Randomized Block Design — Definition, Formula & Examples
Randomized block design is an experimental design where subjects are first sorted into groups (blocks) that share a similar characteristic, and then treatments are randomly assigned within each block. This reduces the effect of that characteristic on the results, making it easier to detect the true effect of the treatment.
A randomized block design is an experimental structure in which experimental units are partitioned into homogeneous groups called blocks based on a known source of variability (the blocking variable). Within each block, treatments are randomly assigned to units so that treatment comparisons are made within blocks, thereby controlling for the blocked source of variation and increasing the precision of estimates of treatment effects.
How It Works
First, identify a variable that could affect your response variable but is not the factor you are studying — this becomes your blocking variable. Group your experimental units into blocks so that units within the same block are as similar as possible with respect to that variable. Then, within each block, randomly assign the treatments. Because each block contains all treatments, any differences due to the blocking variable affect all treatments equally and can be separated out during analysis. This setup isolates the treatment effect more cleanly than a completely randomized design would when a known source of variability exists.
Example
Problem: A researcher wants to test 3 fertilizers (A, B, C) on crop yield. The test field has 4 distinct soil-quality zones. Design the experiment using a randomized block design.
Identify the blocking variable: Soil quality varies across the field and could affect yield independently of fertilizer type. Each soil-quality zone becomes one block, giving 4 blocks.
Assign treatments within blocks: Divide each block into 3 plots (one per fertilizer). Randomly assign fertilizer A, B, or C to the 3 plots within each block. Repeat this independent randomization for all 4 blocks.
Count experimental units: Total plots used in the experiment:
Answer: The experiment uses 4 blocks (one per soil zone) with 3 plots each, for 12 total plots. Each fertilizer appears exactly once per block, and assignments within each block are randomized.
Why It Matters
Randomized block designs appear regularly on the AP Statistics exam, where you must recognize when blocking is appropriate and distinguish it from a completely randomized design. In agricultural science, clinical trials, and manufacturing, blocking on a known nuisance variable (such as age group, field location, or machine batch) can dramatically increase the power of an experiment without adding more subjects.
Common Mistakes
Mistake: Confusing blocking with creating a control group or with stratified random sampling.
Correction: Blocking is an experimental design technique: you group units by a nuisance variable and then randomly assign treatments within each group. A control group is one of the treatments (or lack thereof). Stratified sampling is a sampling method used in observational studies, not an experimental design for assigning treatments.