FOCUS AREAS

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:

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.