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FASTats: Frequently Asked-for Statistics

You can search the index of any or all SAS books (SAS 8.2 through SAS 9.1.3) via the Search tab in the SAS OnlineDoc. Or use the category and keyword search capabilities beginning with the SAS 9.2 documentation. Search for solutions from other SAS users by searching the proceedings from previous SAS Global Forum and SUGI conferences. Or ask other SAS users at the SAS Discussion Forums or in the SAS-L mail list.

Agresti-Coull confidence interval for binomial probability

Beginning in SAS 9.2, BINOMIAL(AGRESTICOULL) option in TABLE statement of Base SAS PROC FREQ.

Alpha (Cronbach's)

ALPHA option in Base SAS PROC CORR.

Alternating Logistic Regression (ALR)

Beginning in SAS 8, use the LOGOR= option in the REPEATED statement in the SAS/STAT procedure GENMOD. ALR is a form of the Generalized Estimating Equation (GEE) method for modeling repeated (longitudinal) binary-response data.

ANOVA on summary statistics

For comparing two group means, use SAS/STAT PROC TTEST. See the example in the TTEST documentation. For comparing more than two group means, see this sample program.

Automatic Interaction Detector (AID)

See CHAID below.

Autoregressive Conditional Heteroscedasticity (ARCH)

SAS/ETS PROC AUTOREG.

Area under a curve, estimation of

Area under ROC curve

See ROC curve.

Balanced Incomplete Block Designs (BIBDs)

In the BLOCKS statement in SAS/QC PROC OPTEX, use the structure=(b)k block specification to construct block designs with b blocks of size k. See the Balanced incomplete block design example in the OPTEX chapter of the SAS/QC User's Guide.

Balanced Repeated Replication (BRR) and Jackknife variance estimation

Beginning in SAS 9.2, these replication methods are available via the VARMETHOD= option in the survey procedures in SAS/STAT software -- SURVEYFREQ, SURVEYLOGISTIC, SURVEYMEANS, and SURVEYREG.

Bartholomew test of ordering of proportions

Not available. But the Cochran-Armitage test of linear trend, which tests a stricter alternative hypothesis, is available.

Bartlett test for variance homogeneity

Bayesian Methods

Berkson estimation

See Minimum chi-square estimation (Berkson)

Bhapkar's test

Use the REPEATED statement in the SAS/STAT procedure CATMOD to test marginal homogeneity as in the test of SIDE in the example Repeated Measures, 4 Response Levels, 1 Population in the CATMOD chapter of the SAS/STAT User's Guide. See Agresti (1990), Categorical Data Analysis, pp. 359, 499. Bhapkar's test is asymptotically equivalent to the Stuart-Maxwell test.

Binomial probability, test of or confidence interval for

Binomial probabilities, comparing each to overall

Binomial probabilities, comparing two

Biserial correlation

BISERIAL macro. See also point biserial correlation.

Bivariate normal data, Generating

Use the MVN macro.

Bivariate Logit model

See Multivariate logit model.

Bivariate Probit model

SAS/ETS PROC QLIM beginning in SAS 9.

Bivariate Tobit model

SAS/ETS PROC QLIM beginning in SAS 9.

Bonferroni t-test

SAS/STAT procedures GLM, ANOVA, and MULTTEST.

Bootstrapping

Box-and-whisker plots

Low-resolution: PLOTS option in Base SAS PROC UNIVARIATE.

High- or low-resolution: SAS/QC PROC SHEWHART.

High-resolution: SAS/STAT PROC BOXPLOT, SAS/GRAPH PROC GPLOT (I=BOXxxx option in SYMBOL statement), and SAS/INSIGHT.

Box-Behnken Designs

SAS/QC ADX Interface.

Box-Cox Transformation

Beginning with SAS 8.2, use the BOXCOX transformation in the MODEL statement in SAS/STAT PROC TRANSREG to transform the response variable in a model on independent observations (fit by procedures such as SAS/STAT procedures REG or GLM). For example:

   model BoxCox(y) = identity(x1-x5);

Also beginning in SAS 8.2, you can use the BOXCOX option in the MODEL statement of SAS/ETS PROC QLIM. This option allows transformation of both dependent and independent variables. Prior to SAS 8.2, use the ADX Interface or ADXTRANS macro in SAS/QC. For an autoregressive model, use the BOXCOXAR macro in SAS/ETS.

Box-Tidwell Transformation

Used in logistic regression to test linearity in the logit, this can be done in SAS/STAT PROC LOGISTIC by adding a variable to your model of the form x*log(x). Significance of the parameter estimate for this term indicates nonlinearity.

Bradley-Terry model

SAS/STAT PROC LOGISTIC. See this example.

Breslow-Day test (of homogeneity of odds ratios)

Base SAS PROC FREQ, CMH option.

Brier score

Not computed by any procedure, but Logistic Regression Examples Using the SAS System gives a formula, and it could be computed easily using predicted values from LOGISTIC, PROBIT, or GENMOD.

CART (Classification and Regression Trees)

CART is part of the capability of the SAS Enterprise Miner.

