Experimental Design: Make the Comparison Fair — Worked Solutions

A versus B is the treatment comparison. Chance determines allocation. Twenty seedlings per treatment supply replication. Equal watering and light schedules directly control those extraneous sources of height variation.

The inactive matching pill is a placebo and can serve as a control treatment; no pill is another comparison group. The placebo effect is 5−2=3 improvement points. Active-minus-placebo is 8−5=3 points here, but it is a different comparison even though the numbers happen to match.

A and B are single-blind or single-masked: one side knows and the other does not, covering both directions of the definition. C is double-blind or double-masked because neither participants nor interacting research staff know the treatment.

Water amount is extraneous to the fertilizer comparison but affects growth. Because water level is tied to fertilizer, it is difficult to separate their effects. Give every seedling the same water amount and randomly assign fertilizer; control removes this systematic difference and random assignment aims for approximately similar distributions of other extraneous factors.

A is completely randomized; equal treatment sizes are not required. B is randomized block, with age as an extraneous blocking variable; all treatments occur within each block and age variation is separated for more precise comparisons. C is matched pairs, a randomized block design with exactly two treatments and one of each assigned within each pair.

Random assignment supports a cause-and-effect treatment comparison by reducing confounding among the participating units. Volunteer recruitment is practical here but does not randomly select the broader population; the results concern participants and may apply to similar headache sufferers, not automatically everyone.

Compare A and B; randomly allocate volunteers to material groups; use multiple volunteers in each group, such as 36 each; keep room, volume, duration, and assessor instructions the same. These supply comparison, random assignment, replication, and direct control.

Baseline hearing affects response but is not the investigated material factor. Random assignment aims to make distributions of baseline hearing and other extraneous variables approximately alike across treatment groups. Direct control keeps room and sound settings identical. Assigning all high-baseline people to A ties baseline ability to material and makes their influences hard to separate.

Randomly choose 30 volunteers for A and assign the remaining 42 to B, using a chance mechanism across all volunteers. The groups are unequal but the design is still completely randomized; equal sizes are common, not required.

Group volunteers into similar baseline-hearing blocks, then randomly assign A and B within each block. Every block contains both treatments. Baseline hearing is a blocking variable because it affects word recognition; separating its variation lets within-block treatment comparisons avoid large baseline differences and can improve precision.

Pair volunteers with similar baseline hearing and randomly assign A to one and B to the other, so each pair receives both. Alternatively each volunteer tests both materials and A-first/B-first order is randomized across volunteers. Both are two-treatment randomized block designs. The stated disappearance of material effects makes the repeated-condition option feasible, though comparable sessions still matter.

A same-person matched-pairs design directly compares two materials for the same volunteer, reducing baseline-hearing variation; 72 volunteers can each supply both responses because effects disappear between sessions. If an earlier material had lasting effects, this option would be less appropriate and baseline-hearing blocks with separate groups could be better. A well-justified randomized block plan is also acceptable.

The arrangement is double-blind/double-masked if neither participants nor interacting assessors can identify the material. If assessors know but participants do not, it is single-blind. If participants know but assessors do not, it is also single-blind. A visible code preserves masking only while its meaning remains concealed.

The matching inactive placebo supplies a control comparison, and the no-treatment group supplies the reference for the placebo effect. Placebo effect is 2−1=1 improvement point. Active-minus-placebo is 6−2=4 points and concerns the active ingredient comparison, not the placebo effect.

Random assignment supports a cause-and-effect comparison of materials under the lab conditions because it reduces systematic confounding. Recruiting volunteers rather than randomly selecting adults means the result is not automatically generalizable to all adults. It applies to participating volunteers and may be relevant to similar units; practical or ethical recruitment limits do not erase this distinction.