Question

Suppose that a placebo gives headache relief to 15% of patients who take it. A drug company tests a new drug using a sample of 1,000 people. They find that the new drug gives relief to a higher proportion of people, and the difference is statistically significant. Which of the following best describes how we should interpret these results?

a. Because of the large size of the sample, these results are strong evidence that the new drug will help a much larger proportion of the population.

b. With a large sample, statistically significant results suggest a large improvement over the placebo.

c. With a large sample, statistically significant results may actually be only a small improvement over the placebo.

d. Regardless of the sample size, a statistically significant result means there is a meaningful difference in headache relief.

Answer 1

The correct interpretation of a new drug showing statistically significant improvement over a placebo in a large sample is that the improvement may be small. Statistical significance alone doesn't indicate the size of the effect.

Step-by-step explanation:

If a placebo gives headache relief to 15% of patients and a new drug shows improvement in a larger proportion of a sample of 1,000 people, with the difference being statistically significant, the results should be interpreted with caution. Specifically, answer (c) 'With a large sample, statistically significant results may actually be only a small improvement over the placebo' is the correct interpretation. While statistical significance means the difference observed is likely not due to chance, it does not necessarily indicate the size of the effect. Even with a large sample size, the improvement could be minimal, though still significant. The statistical significance indicates that there's good evidence the new drug has some effect, but without additional information such as effect size, we cannot assume the improvement is large.