Introduction
Experimental design determines how data is collected in the first place, so that the resulting analysis can support valid causal conclusions — a well-designed experiment is what actually allows the causation that Chapter 4 explicitly warned correlation alone cannot establish.
1. Experimental units, treatments, and response variables
The experimental unit is the smallest entity to which a treatment is applied (a person, plot of land, or sample). A treatment is the specific condition or intervention being studied and compared. The response variable is the outcome measured to assess the treatment’s effect. Precisely defining all three at the outset is essential, since ambiguity in any of them undermines the interpretability of the entire experiment’s results.
2. Randomization, replication, and local control (blocking)
These are the three foundational principles of good experimental design. Randomization — randomly assigning experimental units to treatments — protects against systematic bias, ensuring that any unmeasured confounding factors are distributed roughly evenly across treatment groups on average, making a genuinely causal comparison possible. Replication — applying each treatment to multiple experimental units — allows the natural variability between units to be estimated and distinguished from a genuine treatment effect. Local control (blocking) — grouping similar experimental units together before applying treatments within each group — removes a known source of variability from the comparison, increasing the experiment’s precision.
3. Completely randomized and randomized block designs
A completely randomized design (CRD) assigns treatments to experimental units entirely at random, with no blocking — simplest to design and analyse, but least able to control for known sources of variability among units. A randomized block design (RBD) first groups units into blocks (using local control, based on some known source of variability, such as different fields or time periods), then randomly assigns all treatments within each block separately — this removes the block-to-block variability from the treatment comparison, generally increasing precision compared to a CRD when a genuinely relevant blocking factor exists.
4. Latin square and other named designs
A Latin square design simultaneously controls for two blocking factors (arranged in rows and columns) rather than the single blocking factor of an RBD, with each treatment appearing exactly once in every row and every column — a more restrictive but powerful design when two known nuisance factors both need to be controlled for. Other syllabus-named designs generally extend these same core principles (randomization, replication, blocking) to progressively more complex situations, such as controlling for additional factors or unequal unit numbers.
5. Analysis of Variance (ANOVA) concepts
ANOVA partitions the total observed variation in the response variable into components attributable to different sources — the treatment (the variation of genuine interest), any blocking factors, and residual/error variation (unexplained, “random” variability) — and compares the treatment variation to the error variation, via an F-test (Chapter 7), to assess whether the treatments have a statistically significant effect. This partitioning is summarised in an ANOVA table, listing each source’s sum of squares, degrees of freedom, mean square, and the resulting F-statistic — constructing and correctly interpreting such a table is the central practical and examinable skill of this topic.
Key Takeaways
- Clearly defining experimental units, treatments, and response variables at the outset is essential to a well-designed, interpretable experiment.
- Randomization protects against bias, replication allows genuine variability to be estimated, and local control/blocking removes known variability sources — the three foundational design principles.
- A completely randomized design uses no blocking; a randomized block design blocks for one known factor; a Latin square design simultaneously controls for two known factors.
- ANOVA partitions total variation into treatment, (blocking,) and error components, using an F-test to assess whether treatment effects are statistically significant, summarised in an ANOVA table.