A matched pairs experiment designed to study the response of people to a certain medication will be conducted using the following volunteers:
| Subject | Gender | Age | Height | Weight |
|---|---|---|---|---|
| A | F | 51 | $5^{\prime} 5^{\prime \prime}$ | 165 |
| B | F | 47 | $57^{\prime \prime}$ | 147 |
| C | M | 50 | $6^{\prime} 0^{\prime \prime}$ | 194 |
| D | F | 42 | $58^{\prime \prime}$ | 145 |
| E | M | 51 | $6^{\prime} 1^{\prime \prime}$ | 225 |
| F | M | 46 | $6^{\prime \prime \prime}$ | 188 |
Which subjects should be blocked together to control for a response associated with a difference in age?
A. A and D
B. D and E
C. B and F
Answer (1)
Calculate the age difference between subjects A and D: ∣51 − 42∣ = 9 .
Calculate the age difference between subjects D and E: ∣42 − 51∣ = 9 .
Calculate the age difference between subjects B and F: ∣47 − 46∣ = 1 .
Subjects B and F have the smallest age difference and should be blocked together: B and F .
Explanation
Understand the problem and provided data We are given a table of volunteers with their gender, age, height, and weight. The goal is to block subjects together to control for a response associated with a difference in age. This means we want to pair subjects with the most similar ages from the given options.
Objective We need to compare the age differences for the pairs (A and D), (D and E), and (B and F).
Calculate the age difference between A and D
Calculate the age difference between A and D: ∣51 − 42∣ = 9 .
Calculate the age difference between D and E
Calculate the age difference between D and E: ∣42 − 51∣ = 9 .
Calculate the age difference between B and F
Calculate the age difference between B and F: ∣47 − 46∣ = 1 .
Select the pair with the smallest age difference Comparing the age differences, we have 9, 9, and 1. The smallest age difference is 1, which corresponds to the pair B and F. Therefore, subjects B and F should be blocked together.
Examples
In medical studies, matching participants based on age helps ensure that differences in medication response are due to the treatment, not age-related factors. For example, when testing a new drug, pairing individuals of similar ages minimizes the chance that age-related physiological differences skew the results, providing a more accurate assessment of the drug's effectiveness.
