An article published in the New England Journal of Medicine in 2005 describes a double-blind, randomized, placebocontrolled trial designed to test whether the antibiotic gatifloxacin could reduce the rate of cardiovascular events such as heart attacks. Approximately 4,000 patients were enrolled in the study, and we will assume that 2,000 each received gatifloxacin and placebo. The proportions with cardiovascular events after two years were 0.237 for the gatifloxacin group and 0.251 for the placebo group.28

a. Which group seemed to do better, as far as the sample was concerned: those who took gatifloxacin or those who took a placebo?

b. If we calculate 0.237(2,000) and 0.251(2,000), are we finding X₁ and X₂, or and , or p₁ and p₂, or n₁ and n₂?

c. Complete all the information in the tables of observed counts, on the top, and expected counts, on the bottom:

d. The chi-square statistic, which is the combined standardized squared difference of observed minus expected counts, can be calculated to be 1.06. Use the fact that the area to the right of 3.84 under the chi-square distribution for a 2-by-2 table is 0.05 to decide if the P-value is not small at all, small, or borderline.

e. Which two of these are correct interpretations of the results?

1. There is evidence of a relationship between heart attacks or not and taking gatifloxacin or not.

2. The data prove that there is no relationship between heart attacks or not and taking gatifloxacin or not.

3. The data fail to provide evidence of a relationship between heart attacks or not and taking gatifloxacin or not.

4. The proportions having heart attacks for populations of people taking gatifloxacin or placebo are equal.

5. The proportions having heart attacks for populations of people taking gatifloxacin or placebo may be equal.

6. There is evidence that the proportions having heart attacks for populations of people taking gatifloxacin or placebo are different.