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
Goodman's linear-by-linear association 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. 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'.
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