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For a given RE-RANDOMISATION distribution, a family of related distributions may be defined according to a range of hypothetical values of the pattern which the TEST STATISTIC measures. For instance, for the PITMAN PERMUTATION TEST(2) to test for a scale shift between two groups, a related distribution may be formed by shifting all the observations in one group by a common amount, where this common shift is regarded as a continuous variable. With finite numbers of data the number of related distributions will be finite, and typically considerably smaller than the number of points of the RANDOMISATION DISTRIBUTION. The likelihood of the OUTCOME VALUE may be calculated for each distribution in the family, and these likelihoods may be then used to define a contiguous set of values which occupy a certain proportion of the total unit weight of the likelihoods integrated over all values of the TEST STATISTIC. The CONFIDENCE INTERVAL is defined by the minimum and maximum values of the range of values so defined. The proportion of the total weight within the range of values is regarded as an ALPHA probability that the value of the TEST STATISTIC lies within this range. Generally the definition of a CONFIDENCE INTERVAL cannot be unique without imposing further constraints. Approaches to providing suitable constraints, such that a CONFIDENCE INTERVAL will be unique, include defining the CONFIDENCE INTERVAL : to include the whole of one TAIL of the distribution; or to be centred in some sense upon the OUTCOME VALUE; or to be centred between TAILS of equal weight. In the case of RE-RANDOMISATION DISTRIBUTIONs, these are DISCRETE DISTRIBUTIONS so there will generally be no range of values with weight corresponding exactly to an arbitrary NOMINAL ALPHA CRITERION LEVEL, and the problem of non-uniqueness is therefore not generally solvable.

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