To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
(B) Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
(D) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from the other block.
(E) The subjects in one block receive one treatment, and the subjects in the other block receive the other treatment.
The correct answer and explanation is :
The correct answer is: (B) Treatments are randomly assigned to subjects within each block.
Explanation:
A randomized block design is an experimental design used to reduce the effect of variability among experimental units (subjects) that is not of primary interest but may influence the outcome. In this context, the variability due to age is being controlled by dividing the subjects into two blocks: those under 40 years and those 40 years or older. This allows researchers to isolate the treatment effect within relatively homogenous age groups, increasing the precision of the comparison.
The key feature of a randomized block design is that within each block, subjects are randomly assigned to treatment groups. This helps ensure that the treatment comparison within each block is not biased by confounding variables.
Let’s evaluate each option:
- (A) Incorrect: The number of subjects in each block does not need to be different or the same. The number may vary depending on the sample, but that is not a defining characteristic of a randomized block design.
- (B) Correct: This is a core principle of randomized block design. Treatments must be randomly assigned within each block to ensure valid comparisons unaffected by block-level variability.
- (C) Incorrect: Blocking by age does not preclude the use of a control group. A control group can be included in each age block.
- (D) Incorrect: A matched-pairs design is different from a randomized block design. In matched-pairs, each subject is paired with another similar subject (or with themselves in crossover designs). This design doesn’t involve pairing across blocks.
- (E) Incorrect: This would invalidate the purpose of blocking. If one block receives only one treatment, the effects of the treatment would be confounded with the block (age), making it impossible to isolate the treatment effect.
Thus, (B) accurately reflects the principle of how treatments are assigned in a randomized block design.