Permutation or randomisation tests are a useful alternative to more standard parametric tests for analysing experimental data. They have the advantage of making no distributional assumptions (such as Normality)about the data, while remaining as powerful as more standard tests. The t-test assumes that the two groups arose by drawing samples from two Normally distributed populations, and that we are investigating whether these populations differ in their mean.
The randomisation test, on the other hand, assumes that some initial set of individuals were randomly allocated to two treatment groups. The number of permutations to be examined soon grows prohibitively large, so, this function uses two approaches: an Exact Method when the possible permutations are less than 20.000 and a Monte Carlo Naive Method when the
permutations are more than 20.000.
Example:
X1=[12 17 14]; X2=[21 16 18];
rndttest(X1,X2)
Answer is:
RANDOMISATION TEST
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Exact Method
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20 randomisations evaluated
Probability (p-value) that the observed difference is accidental: 0.2000
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This p-value is the best one that can be quoted for these data. It is based only on the assumption that individuals are allocated at random to groups. It does not assume anything about Normality of distributions, which may or may not be true. Even when such assumptions are true, the randomisation test is as powerful as a t-test. (If you are curious, a t-test of the experimental data in our example gives p=0.12)
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