Censored regression

SAS/ETS PROC QLIM beginning in SAS 8.2

CHAID (Chi-square Automatic Interaction Detector)

CHAID is part of the capability of the SAS Enterprise Miner.

Chi-square goodness-of-fit test for One-way tables

Chi-square (2-way tables)

CHISQ option in Base SAS PROC FREQ

Chi-square (corrected)

CHISQ option in Base SAS PROC FREQ

Chow test

Use the CHOW= or PCHOW= options on the MODEL statement in SAS/ETS PROC AUTOREG or on the FIT statement in SAS/ETS PROC MODEL. The PCHOW= option produces the predictive Chow test. See Example 11 of the book Forecasting Examples for Business and Economics Using the SAS System for information on testing forecasting models for break points using a Chow Test.

Clopper-Pearson confidence interval for binomial probability

This is the exact confidence interval provided by the BINOMIAL option in the TABLES or EXACT statement of Base SAS PROC FREQ.

Cluster analysis, categorical data

See DISTANCES.

Cochran-Armitage trend test

See Trend test for ordered alternatives

Cochran's Q

Create a 2x2x...x2 table and use the AGREE option in Base SAS PROC FREQ. See the example titled Testing Marginal Homogeneity with Cochran's Q in the FREQ chapter of the SAS/STAT User's Guide. Alternatively, create a three-way table with a stratum variable identifying each subject (or matched group), a variable indicating each occasion (condition or individual within matched group), and a binary response variable. Then use the CMH option. For example, if each subject gives a binary response to each of several drugs, use the statement:

  tables subject*drug*response/cmh2 noprint;

Cohen's kappa

See Kappa.

Combinations and Permutations

You may either want to compute the number of combinations or permutations, or produce a list enumerating the combinations or permutations. Beginning in SAS 9.2, the latter can be done using the ALLCOMB and ALLPERM options (or the LEXCOMB and LEXPERM options) described in the SAS Language Reference: Dictionary. Beginning in SAS 8, see the COMB and PERM options in SAS/STAT PROC PLAN. See also (TS-498: Generating Combinations and Permutations). Permuting the observations in a data set can be done using PROC PLAN or PROC MULTTEST.

Concordance index

Is the area under the receiver operating characteristic (ROC) curve

Concordance, Kendall's Coefficient

See Kendall's Coefficient of Concordance.

Conditional logistic model

Conditional poisson model

See Fixed effects poisson regression.

Confidence ellipse for mean or for prediction

In SAS/INSIGHT, click Analyze ⇒ Multivariate. After running the analysis, in the analysis results window click Curves ⇒ Scatter Plot Conf. Ellipse and select Mean or Prediction and the desired confidence level. Alternatively, use the CONELIP macro.

Confidence interval

On a mean: Use CLM, LCLM or UCLM options in Base SAS PROC MEANS. Beginning in SAS 8, use the CIBASIC option in Base SAS PROC UNIVARIATE.

On a variance or standard deviation: Beginning in SAS 8, use the CIBASIC option in Base SAS PROC UNIVARIATE. Alternatively, use the VARTEST macro.

On a percentile (for example the median): Beginning in SAS 8, use the CIPCTLDF or the CIPCTLNORMAL option in Base SAS PROC UNIVARIATE.

On a binomial probability

On a difference between two binomial probabilities: Arrange the proportions as the two rows of a 2x2 table for analysis by PROC FREQ and specify the RISKDIFF option in the TABLES statement.

On a relative potency

On odds ratios

On a rate

On areas under ROC curves: Use the ROC macro to get confidence intervals for the area under a single ROC curve, or on the difference of areas under two ROC curves, or on a linear combination of the areas under several ROC curves.

On hazard (or risk) ratios: Use the RISKLIMITS option in the MODEL statement of SAS/STAT PROC PHREG. To output these to a data set, use the ODS OUTPUT statement beginning in SAS 8.

On normal regression parameters: Beginning in SAS 8, use the CLB option in the MODEL statement of SAS/STAT PROC REG or the CLPARM= option in the MODEL statement of SAS/STAT PROC GLM.

On logistic and probit regression parameters: Use the CLPARM= option in the MODEL statement of SAS/STAT PROC LOGISTIC. Use the LINK=PROBIT option to request a probit model. To output these to a data set, use the ODS OUTPUT statement beginning in SAS 8.

On proportional hazards or failure time (SAS/STAT PROC LIFEREG) model parameters: Use the ESTSTATS macro.

Conjoint Analysis

SAS/STAT PROC TRANSREG and Market Research Application. See SAS Technical Report R-109, Conjoint Analysis Examples. Also see the examples titled Nonmetric Conjoint Analysis of Tire Data and Metric Conjoint Analysis of Tire Data in the TRANSREG chapter of the SAS/STAT User's Guide.

Control Charts

SAS/QC procedures SHEWHART, MACONTROL, and CUSUM.

