Background

Exact statistics can be useful in situations where the asymptotic assumptions are not met, and so the asymptotic p-values are not close approximations for the true p-values.

In other words, Exact Tests enable us to make reliable inferences when our data are small, sparse, heavily tied, or unbalanced and the validity of the corresponding large sample theory is in doubt. This is achieved by computing exact p-values for a very wide class of hypothesis tests, including one-, two-, and K- sample tests, tests for unordered and ordered categorical data, and tests for measures of association.

Standard asymptotic methods involve the assumption that the test statistic follows a particular distribution when the sample size is sufficiently large. When the sample size is not large, asymptotic results might not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values.

Asymptotic results might also be unreliable when the distribution of the data is sparse, skewed, or heavily tied. See Agresti (2007) and Bishop, Fienberg, and Holland (1975) for more information.

Exact computations in SAS PROC FREQ are based on the statistical theory of exact conditional inference for contingency tables, reviewed by Agresti (1992).

Resource

The book below is available on the internet