Exact nonparametric methods have an advantage over asymptotic methods since they remain valid for very small
sample sizes, as well as for data that are sparse, skewed, or heavily tied.
The SAS/STAT exact inference procedures include the following:
 FREQ Procedure — Produces oneway to nway frequency and contingency (crosstabulation) tables
 GENMOD Procedure — Generalized linear models
 LOGISTIC Procedure — Fits models with binary, ordinal, or nominal dependent variables
 MULTTEST Procedure — Addresses the multiple testing problem by adjusting the pvalues from a family of hypothesis tests
 NPAR1WAY Procedure — Performs nonparametric tests for location and scale differences across a oneway classification
FREQ Procedure
The FREQ procedure produces oneway to nway frequency and contingency (crosstabulation) tables.
For twoway tables, PROC FREQ computes tests and measures of association. For nway tables, PROC FREQ provides
stratified analysis by computing statistics across, as well as within, strata.
The following are highlights of the FREQ procedure's features:
 computes goodnessoffit tests for equal proportions or specified null proportions for oneway frequency tables
 provides confidence limits and tests for binomial proportions, including tests for noninferiority
and equivalence for oneway frequency tables
 compute various statistics to examine the relationships between two classification variables. The statistics for contingency
tables include the following:
 chisquare tests and measures
 measures of association
 risks (binomial proportions) and risk differences for 2 x 2 tables
 odds ratios and relative risks for 2 x 2 tables
 tests for trend
 tests and measures of agreement
 CochranMantelHaenszel statistics

 computes asymptotic standard errors, confidence intervals, and tests for measures
of association and measures of agreement
 computes score confidence limits for odds ratios
 computes exact pvalues, exact midpvalues, and confidence intervals for many test statistics and measures
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 accepts either raw data or cell count data to produce frequency and crosstabulation tables
 creates a SAS data set that contains the computed statistics
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
FREQ Procedure
GENMOD Procedure
The GENMOD procedure fits generalized linear models, as defined by Nelder and Wedderburn (1972). The class of generalized
linear models is an extension of traditional linear models that allows the mean of a population to depend on a linear predictor
through a nonlinear link function and allows the response probability distribution to be any member of an exponential family of
distributions. Many widely used statistical models are generalized linear models. These include classical linear models with normal
errors, logistic and probit models for binary data, and loglinear models for multinomial data. Many other useful statistical models
can be formulated as generalized linear models by the selection of an appropriate link function and response probability distribution.
The following are highlights of the GENMOD procedure's features:
 provides the following builtin distributions and associated variance functions:
 normal
 binomial
 Poisson
 gamma
 inverse Gaussian
 negative binomial
 geometric
 multinomial
 zeroinflated Poisson
 Tweedie
 provides the following builtin link functions:
 identity
 logit
 probit
 power
 log
 complementary loglog
 enables you to define your own link functions or distributions through DATA step
programming statements used within the procedure
 fits models to correlated responses by the GEE method

 perform Bayesian analysis for generalized linear models
 performs exact logistic regression
 performs exact Poisson regression
 enables you to fit a sequence of models and to perform Type I and Type III analyses
between each successive pair of models
 computes likelihood ratio statistics for userdefined contrasts
 computes estimated values, standard errors, and confidence limits for userdefined
contrasts and least squares means
 computes confidence intervals for model parameters based on either the profile
likelihood function or asymptotic normality
 produces an overdispersion diagnostic plot for zeroinflated models
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates SAS data sets that correspond to most output tables
 automatically generates graphs by using ODS Graphics

