Question

Suppose you read the following headline: “Taking an aspirin a day can cut your risk of heart attack by almost half!” Suppose the news report goes on to tell you that the research is based on a very large well-designed randomized experiment with a p-value less than 0.0001. Assume this information is technically correct, given the results of the study. Which of the following statistics could actually represent the results of this study?

The rates of heart attack were 9.4 per thousand for the aspirin group and 17.1 per thousand for the placebo group (non aspirin).

94 people in the aspirin group had a heart attack, compared to 171 people in the non-aspirin group. The risk of a heart attack for the aspirin group was 45% of the risk of a heart attack for the non-aspirin group. Any of the above could have been possible. Answer is: any of above are possible. Please explain why as that is what I am confused on.

Answer 1

Since the p value for the test “Taking an aspirin a day can cut your risk of heart attack by almost half!” is 0.0001

that means the result is almost sure

The rates of heart attack were 9.4 per thousand for the aspirin group and 17.1 per thousand for the placebo group (non aspirin).

Here, if you will calculate people taking aspirin / people not taking aspirin = 9.4/17.1 = 0.549

Which is close to 0.5 ( as in hypothesis certain range around the hypothesized value is accepted )

94 people in the aspirin group had a heart attack, compared to 171 people in the non-aspirin group.

Again take the ratio taking aspirin / people not taking aspirin = 94/171 = 0.549

Which is close to 0.5 ( as in hypothesis certain range around the hypothesized value is accepted )

The risk of a heart attack for the aspirin group was 45% of the risk of a heart attack for the non-aspirin group

Here 45% mean = 0.45 again the number closed to 0.5

Which is close to 0.5 ( as in hypothesis certain range around the hypothesized value is accepted )

In all the three scenario the ratio is close to 0.5