Selecting a Design
Introduced| English | Meaning |
|---|---|
| completely randomized design/kəmˈpliːtli ˈrændəmaɪzd dɪˈzaɪn/ | completely randomized design |
| blocking/ˈblɒkɪŋ/ | blocking |
| randomized block design/ˈrændəmaɪzd blɒk dɪˈzaɪn/ | An experiment that first groups similar subjects into blocks, then randomly assigns treatments within each block. |
| matched-pairs design/mætʃt peəz dɪˈzaɪn/ | An experimental design in which similar units are paired, and the two treatments are randomly assigned within each pair (or each unit receives both treatments in random order) |
The completely randomized design
- The simplest design: a completely randomized design 完全随机设计.
- All experimental units are assigned to treatments purely by chance.
- No grouping first — just randomize everyone into the treatment groups.
- It relies on randomization alone to balance out differences.
Blocking cuts variability
- Sometimes units differ in a known way that affects the response (e.g. age, sex).
- Blocking 区组化 groups similar units into blocks, then randomizes within each block.
- This removes that known source of variation from the comparison.
- "Block what you can, randomize what you can't."
A randomized block design 随机区组设计: group similar subjects, then randomize within each block
Block and matched-pairs designs
- A randomized block design: form blocks of similar units, randomize treatments inside each.
- A matched-pairs design 配对设计: the special case of blocks of size $2$.
- Match two similar units (or use the same unit twice), randomize which gets which treatment.
- Comparing within a matched pair cancels the differences between individuals.
Choosing a design
- Pick the design that controls the biggest known source of variability.
- If a variable (age, baseline skill) clearly affects the response → block on it.
- If no strong nuisance variable stands out → a completely randomized design is fine.
- The goal is a fair comparison where only the treatment differs.
Blocking is not the same as stratifying. Same idea (group similar units), different setting: stratified sampling is about choosing a representative sample; blocking is about designing an experiment to reduce variability. Also, don't block on a variable that has nothing to do with the response — you only block on a known nuisance variable.
Testing a workout plan on people of very different fitness.
- Fitness strongly affects the response → block by fitness level.
- Randomized block design: within each fitness block, randomly assign plan A or B.
- Matched pairs: pair each person with a similar-fitness partner; randomize who gets A.
A completely randomized design assigns all units to treatments by chance. Blocking groups similar units to remove a known source of variability, giving a randomized block design (or a matched-pairs design when blocks have size $2$). Choose the design that controls the largest known nuisance variable.
Write from blocking similar units
- Subjects differ a lot in fitness.
- The designer groups similar fitness levels before assigning the treatment inside each group.
What design step is the grouping?
Blocks remove a known source of variation.
What is grouping by fitness before assignment?
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Similar units share a block.
Units grouped into blocks
Blocking groups similar units before randomizing within each.
A matched-pairs design is a special case of a randomized block design with blocks of size...
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Matched pairs = blocks of size 2.
Blocking groups similar experimental units to remove a known source of variability.
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That's exactly the purpose of blocking.
Fitness strongly affects the response. The best design is to...
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Block on the known nuisance variable (fitness).
The simplest design, assigning all units to treatments purely by chance, is a completely ___ design.
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A completely randomized design uses randomization alone.
Blocking (in experiments) is most like which sampling method?
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Both group similar units — blocking (design) parallels stratifying (sampling).