Cook's D

SAS/STAT procedures REG and GLM (COOKD= options in the OUTPUT statement), PROC RSREG (D option on MODEL statement), PROC LOGISTIC (C= option on the OUTPUT statement -- this value must be divided by the number of parameters in the model). A similar statistic can be computed for generalized linear models. Beginning in SAS 9.2, specify the COOKD= option in the OUTPUT statement. Prior to SAS 9.2, see this example.

Copulas

Beginning in SAS 9.2, normal, normal mixture, and t copulas are supported in SAS/ETS PROC MODEL with the COPULA= option in the SOLVE statement.

Correlations

Biserial: BISERIAL macro
Hoeffding's D: Base SAS PROC CORR (HOEFFDING option)
Intraclass: See Intraclass correlation
Kendall's tau-a: SAS/STAT PROC LOGISTIC
Kendall's tau-b: Base SAS procedures CORR (KENDALL option) and FREQ (MEASURES option)
Partial: Base SAS PROC CORR (PARTIAL statement), SAS/STAT PROC REG (PCORR1 and PCORR2 options), SAS/STAT PROC CANCORR (SQPCORR option)
Pearson: Base SAS procedures CORR and FREQ (MEASURES option)
Point biserial: Base SAS PROC CORR (The point biserial correlation is equivalent to the Pearson product moment correlation between two variables where the dichotomous variable is given any two numeric values.); BISERIAL macro
Polychoric: Base SAS PROC FREQ (PLCORR option), POLYCHOR macro
Polyserial: Not available.
Rank Biserial: BISERIAL macro
Semipartial: SAS/STAT PROC REG (SCORR1, SCORR2 options), CANCORR (SPCORR and SQSPCORR options)
Spearman: Base SAS procedures CORR (SPEARMAN option) and FREQ (MEASURES option)
Stuart's tau-c: Base SAS PROC FREQ (MEASURES option)
Tetrachoric: Base SAS PROC FREQ (PLCORR option), POLYCHOR macro

Correlation, compare two populations using Fisher Z transformation

Correlation, confidence interval for, using Fisher Z transformation

Correspondence Analysis

SAS/STAT PROC CORRESP performs simple and multiple correspondence analysis. Also, the Market Research Application.

Correspondence Analysis, canonical

Not available.

Correspondence Analysis, detrended

Not available.

Covariance matrices, testing the equality of

SAS/STAT PROC DISCRIM with the POOL=TEST option provides Bartlett's test of the equality of two or more independent covariance matrices. You can input the raw data, or the covariance, correlation, or sums of squares and crossproducts (SSCP) matrices. The test assumes that the variables are normally distributed. Here is an example.

Cox Regression

SAS/STAT PROC PHREG

CPK (process capability indices)

SAS/QC PROC CAPABILITY.

CPM (Critical Path Method)

SAS/OR PROC CPM.

Crossover analysis

Analysis of data from AB/BA crossover designs with the CROSSOVER= option in the VAR statement of SAS/STAT PROC TTEST.

Crossvalidation

d (Somer's)

See Somer's d.

D-Optimal designs

SAS/QC PROC OPTEX.

Deciles

See Quantiles

Decision trees

SAS/OR PROC DTREE.

Deming regression

See Errors-in-variables regression.

Dendrogram

SAS/STAT PROC TREE.

Density estimation, Parametric and Nonparametric

Both Parametric density estimation (fitting theoretical distributions to data) and nonparametric, kernel density estimation are available.

Derivatives

The DERIVS sample program uses SAS/ETS PROC EXPAND to fit a cubic smoothing spline to paired (X,Y) data. The first and second derivatives of the spline are computed and output to a SAS data set. Finally, the first and second derivatives are plotted against X.

Descriptive statistics

Many descriptive, or summary, statistics are available in Base SAS procedures MEANS, SUMMARY, and UNIVARIATE, including such statistics as the number of observations (N), mean, median, mode, total (sum), minimum, maximum, mode, extreme values, range, standard deviation, variance, standard error, skewness, kurtosis, percentiles, and others. Many other procedures provide various subsets of these accompanying their primary analytical results.

Design of experiments

SAS/QC procedures FACTEX, OPTEX and the ADX Interface. See the SAS/QC User's Guide and Getting Started with the SAS ADX Interface for Design of Experiments

Design matrix, create in a data set

The SAS/STAT procedures GLMMOD, LOGISTIC, and TRANSREG can all create a design matrix and write it to a data set as shown in this note.

DETMAX

SAS/QC PROC OPTEX.

Dickey-Fuller test for unit root

SAS/ETS DFTEST macro or STATIONARITY=ADF option in the IDENTIFY statement of SAS/ETS PROC ARIMA or the White Noise and Stationarity Tests window of the SAS/ETS Time Series Forecasting System. If the test statistic has been computed but the p-value associated with the statistic is needed, use either the SAS/ETS DFPVALUE macro or the SAS/ETS PROBDF function.

Differential equations

See ODE (Ordinary Differential Equations)

Discrete Choice model

Distances

Beginning in SAS 9.1, use SAS/STAT PROC DISTANCE. Prior to SAS 9.1, use the DISTANCE macro.

