What the exam asks
- Identify whether a described study uses a completely randomized design, a randomized block design, or a matched pairs design.
- Describe step-by-step how to implement random assignment using a random number generator, slips of paper, or a coin/die, both overall and within blocks.
- Explain the statistical advantage of blocking in the context of the specific blocking and response variables.
- Justify why a randomized block or matched pairs design is preferable to a completely randomized design for a given scenario.
- Determine the valid scope of inference: whether a cause-and-effect conclusion is justified and to what group of units the results can be generalized.
Core ideas
Comparing the three experimental designs
| Design | How units are grouped | How treatments are assigned | Best used when... |
|---|---|---|---|
| Completely randomized design (CRD) | All experimental units are kept in one single pool. | Units are assigned completely at random to the treatments. | Experimental units are relatively homogeneous (similar) in characteristics that affect the response variable. |
| Randomized block design (RBD) | Units are first sorted into blocks (homogeneous groups) based on a variable known or expected to affect the response. | Random assignment to treatments happens separately within each block. | A known non-treatment variable (like age, soil plot location, or initial fitness) strongly influences the response variable. |
| Matched pairs design | A special case of blocking where blocks have size 2 (two very similar units paired together) or size 1 (each unit receives both treatments). | Within each pair of units, one is randomly assigned to Treatment A and the other to Treatment B. If one unit gets both, the order of treatments is randomized. | You are comparing two treatments and can form tight pairs based on a key variable, or each unit can be measured under both treatments. |
The purpose of blocking
Even with random assignment, natural variability among experimental units creates “noise” in the response variable, making it harder to tell if differences between treatment groups are due to the treatments or just unit-to-unit variation.
Blocking groups similar experimental units together before random assignment. By comparing treatments within each block, blocking separates out the variation in the response variable caused by the blocking variable. This reduces unexplained variation within treatment groups and allows a more precise comparison of the treatments.