Experiments compare treatments to see whether one causes a different response than another. In real data, people, plants, classrooms, or other experimental units often differ in ways that affect the outcome. Blocking is a design strategy that groups similar units before random assignment so those differences do not hide the treatment effect.
Matched pairs is a special blocking design that makes very close comparisons, often using pairs of similar subjects or the same subject twice.
The main idea is to control variation from known sources before the experiment begins. Researchers first form blocks based on an important variable, such as age group, ability level, field location, or baseline health, then randomly assign treatments within each block. This keeps randomization while making treatment groups more comparable.
When variation inside each block is smaller than variation in the full population, treatment estimates become more precise.
Key Facts
- Blocking means grouping similar experimental units, then randomly assigning treatments within each group.
- Matched pairs is a blocking design with blocks of size 2, often one pair member per treatment.
- A common matched-pairs difference is d = response under treatment A - response under treatment B.
- Blocking reduces unexplained variability when the blocking variable is related to the response.
- Randomization is still required within blocks to protect against bias.
- More precise comparisons usually have smaller standard error, such as SE = s_d / sqrt(n) for matched-pairs differences.
Vocabulary
- Block
- A block is a group of experimental units that are similar in a way expected to affect the response.
- Blocking variable
- A blocking variable is the characteristic used to form blocks, such as gender, starting score, location, or age group.
- Matched pairs design
- A matched pairs design compares two treatments using pairs of closely matched units or two measurements on the same unit.
- Random assignment
- Random assignment is the process of using chance to decide which treatment each experimental unit receives.
- Precision
- Precision describes how tightly an estimate would vary from sample to sample, often reflected by a smaller standard error.
Common Mistakes to Avoid
- Blocking after random assignment is wrong because blocks must be formed before treatments are assigned to control known sources of variation.
- Using a blocking variable unrelated to the response is weak design because it does little to reduce variability or improve precision.
- Forgetting to randomize within each block is wrong because blocking alone does not prevent bias in treatment assignment.
- Treating matched pairs as two independent samples is wrong because paired observations are linked, so the analysis should focus on within-pair differences.
Practice Questions
- 1 A study tests two fertilizers on 24 garden plots. The plots are first grouped into 6 blocks of 4 plots based on soil quality, then 2 plots in each block get fertilizer A and 2 get fertilizer B. How many plots receive each fertilizer in total?
- 2 In a matched-pairs study, 8 students take a practice test before and after a study program. Their score changes are 5, 7, 4, 10, 6, 3, 8, and 5 points. Find the mean change.
- 3 A researcher wants to compare two teaching methods in a school with both ninth-grade and twelfth-grade students. Explain why grade level might be a good blocking variable and describe how random assignment should be done.