Distribution Fitting

See Density estimation

Distributions, Comparing

Use the EDF option in SAS/STAT PROC NPAR1WAY to compare the distributions of two or more samples.

Duncan multiple range test

SAS/STAT procedures GLM and ANOVA.

Dunnett's test

SAS/STAT procedures GLM and ANOVA.

Durbin-Watson statistic

SAS/STAT PROC GLM (CLI or CLM options), SAS/STAT PROC REG (DW option), SAS/ETS PROC AUTOREG (DW= option), SAS/ETS PROC MODEL (DW option in FIT statement).

ED50

See LD50.

EM (Expectation Maximization) algorithm

Used in SAS/STAT PROC MI (see the EM statement) to compute the maximum likelihood estimate (MLE) of the data with missing values, assuming a multivariate normal distribution for the data. Used in SAS/Genetics PROC HAPLOTYPE to generate maximum likelihood estimates of haplotype frequencies.

Empirical distribution functions, comparison of

EDF option in SAS/STAT PROC NPAR1WAY.

Equality of Means

SAS/QC PROC ANOM, SAS/STAT procedures ANOVA, GLM, MULTTEST, and TTEST.

Equality of Variances

Equivalence (noninferiority, superiority) tests

For binomial proportion and difference in proportions:  EQUIV, NONINF, and SUP suboptions of BINOMIAL and RISKDIFF options in Base SAS PROC FREQ.

For mean, mean ratio, or mean difference:  TOST option in SAS/STAT PROC TTEST provides Schuirman's two one-sided test (TOST) for normal or lognormal data.

Equivalence test, power and sample size for

SAS/STAT PROC POWER for binomial proportion test, one-sample test for mean of normal or lognormal data, and paired-sample or two-sample tests for mean difference of normal data or for mean ratio of lognormal data.

Errors-in-variables regression

This is a regression model that minimizes the perpendicular distances from the data points to the fitted line. Use SAS/OR PROC NLP with an appropriate minimization criterion. For example:

   proc nlp;
      min dist;
      parms b1=1, b0=1;
      dist=(y - (b0 + b1*x))**2 / (1 + b1*b1);
      run;

Alternatively, use SAS/STAT PROC CALIS (See Specifying Structural Equation Models in the Introduction to Structural Equations with Latent Variables chapter of the SAS/STAT User's Guide).

Eta-squared

EFFECTSIZE option (experimental in SAS 9.2) in the MODEL statement in SAS/STAT PROC GLM.

Exact and Monte Carlo methods

Exact confidence interval for binomial probability, p

See Confidence interval for binomial probability, p

Exact logistic regression

Beginning with SAS 8.1, you can perform exact logistic regression by using the EXACT statement in SAS/STAT PROC LOGISTIC. See also the EXACTOPTIONS option in the PROC LOGISTIC statement.

Exact poisson regression

Not available.

Experimental Design

See Design of Experiments.

Exponentially weighted moving average (EWMA) models

EWMA models can be fit for forecasting purposes. For information on using EWMA models in quality control, see SAS/QC PROC MACONTROL.

Factor analysis, Q-mode

Factorial

Beginning in SAS 8, use the Base SAS FACT function. For example, FACT(7) computes 7! ("seven factorial"). Prior to SAS 8, use the Base SAS GAMMA function. The factorial of an integer, x, is returned by GAMMA(x+1).

Firth's penalized maximum likelihood estimation method

Beginning in SAS 9.2, FIRTH option in MODEL statement of SAS/STAT PROC LOGISTIC. Firth's method is useful in cases of nonconvergence due to separation in logistic regression. It is also useful to remove bias in the parameter estimates when modeling a rare event. Such bias can result in underestimation of the event probability.

Fishbone diagrams

SAS/QC PROC ISHIKAWA.

Fisher's exact test

Base SAS PROC FREQ (FISHER option in the EXACT statement), SAS/STAT PROC MULTTEST (FISHER option in the TEST statement).

Fisher's least significant difference

SAS/STAT procedures ANOVA and GLM.

Fixed effects (conditional) logistic regression

SAS/STAT PROC PHREG using the STRATA statement. See the Conditional Logistic Regression for m:n Matching example in the PHREG documentation. Beginning in SAS 9, SAS/STAT PROC LOGISTIC using the STRATA statement.

Fixed effects poisson regression

The conditional model which conditions out the strata parameters is not directly available, but can be fit using SAS/STAT PROC NLMIXED by specifying the conditional log likelihood function. However, the conditional and unconditional models yield identical estimates of the non-strata parameters (See Fixed Effects Regression Methods for Longitudinal Data Using SAS). The unconditional model can be fit in SAS/STAT PROC GENMOD by specifying the strata identifier variable in both the CLASS and MODEL statements.

Fold-over designs

Fold-over Plackett-Burman designs are directly available in the ADX Interface in SAS/QC. Fractional factorial designs, created by ADX or SAS/QC PROC FACTEX, can be folded over using the DATA step. See the example titled Fold-Over Design in SAS/QC User's Guide. These designs reduce the aliasing in the original design.

