Randomization, Blocking & Scope of Conclusions

You’ll be able to

Describe randomized block and matched-pairs designs and their purpose
Explain how blocking reduces variability
State the scope of conclusions permitted by a study’s design

Blocking: control what you can, randomize the rest

A randomized block design groups experimental units into blocks that are similar with respect to a variable expected to affect the response, then randomizes treatments within each block. Blocking works like stratifying does for sampling: it removes a known source of variability so the treatment effect stands out. You block on a variable you can anticipate matters (sex, age group, field location) and randomize to handle the rest.

Matched pairs

A matched-pairs design is a special block design with blocks of size two. Either two similar units are paired and each treatment is randomly assigned within the pair, or — most powerfully — a single subject receives both treatments in random order, serving as their own control. Matching removes person-to-person differences, sharpening the comparison.

What conclusions are you allowed to draw?

A study’s design fixes its scope of conclusions. Random assignment of treatments → you may infer cause and effect. Random selection from a population → you may generalize to that population. Both → causal conclusion generalizable to the population. Neither → you can only describe the individuals studied. Match the claim to the design.

Scope of conclusions grid

random assign → causation · random select → generalize · both → causal + general · neither → describe only

Two independent design choices, two independent permissions. Never claim causation without random assignment or generalization beyond the sampled population without random selection.

Worked example

A researcher tests two shoe types on running speed. She has 30 runners and knows fitness varies widely. Describe a matched-pairs design and explain its benefit.

1.Have each of the 30 runners run with both shoe types, so each runner is their own pair (block of size two).
2.Randomize the order for each runner — flip a coin to decide which shoe each runner wears first — to prevent order effects.
3.Record each runner’s speed with each shoe and analyze the differences within runners.
4.Because each runner is compared to themselves, differences in fitness between runners are removed from the comparison.

Answer: Have every runner use both shoe types in a randomized order and compare each runner’s two times. This matched-pairs design cancels out runner-to-runner fitness differences, so any speed difference is more clearly attributable to the shoes.

Checkpoint

What is the main purpose of blocking in an experiment?

On the exam

A classic free-response ending: "Can we conclude the treatment caused the difference, and can we generalize to all ___?" Answer both parts using the design — cite random assignment for causation and random selection for generalization. Missing either random feature limits the claim.

Checkpoint

Volunteers (not randomly selected) are randomly assigned to a new diet or a control. The diet group loses significantly more weight. What conclusion is justified?

Answer the 2 checkpoints as you read.