Selecting a Design
Introduced| English |
|---|
| completely randomized design/kəmˈpliːtli ˈrændəmaɪzd dɪˈzaɪn/ |
| blocking/ˈblɒkɪŋ/ |
| matched-pairs design/mætʃt peəz dɪˈzaɪn/ |
| randomized block design/ˈrændəmaɪzd blɒk dɪˈzaɪn/ |
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."
Block and matched-pairs designs
- A randomized block design 随机区组设计: 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.
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...
Matched pairs = blocks of size 2.
Blocking groups similar experimental units to remove a known source of variability.
That's exactly the purpose of blocking.
Fitness strongly affects the response. The best design is to...
Block on the known nuisance variable (fitness).
The simplest design, assigning all units to treatments purely by chance, is a completely ___ design.
A completely randomized design uses randomization alone.
Blocking (in experiments) is most like which sampling method?
Both group similar units — blocking (design) parallels stratifying (sampling).