Forest plot

Fractional Factorial Designs

SAS/QC PROC FACTEX and the ADX Interface.

Freeman-Halton test

This is the extension of Fisher's exact test to tables larger than 2x2 and is available via the FISHER option in the EXACT statement in Base SAS PROC FREQ.

Friedman's test

Base SAS PROC FREQ, CMH2 option. The ANOVA or Row Mean Scores Differ CMH statistic is Friedman's test if there is only one response per treatment-block combination. See the example titled Computing Friedman's Chi-Square Statistic in the FREQ chapter of the SAS Procedures Guide. For more than one response per combination, this statistic is a generalization of Friedman's test. Alternatively, you can obtain an F-approximation to Friedman's test by using Base SAS PROC RANK to rank the data within blocks and then SAS/STAT PROC GLM to fit a two-way ANOVA model. For more information, see the article by Ipe (1987) in the Proceedings of the Twelfth Annual SAS Users Group International Conference (SUGI12). By using the LSMEANS statement with the PDIFF option, you can also obtain approximations to the rank-sum multiple comparisons of treatment effects. For example:

  proc rank data=in out=ranked;
    by block; var y; ranks ry; 
    run;
  proc glm data=ranked;
    class block trt;
    model ry = block trt;
    lsmeans trt / pdiff;
    run;

Full-information maximum likelihood (FIML)

SAS/ETS procedures SYSLIN and MODEL

Gage (or gauge) repeatability and reproducibility (R&R)

Beginning in SAS 9.2, the METHOD=GRR option in SAS/STAT PROC VARCOMP. Also, the GAGE application in the SAS/QC Sample Library. See the paper by LaBarr (1994) in the Proceedings of the Nineteenth Annual SAS Users Group International Conference (SUGI19).

GAM (Generalized Additive Models)

GARCH (Generalized Autoregressive Conditional Heteroscedasticity)

SAS/ETS PROC AUTOREG. Also, SAS/ETS PROC MODEL with the H.var specification. See these examples of estimating GARCH models.

Geary's c

AUTOCORR option (experimental in SAS 9.2) in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.

GEE (Generalized Estimating Equations)

Generalized (Non)Linear (Mixed) Models

SAS/STAT procedures GENMOD, GLIMMIX, and NLMIXED. Particular models in this class are also fit by other procedures. For example, logistic models can also be fit with SAS/STAT PROC LOGISTIC and probit models by SAS/STAT PROC PROBIT.

Genetic algorithms

Beginning in SAS 9.1 (experimental in that release), use SAS/OR PROC GA. Beginning in SAS 9.0, use the SAS/IML functions GAxxxxxx. See the SAS/IML User's Guide or the SAS/OR User's Guide: Local Search Optimization for discussion and examples. You can use these tools to optimize problems involving integer, continuous, binary, or combinatorial variables, especially for finding optima for problems where the objective function may have discontinuities or may not otherwise be suitable for optimization by traditional calculus-based methods.

Geometric mean

Beginning in SAS 9.2, use the DIST=LOGNORMAL option in SAS/STAT PROC TTEST to obtain point and confidence interval estimates of the geometric mean. Beginning in SAS 9.1, you can compute the geometric mean of values across variables within an observation using the Base SAS function GEOMEAN or GEOMEANZ. To compute the geometric mean of values in a variable, use Base SAS Sample Library program GEOMEAN.

Gini index (of diagnostic test performance)

This is another measure of logistic model fit. It is related to the area under the ROC curve, c, by gini = 2c-1.

Gini's mean difference

ROBUSTSCALE option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. Also available in SAS/INSIGHT. This is a robust estimate of the population standard deviation.

Goodness-of-fit test

See Distribution Fitting and Chi-square goodness-of-fit test for One-way tables

Granger causality test

Beginning in SAS 8.1, the CAUSAL statement in PROC VARMAX. Also, see this example which uses the autoregressive specification of a bivariate vector autoregression.

Group sequential methods

See Sequential methods, design and testing.

Guttman scaling

There was a procedure, PROC GUTTMAN, in the Version 5 supplemental library that handled up to twelve items. This procedure is not available after Version 5. Guttman recommended correspondence analysis as an alternative (see Measurement and Prediction, Stouffer and Guttman, Wiley 1966). SAS/STAT PROC CORRESP performs correspondence analysis. A similar method is the Rasch model. See Andrich (1988), Rasch Models for Measurement, Sage Publication 07-068.

Harmonic means

Beginning in SAS 9.1, you can compute the harmonic mean of values in an observation using the Base SAS function HARMEAN or HARMEANZ.

Hausman specification test

HAUSMAN option in the FIT statement in SAS/ETS PROC MODEL. Beginning in SAS 9.2, the Hausman test for the IIA (Independence of Irrelevant Alternatives) assumption can be performed using %IIA macro available in the PROC MDC documentation example Hausman's Specification and Likelihood Ratio Tests.

Hazards ratios

By default, SAS/STAT PROC PHREG produces hazards ratio estimates for predictors not involved in interactions. The RISKLIMITS option in the MODEL statement provides confidence intervals. Beginning in SAS 9.2, the HAZARDRATIO statement can be used to obtain estimates and confidence intervals even when predictors are involved in interactions.

