? (Careful, this one can be tricky.)
d. What can you say about the Relative Risk in
this example? In other words, interpret the results from Part 1C, making sure
to reference the numerical results in a meaningful manner. Also, make sure to
answer whether the intervention is effective or not.
2.
Again, refer to the data in Question 1.
a.
What
is the odds ratio of failing the assessment for those who received the
intervention versus for those who did not receive the intervention?
b.
What
is the odds ratio of failing the assessment for those who did not receive the
intervention versus for those who did receive it?
c.
Is
the Odds Ratio significant? What is the pvalue? What is the confidence
interval for each comparison?
d.
What
can you say about the odds of failing in this example? In other words,
interpret the results from Part 2C, making sure to reference the numerical
results in a meaningful manner. Also, make sure to answer whether the
intervention is effective or not.
3.
R
calculated the ratio confidence intervals (for risk and for odds) for you. How
would you do each by hand?
Hint: Remember the discussion during lecture about the log of the
odds and taking the exponent (which is the opposite of a log).
Note: Show your calculations
if you would like to illustrate your point or check your work, but your answer
should be a few sentences describing the process.
4.
In
the United States, the estimated annual probability that a woman over the age
of 35 dies of lung cancer equals 0.001304 for current smokers and 0.000121 for
nonsmokers. (Question 2.7 in the Agresti book, pg.
56).
a.
Calculate
and interpret the difference of proportions and the relative risk. Which is
more informative for these data? Why?
b.
Calculate
and interpret the odds ratio. Explain why the relative risk and odds ratio take
similar values.