Package: exactcond 0.2.0

exactcond: Exact Conditional Reference Distributions for Tables and Selected Linear Models

Reference distributions that are exact at every sample size, obtained by conditioning on a statistic sufficient for the nuisance parameter rather than by appealing to an asymptotic approximation. Two forms of conditioning are supplied. For a two-way table the row and column totals are sufficient for the marginal parameters, so conditioning on both margins leaves the Fisher-Yates law, sampled here exactly by random permutation of the column labels; statistics include the linear-by-linear association of Goodman (1979) <doi:10.1080/01621459.1979.10481650> and, for nominal rows against an ordinal column, the dispersion of the row mean scores, whose components are the group contrasts themselves. A two-table form conditions further on the total score to cancel a common association parameter, giving a nuisance-free test that two tables share it. For a linear model under a null in which the tested structure is absent, a statistic invariant to the coefficients and the error scale depends on the data only through the residual direction, which is uniform on the sphere of the residual space; the reference stays exact when the statistic is maximised over candidate structures, and so remains valid after a spatial weight matrix has been chosen by fit. Permutation tests for a battery of categorical items and for differences between correlation networks follow the nonparametric combination of Pesarin and Salmaso (2010) <doi:10.1002/9780470689516>, with exchangeability blocks as in Winkler et al. (2014) <doi:10.1016/j.neuroimage.2014.01.060>. Every replicate draws from its own stream, so results do not depend on the thread count. The same C sources back the 'Python' package 'exactcond'.

Authors:M. Theodor Loots [aut, cre]