Heckman model

See Sample selection models.

Heteroscedasticity or Homoscedasticity tests

Hierarchical Linear Models (HLMs)

Use SAS/STAT PROC MIXED with RANDOM statements. HLMs are commonly called random coefficients models. See this usage note for more.

Hodrick-Prescott filter

Beginning in SAS System 9, the TRANSFORM= option in the CONVERT statement of SAS/ETS PROC EXPAND.

Hoeffding's D

See Correlations:Hoeffding's D

Homogeneity of Variance, tests of

Hotelling's T-square

See SAS System for Linear Models

Impute missing values

See Missing value Imputation

Independence of Irrelevant Alternatives (IIA)

See Hausman specification test

Independent Component Analysis (ICA)

Not available. This is a multivariate variable reduction method related to principal components analysis which finds independent, not just uncorrelated, components for possibly nonnormal data.

Integration

SAS/IML (CALL QUAD); see also Area under a curve, estimation of.

Interim analysis

See Sequential methods, design and testing.

Interquartile range

Base SAS PROC UNIVARIATE, SAS/QC PROC CAPABILITY, SAS/INSIGHT.

Intraclass correlation

Use the INTRACC macro. SAS/STAT PROC NESTED can also compute an intraclass correlation. Using the second example in the INTRACC macro description, these statements produce the intraclass correlation in the PAIR row and Percent of Total column of the NESTED results:

proc sort data=table1 out=tt; 
  by pair; 
  run;
proc nested data=tt;
  class pair;
  var score;
  run;

For categorical ratings, the kappa statistic has the properties of an intraclass correlation coefficient and can be used for interrater reliability.

Inverse Mill's ratio

See Mill's ratio.

Ishikawa diagrams

SAS/QC PROC ISHIKAWA and SAS/QC SQC Menu System

Item analysis

See the ITEM macro.

Item Response Theory

Includes the Rasch model.

Jackknifing

Jeffreys confidence interval for binomial probability

Beginning in SAS 9.2, BINOMIAL(JEFFREYS) option in TABLE statement of Base SAS PROC FREQ.

Jonckheere-Terpstra test

See Trend test for ordered alternatives.

Kalman filter

SAS/IML functions KALCVF, KALCVS, KALDFF, and KALDFS.

Kappa (Cohen's, weighted or unweighted)

Base SAS PROC FREQ (AGREE option).

Kappa for Multiple raters

MAGREE macro

Kendall's Coefficient of Concordance

MAGREE macro

Kendall correlation

Base SAS PROC CORR (KENDALL option).

Kendall's Tau-a

Base SAS PROC FREQ (MEASURES option).

Kernel Density Estimation

Base SAS PROC UNIVARIATE (use KERNEL option in HISTOGRAM statement); SAS/INSIGHT (use Analyze ⇒ Distribution and then Curves ⇒ Kernel Density...); SAS/QC PROC CAPABILITY (use KERNEL option in the HISTOGRAM or COMPHISTOGRAM statements); SAS/STAT procedures KDE and DISCRIM (KERNEL= and R= options).

Kernel Regression

SAS/INSIGHT for a single predictor only (prior to SAS 8), or up to two predictors (SAS 8 or later). For a single predictor, use Analyze ⇒ Fit and then Curves ⇒ Kernel... . For two predictors, use Analyze ⇒ Fit and then Graphs ⇒ Surface Plot ⇒ Kernel... .

Kriging

SAS/STAT PROC KRIGE2D.

Kuder-Richardson 20 (KR20)

For binary data, this statistic is equivalent to coefficient alpha and can be computed with the ALPHA option in Base SAS PROC CORR.

Kurtosis

Base SAS procedures UNIVARIATE and MEANS.

Latent Class Analysis or Finite Mixture Models

Not available.

Latent Class Regression

Not available.

Latent Structure Analysis

This is a broad class of methods including Latent Trait Analysis, Latent Class Analysis, and Latent Class Regression. For more information, see this web site.

Latent Trait Analysis

Also called Item Response Theory. One method is factor analysis of binary or ordinal data.

LD50

SAS/STAT PROC PROBIT, INVERSECL option.

Least Absolute Shrinkage and Selection Operator (LASSO)

SELECTION=LASSO in SAS/STAT PROC GLMSELECT

Least Angle Regression (LAR)

SELECTION=LAR in SAS/STAT PROC GLMSELECT

Least Absolute Value (LAV, L₁, or median) regression

LAV regression minimizes the absolute values of the residuals. This is the default model fit by SAS/STAT PROC QUANTREG. SAS/OR PROC NLP with appropriate minimization criterion can also be used. For example:

   proc nlp tech=quanew;
      min dist;
      parms b1=1, b0=1;
      dist=abs(y - (b0 + b1*x));
      run;

Alternatively, use CALL LAV in SAS/IML.

Levene's test of equal variances

Likelihood Ratio test for model comparison

Likelihood ratio chi-square

Base SAS PROC FREQ (CHISQ option).

