Design of experiments

Definition

Let $T$ be a finite set of treatments and let $U$ be a finite set of $n$ experimental units. An experimental design for $T$ on $U$ is a map $d \colon U \to T$ , which assigns treatment $d(u)$ to unit $u$ . The number $r_t = \abs{d^{-1}(t)}$ is the replication of treatment $t$ . After the treatments are applied, a response $y_u$ is observed on each unit. A statistical model relates $y_u$ to the treatment $d(u)$ and to the unit $u$ . Design of experiments is the choice of $T$ , $U$ and $d$ , together with the plan of analysis, before the data are collected.

Remarks

Example: two diets $T = \set{A, B}$ and four animals $U = \set{1, 2, 3, 4}$ . The map $d(1) = A$ , $d(2) = B$ , $d(3) = B$ , $d(4) = A$ is a design with $r_A = r_B = 2$ .

Non-example: in an observational study the units choose their own treatments, for example smokers and non-smokers. The map $d$ is not chosen by the investigator, so this is not a designed experiment. Differences in response may then come from other differences between the groups.

For experiments with a quantitative input $x$ in a region $\mathcal{X}$ , a design is a choice of the input values $x_1, \dots, x_n \in \mathcal{X}$ . In the approximate theory, it is a probability measure on $\mathcal{X}$ with finite support.

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Statistical model concept
Design of experiments definition

Tag	`SCYW8DVPKQ`
URI	`m2://SCYW8DVPKQ`
Kind	definition
Writing	W0 stub
MSC	62K99, 62K05
Defines	Design of experiments
Uses	Statistical model

Design of experiments

Definition

Remarks

Reading path

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