For further details, see
GENMOD Procedure
LOGISTIC Procedure
The LOGISTIC procedure fits linear logistic regression models for discrete response data by the method of maximum likelihood.
It can also perform conditional logistic regression for binary response data and exact logistic regression for binary and nominal
response data. The maximum likelihood estimation is carried out with either the Fisher scoring algorithm or the NewtonRaphson
algorithm, and you can perform the biasreducing penalized likelihood optimization as discussed by Firth (1993) and Heinze and
Schemper (2002). You can specify starting values for the parameter estimates. The logit link function in the logistic regression
models can be replaced by the probit function, the complementary loglog function, or the generalized logit function.
The LOGISTIC procedure also enables you to do the following:
 fit stratified conditional logistic regression of binary response data
 fit partial proportional odds logistic regression models
 fit adjacentcategory logit models to ordinal response data
 add or relax constraints on parameters in nominal response models and partial proportional odds models
 compute the partial correlation statistic for each model parameter (excluding the intercept)
 control the ordering of the response categories
 compute a generalized R^{2} measure for the fitted model
 reclassify binary response observations according to their predicted response probabilities
 test linear hypotheses about the regression parameters
 perform exact tests of the parameters for the specified effects and optionally estimates
the parameters and exact conditional distributions
 specify contrasts to compare several receiver operating characteristic curves

 score a data set by using a previously fitted model
 specify units of change for continuous explanatory variables so that customized odds ratios can be estimated
 perform BY group processing, which enables you to obtain separate analyses on grouped observations
 perform weighted estimation
 create a data set for producing a receiver operating characteristic curve for each fitted model
 create a data set that contains the estimated response probabilities, residuals, and influence diagnostics
 create a data set that contains the estimated parameter vector and its estimated covariance matrix
 create a data set that corresponds to any output table
 automatically create graphs by using ODS Graphics

For further details, see
LOGISTIC Procedure
MULTTEST Procedure
The MULTTEST procedure addresses the multiple testing problem by adjusting the pvalues from a family
of hypothesis tests.
PROC MULTTEST approaches the multiple testing problem by adjusting the pvalues from a family of hypothesis tests.
An adjusted pvalue is defined as the smallest significance level for which the given hypothesis would be rejected,
when the entire family of tests is considered. The decision rule is to reject the null hypothesis when the adjusted
pvalue is less than α. For most methods, this decision rule controls the familywise error rate at or below
the α level. However, the false discovery rate controlling procedures control the false discovery rate at or
below the α level. The following are highlights of the MULTTEST procedure's features:
 provides the following pvalue adjustments:
 Bonferroni
 Šidák
 stepdown methods
 Hochberg
 Hommel
 Fisher combination
 bootstrap
 permutation
 adaptive methods
 false discovery rate
 positive FDR
 handles data arising from a multivariate oneway ANOVA model, possibly
stratified, with continuous and discrete response variables; it can also accept raw pvalues as input data
 performs a t test for the mean for continuous data with or without a homogeneity
assumption, and the following statistical tests for discrete data:
 CochranArmitage linear trend test
 FreemanTukey double arcsine test
 Peto mortalityprevalence (logrank) test
 Fisher exact test

 provides exact versions of the CochranArmitage and Peto tests that use permutation distributions and
asymptotic versions that use an optional continuity correction.
 enables you to use a stratification variable to construct MantelHaenszeltype tests
 enables you to perform one or twosided tests
 enables you to specify linear contrasts that compare means or proportions of the treated groups
 creates output data sets containing raw and adjusted pvalues, test statistics and
other intermediate calculations, permutation distributions, and resampling information
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any table
 automatically creates graphs by using ODS Graphics

For further details, see
MULTTEST Procedure
NPAR1WAY Procedure
The NPAR1WAY procedure performs nonparametric tests for location and scale differences across a oneway classification.
PROC NPAR1WAY also provides a standard analysis of variance on the raw data and tests based on the empirical distribution function.
The following are highlights of the NPAR1WAY procedure's features:
 performs nonparametric tests for location and scale differences across a oneway classification based on the following scores of a response variable
 Wilcoxon
 median
 Van der Waerden (normal)
 Savage
 SiegelTukey
 AnsariBradley
 Klotz
 Mood
 Conover
 raw data
 computes tests based on simple linear rank statistics when the data are classified into two samples
 computes tests based on oneway ANOVA statistics when the data are classified into more than two samples

 provides asymptotic, exact pvalues, and exact midpvalues for tests
 provides HodgesLehmann estimate of location shift including exact confidence limits
 provides tests based on Conover scores inclusing exact tests
 provides stratified rankbased analysis of twosample data
 computes the following empirical distribution function (EDF) statistics:
 KolmogorovSmirnov test
 Cramervon Mises test
 Kuiper test
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
NPAR1WAY Procedure