Linear programming (optimization)

SAS/OR PROC LP.

Linearity in the logit, testing

See Box-Tidwell Transformation

Ljung-Box Q statistic

SAS/ETS PROC ARIMA. The White Noise and Stationarity Tests window of the SAS/ETS Time Series Forecasting System.

Loess curve-fitting

SAS/INSIGHT, SAS/STAT PROC LOESS, and PROC GAM.

Loglinear models

SAS/STAT PROC GENMOD (DIST=POISSON option) or PROC CATMOD (LOGLIN statement).

M estimation

See Robust Regression

MAD (Median Absolute Deviation)

SAS/IML function MAD, SAS/STAT procedures DISTANCE, ROBUSTREG, and STDIZE.

Mahalanobis distances

Can be obtained by computing the square root of the uncorrected sum of squared principal component scores within each output observation from SAS/STAT PROC PRINCOMP using the STD option. For example:

proc princomp std out=scores noprint;
   var x1-x10;
   run;
data mahdist;
   set scores;
   mdist = sqrt(uss(of prin1-prin10));
   run;

Also, the SAS/IML function MVE computes Mahalanobis distances.

Major axis regression

See Errors-in-variables regression

Mann-Whitney U Test

Equivalent to the Wilcoxon rank sum test.

Mantel-Haenszel chi square

Base SAS PROC FREQ (CHISQ and CMH options).

Marginal effects in logit and probit models

Marginal Homogeneity, test of

For binary responses, use McNemar's test or Cochran's Q, both provided by the AGREE option in Base SAS PROC FREQ. For multilevel responses, use the REPEATED statement in SAS/STAT PROC CATMOD. See Bhapkar's test and Stuart-Maxwell test.

Market Research methods

These methods include: conjoint analysis, discrete choice analysis, and perceptual mapping methods. Most of these methods are available in the Market Research Application.

MARS (Multivariate Adaptive Regression Splines)

Not available.

Maximum likelihood estimation in linear models

McFadden's model

See Conditional Logistic model.

McNemar's test

AGREE option in Base SAS PROC FREQ. Alternatively, create a three-way table with a stratum variable identifying each subject (or matched group), a variable indicating each occasion (condition or individual within matched group), and a binary response variable. Then use the CMH option. For example, if each subject gives a binary response to each of two drugs, use the statement:

  tables subject*drug*response/cmh2 noprint;

Means, test of equality of

See Equality of Means

Median

See Quantiles

Mills ratio

Beginning in SAS 9.2, the inverse Mills ratio can be computed for censored or truncated continuous responses, binary discrete responses, and endogenous selection variables via the MILLS option in the OUTPUT statement of SAS/ETS PROC QLIM. In SAS 9.1, the MILLS option computes the inverse mills ratio for censored or truncated continuous responses. Prior to SAS 9.1, and in the context of Heckman's two-step sample selection model, there is a user-contributed program that computes inverse Mills ratio.

Minimum aberration designs

SAS/QC PROC FACTEX (MINABS option in the MODEL statement)

Minimum chi-square estimation (Berkson)

This is an alternative method for estimating the parameters of a logistic regression model requiring multiple observations at each setting of the covariates. See Maddala (1983), Limited dependent and qualitative variables in econometrics. It is not directly available in any procedure. SAS/STAT procedures LOGISTIC, PROBIT, and GENMOD estimate the logistic model by maximum likelihood.

Missing value imputation

SAS/STAT PROC MI and PROC MIANALYZE; Base SAS PROC STANDARD (REPLACE option replaces missing values with the mean or a constant); SAS/STAT PROC STDIZE (see the MISSING=, REPLACE, and REPONLY options); SAS/STAT PROC PRINQUAL (METHOD=MGV and REPLACE options). For time series data, see SAS/ETS PROC EXPAND.

Mixed logit model

Mixture designs and analysis

Mixture designs such as simplex-centroid and simplex-lattice designs, possibly with constraints or including process variables, can be produced and analyzed by the SAS/QC ADX Interface. See Getting Started with the ADX Interface for Design of Experiments.

Monte Carlo estimation of exact p-values

See Exact and Monte Carlo methods

Monte Carlo Simulation

See Simulation.

Moran's I

AUTOCORR option (experimental in SAS 9.2) in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.

Moving average

MLOGIT or MPROBIT procedures

These are not procedures written or supported by SAS Institute. The last known contact for these procedures is Salford Systems. See Multinomial Logit model, Conditional logistic model, Multinomial Probit model, or Mill's ratio.

Multidimensional preference analysis

SAS/STAT PROC PRINQUAL and Market Research Application.

Multidimensional scaling

SAS/STAT PROC MDS and Market Research Application.

Multinomial Logit model

Multinomial Probit model

SAS/ETS PROC MDC beginning in SAS 8.2

Multiple Comparisons

See Student's t-test

Multiple comparisons (repeated measures)

In SAS/STAT PROC MIXED, use the PDIFF option in the LSMEANS statement to generate multiple comparisons on repeated measures.

