# Notes on designing an experiment

## Randomization used

Here you write down the method of randomization used. For an experiment with no blocks this will normally be `complete randomization'.

Why do we randomize? It is to avoid

• systematic bias (for example, doing all the tests on treatment A in January then all the tests on treatment B in March)
• selection bias (for example, choosing the most healthy patients for the treatment that you are trying to prove is best)
• accidental bias (for example, using the first rats that the animal handler takes out of the cage for one treatment and the last rats for the other)
• cheating by the experimenter.

Cheating is not always badly intentioned. For example, an experimenter may decide to

• give the extra milk rations to those schoolchildren who are most undernourished
• choose to put a patient in a trial if (s)he thinks that the patient will particularly benefit from the new treatment
• try to balance numbers over some nuisance factor without troubling the statistician
• make life a little easier in the waking example by doing all the students with W and then all those with Z.

How do we randomize? Write down a systematic plan. Then choose a random permutation (from a computer, or shuffle a pack of cards) and apply it to the systematic plan.

In the wakingexample, suppose that the experimental units are the students whose names begin with B, C, F, H, I, K, N, O, R, S, T. The obvious way to number these is
 1 2 3 4 5 6 7 8 9 10 11 B C F H I K N O R S T
A suitable systematic plan is
 1 2 3 4 5 6 7 8 9 10 11 W W W W W W Z Z Z Z Z
Suppose that the random permutation of the numbers 1, 2, ..., 11 is

 10 5 7 11 8 6 1 9 3 2 4

We keep the systematic order for the experimental units but use the randomized order for the treatments. This gives us the randomized allocation
 1 2 3 4 5 6 7 8 9 10 11 B C F H I K N O R S T 10 5 7 11 8 6 1 9 3 2 4 Z W Z Z Z W W Z W W W

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Page updated 17/11/01