Selecting a Design

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.

Write from blocking similar units

• Subjects differ a lot in fitness.
• The designer groups similar fitness levels before assigning the treatment inside each group.