Experimental Design Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardA study wants to test three fertilizer types (A, B, C) on crop yield across 12 fields. Design a completely randomized design (CRD) and a randomized block design (RBD) if the 12 fields have 4 different soil quality levels.
Solution
- 1 CRD: randomly assign 4 fields to each fertilizer (4 fields × 3 treatments = 12 total); ignores soil quality differences
- 2 RBD: group 12 fields into 4 blocks by soil quality (3 fields per block); within each block, randomly assign one field to each fertilizer
- 3 RBD advantage: soil quality is controlled — each fertilizer is tested in each soil type; reduces variability from soil differences
- 4 Use RBD when known confounders (like soil quality) would add variability — blocking removes this noise, giving more power
Answer
CRD: randomly assign fertilizers to all 12 fields. RBD: block by soil quality first, then randomize within blocks.
Blocking is used when a known source of variability (a confounder) exists. By ensuring each treatment appears in each block, blocking controls for the confounding variable. This reduces within-group variability and increases the power to detect treatment effects.
About Experimental Design
The deliberate planning of a study in which the researcher imposes treatments on subjects and measures responses, using control groups, randomization, replication, and (where possible) blinding to establish cause-and-effect relationships.
Learn more about Experimental Design →More Experimental Design Examples
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