Chi-square Lab #2
10/4/01
1. About two weeks ago I gave you a lab in which I asked you to investigate the effects of a drug named Ritonavir for the treatment of AIDS. That lab looked at the results of drawing 72 deaths and assigning them at random to Drug and Control conditions. Although that is one way of looking at the data, and it served our purposes well, there is a much better way that involves the chi-square distribution.
What that lab did not take into account was the question of how many people lived. A 26/46 split might be a very big deal if we are talking about 100 AIDS patients in each group, but a very little deal if we are talking about 1000 patients in each group. As I say in the text when I'm talking about chi-square, the total number of observations in your analysis should equal the number of subjects in the study.
So, we are going back to that example and treat it appropriately as a contingency table. The data are shown below:
Survived
Died
Total
Ritonavir
472
71
543
Placebo
399
148
547
Total
871
219
1090
Enter the data by creating a column headed Drug and another headed Outcome. Fill in these columns to create the four cells of the design. (Note: Your data will only have 4 rows.)
Now create a column named Freq and enter the four cell frequencies.
a) From the Data menu select Weight cases, and then select freq as the weighting variable.
b) Now run Crosstabs specifying Drug condition on the rows and Outcome on the columns. Be sure to select Chi-square and Risk from the Statistics option.
c) The resulting chi-square should be equal to the one I gave in class on Tuesday, which was 33.18. Is that what you get?
d) What do you make of the Likelihood ratio statistic?
e) What will you conclude from the Odds ratios?
f) Write a brief description of the study and your findings.
2. Go back to the example you used last time from Siegel (1975) on morphine and death in rats. In that example I left out one group to make things simpler. Siegel really had 3 groups:
Group A—Increasing doses of morphine in Room A followed by test in Room A.
Group B—Increasing doses of morphine in Room A followed by test in Room B.
Group C—Doses of placebo in Room A followed by test of morphine in Room A. (In this condition the morphine dose was equal to the test dose in the other groups.)
The data for 30 subjects in each group were
Survived
Died
Group A 21
9
Group B 11
19
Group C 1
29
Calculate
for these data using procedures similar to the ones above. Draw the appropriate conclusions and write up a short description of the study and its results, including the questions in item 3 below..
3. The odds that an animal will survive in Group A are equal to the number who survived divided by the number who died. (e.g. for Group A the odds of survival are 21/9 = 2.33/1 = 2.33, meaning that an animal is 2.33 times as likely to survive as to die.) The odds ratio is just the ratio of two odds.
a) What is the odds ratio for Groups A and B, and what does it tell us?
b) What is the odds ratio for Groups A and C, and what does it tell us?
4. In the book I talk about the Dabbs and Morris (1991) study of the relationship between delinquency and testosterone. Below are the data separated by High and Low SES subjects. Run an appropriate analysis within each SES group. What conclusions would you draw from these data?
Low SES
Delinquent
Not Delinq.
Normal 190
1104
High 63
140
High SES
Delinquent
Not Delinq.
Normal 53
1114
High 3
70
a) Calculate the odds ratios for the two analyses above. What do these results tell you?
b) Write up the results of this experiment as if they were your own data. Be brief, but describe the study, give the results, talk about significance, present odds and odds ratios, and draw the appropriate conclusions.
5. Last class I mentioned "effect size," and suggested that odds ratios are more than one way to get a measure of the size of an effect. The basic idea is that we could have a statistically significant effect that is trivial, and another statistically significant effect that is important. In the book I mention a paper by Rosenthal (1960), who looked at data on the effect of daily aspirin on the incidence of heart attacks. One group took aspirin for an extended period, and another took a placebo. The researchers counted the number of participants who had a heart attack over the course of the study. The results follow:
Heart Attack
No Heart Attack
Aspirin 104
10,933
Placebo 189
10,845
Compute the chi-square statistic from this table.
Compute an odds ratio as a measure of the magnitude of the effect.
Does this seem like a satisfactory measure of magnitude?
Do you think that the researchers found an important effect?
In the book I talk about Cramer's Phi (V), which is a commonly used measure of the effect. Think of it as the correlation between the treatment and the outcome.
Calculate Cramer's phi and compare it to the odds ratio as a measure of the magnitude of the effect?
If I asked you to participate in a debate over the optimal measure of effect size, among those you have seen, which side would you like to be on, and what would you argue?
Partial answers and explanations for these problems can be found at Class12ans.html .
Last revised: 10/05/01