1.1 Basic terminology
- (i)
- A factor is an input variable whose effect on the response is studied. Its chosen values are its levels. A factor may be quantitative (temperature: \(150\), \(160\), \(170\,^\circ \)C) or qualitative (brand of tyre: \(A\), \(B\)).
- (ii)
- A treatment is the combination of factor levels applied to a unit. With one factor the treatments are its levels; with several they are the combinations of their levels.
- (iii)
- An experimental unit is the smallest piece of material to which a treatment is applied independently of the others: a plot of land, an animal, a batch of raw material, a run of a machine.
- (iv)
- A measurement unit (or observational unit) is the object on which the response is measured. It may be the experimental unit or a part of it.
- (v)
- The response is the variable measured to assess the effect of the treatments.
- (vi)
- Experimental error is the variation among experimental units that receive the same treatment.
The distinction between experimental and measurement units matters more than any other in this course, because experimental error, and so every test and confidence interval, must be measured between experimental units.
Example 1.1.2. Two diets are compared on pigs. Eight pens hold five pigs each; four pens are chosen at random to receive diet \(1\) and the other four diet \(2\), and every pig is weighed after six weeks. The diet is applied to a whole pen, so the experimental unit is the pen, and there are four replicates of each diet, not twenty. The pigs are measurement units. Pigs in the same pen share a trough, a draught and a pen-mate who bullies them, so their weights are correlated; treating the \(40\) weights as \(40\) independent replicates understates the experimental error and overstates the evidence. This mistake is called pseudo-replication.
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