1.2 Principles of experimental design
Three principles underlie every design in this course.
- (i)
- Replication is the repetition of the basic experiment: each treatment is applied independently to more than one experimental unit.
- (ii)
- Randomisation is the use of a chance mechanism to allocate the treatments to the experimental units, and to fix the order in which the individual runs of the experiment are performed.
- (iii)
- Blocking is the grouping of experimental units into sets (blocks) that are more alike than the units as a whole, and the comparison of treatments within the blocks. Equivalently, it fixes the levels of a nuisance factor while the factors of interest are varied.
Each principle has two jobs.
Replication
- It allows the experimenter to obtain an estimate of the experimental error, which is the yardstick against which differences between treatments are judged. Without replication there is no way to tell a treatment difference from unit-to-unit variation.
- It makes the estimates more precise: if \(\sigma ^2\) is the variance of a single observation, the mean of \(r\) replicates has variance \(\sigma ^2/r\).
Replication is not the same as repeated measurement. Weighing the same pig three times reduces measurement error but tells us nothing about variation between pigs.
Randomisation
- It makes valid the assumption, required by the statistical methods, that the observations (or errors) are independently distributed random variables.
- It helps average out the effects of factors that are unknown or not controlled, so that no treatment is systematically favoured.
Blocking
- It improves the precision of comparisons between the factors of interest.
- It reduces or eliminates the effect of known nuisance factors on those comparisons.
The rule that follows is short: block what you can, randomise what you cannot.
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