# Exact Methods

Exact methods can be useful in situations where the asymptotic assumptions are not met. Standard asymptotic methods are based on 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 may not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values. Asymptotic results may also be unreliable when the distribution of the data is sparse, skewed, or heavily tied.

SAS/STAT software provides exact computations for the following analysis:

• One-Sample Tests
• Two-Sample Tests
• k-Sample Tests
• Two-Way Table Tests
• Measures of Association
• Measures of Agreement
• Logistic Regression
• Poisson Regression
• Power of Tests and Sample Size

The FREQ and NPAR1WAY procedures compute exact p values using fast and efficient network algorithms. These algorithms provide a substantial advantage over direct enumeration, which can be very time-consuming and feasible only for small problems. These procedures also can estimate exact p-values by Monte Carlo simulation. This can be useful for problems that are so large that exact computations require a great amount of time and memory, but for which asymptotic approximations may not be sufficient.

Inference in exact logistic and exact poisson regression is based on enumerating the exact distributions of sufficient statistics for parameters of interest in the model, conditional on the remaining parameters. Hirji, Mehta, and Patel (1987) developed an efficient algorithm for generating the required conditional distributions, thus making these methods computationally available. This technique is available in the LOGISTIC and GENMOD procedures.

You request exact analysis in each of these procedures with EXACT statements. The POINT option in the EXACT statement requests exact point probabilities for the test statistics. Further details are available in the SAS/STAT documentation.

The following table summarizes SAS/STAT software's exact methods capabilities:

 One-Sample Tests   PROC FREQ Two-Sample Tests   PROC NPAR1WAY k-Sample Tests   PROC NPAR1WAY chi-square goodness-of-fit likelihood ratio chi-square test for one-way tables binomial proportion confidence limits for the binomial proportion sign test (UNIVARIATE) Fisher's exact test location tests Wilcoxon-Mann-Whitney test median test Van der Waerden test (normal scores) Savage test permutation test with general scores Kolmogorov-Smirnov test Conover test Hodges-Lehmann estimate and confidence limits scale tests Siegel-Tukey test Ansari-Bradley test Klotz test Mood test Conover test location tests Kruskal-Wallis test Brown-Mood test (median test) Van der Waerden test (normal scores) Savage test one-way ANOVA with general scores scale tests Siegel-Tukey test Ansari-Bradley test Klotz test Mood test Two-Way Tables   PROC FREQ Measures of Association   PROC FREQ Measures of Agreement   PROC FREQ Pearson chi-square likelihood ratio chi-square Mantel-Haenszel chi-square Fisher-Freeman-Halton test Jonckheere-Terpstra test Cochran-Armitage test McNemar's test and confidence limits for odds ratios in 2x2 tables confidence limits for risk difference and relative risk Barnard's unconditional test for the risk (proportion) difference Zelen's test for equal odds ratios in stratified 2x2 tables test and confidence limits for the common odds ratio in stratified 2x2 tables Pearson correlation coefficient Spearman correlation coefficient Kendall's Tau-b Stuart's Tau-c Somers' D McNemar's test simple kappa coefficient weighted kappa coefficient Logistic Regression   PROC LOGISTIC   PROC GENMOD Poisson Regression   PROC GENMOD Power of Tests and Sample Size   PROC POWER dichotomous model generalized logit exact probability test exact conditional score test output data sets containing derived distributions parameter estimation median unbiased estimate odds ratio for reference parameterization one or two-sided confidence limits stratified analysis exact probability test exact conditional score test output data sets containing derived distributions parameter estimation median unbiased estimate one or two-sided confidence limits stratified analysis exact binomial Fisher's exact

The information provided in this document is current as of SAS/STAT 14.1.