A permutation test is illustrated here for a two-sample comparison. The notation is as follows: Two independent groups with sample sizes n and m have independently and identically distributed values X 1, …, X n and Y 1, …, Y m , respectively, n + m = N. The means are denoted by \(\overline{X}\) and \(\overline{Y },\) and the distribution functions by F and G. These distribution functions of the two groups are identical with the exception of a possible location shift: F(t) = G(t − θ) for all t, − ∞ < θ < ∞. The null hypothesis states H 0 : θ = 0, whereas θ≠0 under the alternative H 1.
In this case Student’s t test (see Student’s t-Tests) can be applied. However, if F and G were not normal distributions, it may be better to avoid using the t distribution. An alternative method is to use the permutation null distribution of the t statistic.
In order to generate the permutation distribution all possible permutations under the null hypothesis have to be generated. In the two-sample case,...
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References and Further Reading
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Neuhäuser, M. (2011). Permutation Tests. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_444
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