Nonparametric Analysis
In statistical inference, or hypothesis testing, the traditional tests are called parametric tests because they depend on the
specification of a probability distribution (such as the normal) except for a set of free parameters. Parametric tests are said
to depend on distributional assumptions. Nonparametric tests, on the other hand, do not require any strict distributional assumptions.
Even if the data are distributed normally, nonparametric methods are often almost as powerful as parametric methods.
The SAS/STAT nonparametric analysis procedures include the following:
 FREQ Procedure — Oneway to nway frequency and contingency (crosstabulation) tables
 KDE Procedure — Univariate and bivariate kernel density estimation
 NPAR1WAY Procedure — 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
KDE Procedure
The KDE procedure performs univariate and bivariate kernel density estimation. Statistical density estimation involves
approximating a hypothesized probability density function from observed data. Kernel density estimation is a nonparametric
technique for density estimation in which a known density function (the kernel) is averaged across the observed data points
to create a smooth approximation. PROC KDE uses a Gaussian density as the kernel, and its assumed variance determines the
smoothness of the resulting estimate.
The following are highlights of the KDE procedure's features:
 computes a variety of common statistics, including estimates of the percentiles of the hypothesized probability density function
 produces a variety of plots, including univariate and bivariate histograms, plots of the kernel density estimates, and contour plots
 saves kernel density estimates into SAS data sets

 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 perform weighted estimation
 create a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
KDE 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