Researchers at a large pharmaceutical company are conducting a clinic trial to determine the effectiveness of a new therapeutic for COVID-19. Patients are recruited for the clinical trial immediately following a positive test result for COVID-19. Half of the patients, assigned at random, will receive the new therapeutic. The other half will receive an off-label therapeutic currently in wide use by a subset of all doctors treating COVID-19 patients. Patients will be tested daily and the number of days between the initial positive test result and a negative test result are recorded. Assuming that all conditions for inference are met, which of the following significance tests should be conducted to determine whether the use of the new COVID-19 therapeutic results in a smaller average number of days until a negative test than the widely used off-label therapeutic? (A) Paired t-test, one-sided (B) Two-sample z-test, one-sided (C) Two-sample z-test, two-sided (D) Two-sample t-test, one-sided (E) Two-sample t-test, two-sided
Question
Researchers at a large pharmaceutical company are conducting a clinic trial to determine the effectiveness of a new therapeutic for COVID-19. Patients are recruited for the clinical trial immediately following a positive test result for COVID-19. Half of the patients, assigned at random, will receive the new therapeutic. The other half will receive an off-label therapeutic currently in wide use by a subset of all doctors treating COVID-19 patients. Patients will be tested daily and the number of days between the initial positive test result and a negative test result are recorded. Assuming that all conditions for inference are met, which of the following significance tests should be conducted to determine whether the use of the new COVID-19 therapeutic results in a smaller average number of days until a negative test than the widely used off-label therapeutic? (A) Paired t-test, one-sided (B) Two-sample z-test, one-sided (C) Two-sample z-test, two-sided (D) Two-sample t-test, one-sided (E) Two-sample t-test, two-sided
Solution
The correct answer is (D) Two-sample t-test, one-sided.
Here's why:
The two groups of patients (those receiving the new therapeutic and those receiving the off-label therapeutic) are independent of each other, so a paired t-test (option A) would not be appropriate.
A z-test (options B and C) would be used if we knew the population standard deviations, but the problem does not provide that information.
A two-sample t-test is used to compare the means of two independent groups, which is what we have in this scenario.
Finally, we choose a one-sided test (rather than a two-sided test) because the researchers are specifically interested in whether the new therapeutic results in a smaller average number of days until a negative test. They are not interested in whether the new therapeutic results in a larger number of days until a negative test. Therefore, a one-sided test is more appropriate.
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