Multiple testing, p-value adjustment for

Many adjustment methods are available in SAS/STAT PROC MULTTEST. Also, see SAS/Genetics PROC PSMOOTH.

Multivariate GARCH models

Beginning in SAS 8.2, experimental GARCH= option in the MODEL statement of SAS/ETS PROC VARMAX. The GARCH= option remains experimental in SAS 9.0 and SAS 9.1.

Multivariate logit model

Multivariate normal data, Generating

Use the MVN macro.

Multivariate normality, Test of

See Normality, test of.

Multivariate probit models

SAS/ETS PROC QLIM beginning in SAS 9.1.

Negative binomial regression

Beginning in SAS 8, use the DIST=NB option in the MODEL statement of SAS/STAT PROC GENMOD.

Negative predictive value

Nested Logit models

Neural Networks

Neural node in SAS Enterprise Miner.

Noncentrality parameter for F, t, or chi-square

Base SAS functions FNONCT, TNONCT, and CNONCT respectively

Noninferiority test for binomial proportion or difference in proportions

See Equivalence tests.

Nonparametric methods

See the Introduction to Nonparametric Analysis chapter in the SAS/STAT User's Guide.

One sample: Base SAS PROC UNIVARIATE provides tests for location (median).

Two or more independent samples: SAS/STAT PROC NPAR1WAY provides tests for location and scale differences.

Two dependent samples: Base SAS PROC UNIVARIATE provides tests for location (median). Base SAS PROC FREQ provides McNemar's test.

More than two dependent samples: Friedman's test in Base SAS PROC FREQ

Regression: See Robust (or Resistant) Regression

Correlation: Base SAS procedures CORR and FREQ. See Correlations.

Trend: The Jonckheere-Terpstra test is a nonparametric test of trend.

Density estimation: See Kernel Density Estimation

Discriminant Analysis: SAS/STAT PROC DISCRIM with METHOD=NPAR option and either the K= (nearest neighbor) or the R= (kernel density estimation) option.

Normality, test of

Univariate tests of normality are provided in the Base SAS PROC UNIVARIATE, SAS/QC PROC CAPABILITY, and SAS/INSIGHT. Tests of multivariate normality can be obtained using the MULTNORM macro and the NORMAL option in the FIT statement of SAS/ETS PROC MODEL.

Numerical integration

SAS/IML (CALL QUAD).

ODE (Ordinary Differential Equations), solving

SAS/ETS PROC MODEL; SAS/IML CALL ODE.

Omega-squared

EFFECTSIZE option (experimental in SAS 9.2) in the MODEL statement in SAS/STAT PROC GLM.

Odds Ratios

Model-based methods: By default, SAS/STAT PROC LOGISTIC produces odds ratio point estimates and confidence intervals (CLODDS= to select Wald or profile likelihood intervals) for predictors not involved in interactions. Beginning in SAS 9.2, the ODDSRATIO statement provides estimates and confidence intervals even when predictors are involved in interactions. The ODDSRATIO option, along with the DIFF= or SLICEDIFF= option, in the LSMEANS statement of PROC GLIMMIX provides point estimates (add CL option for confidence intervals). Custom odds ratios can be computed in the SAS/STAT procedures CATMOD, LOGISTIC, GENMOD, and GLIMMIX by determining the contrast of logistic model parameters that represents the desired difference in log odds for two groups and then using the CONTRAST or ESTIMATE statement with the ESTIMATE=EXP or EXP option.

Nonmodeling methods: The RELRISK or MEASURES option in Base SAS PROC FREQ for 2x2 tables and the CMH option for stratified 2x2 tables provide point estimates and confidence intervals. The OR and COMOR options in the EXACT statement provide exact confidence intervals and tests. Also, OR option in SAS/Genetics PROC CASECONTROL.

Optimization

SAS/OR procedures LP, NETFLOW, NLP, TRANS, OPTMODEL, OPTLP, OPTQP, and OPTMILP and SAS/ETS PROC MODEL. Also, see the nonlinear optimization subroutines in SAS/IML.

Ordered (or ordinal) logistic models

SAS/STAT procedures LOGISTIC, PROBIT, GENMOD, and CATMOD. SAS/ETS PROC QLIM.

Ordered (or ordinal) probit models

SAS/STAT procedures PROBIT, LOGISTIC, and GENMOD. SAS/ETS PROC QLIM.

Orthogonal regression

See Errors-in-variables regression

Outlier detection

In the context of regression, SAS/STAT PROC ROBUSTREG. See also Chapter 9 of SAS System for Statistical Graphics or the example titled Outliers in the FASTCLUS chapter of the SAS/STAT User's Guide.

p, test or confidence interval for

See Binomial Probability.

Paired t-test

See Student's t-test

Pareto charts

SAS/QC PROC PARETO and SQC Menu System

Partial correlation

See Correlations

Partial least squares

SAS/STAT PROC PLS.

Partial Proportional Odds Model

Partial regression leverage plots

PARTIAL option in SAS/STAT PROC REG. Low-resolution plots available with the LINEPRINTER option in the PROC REG statement. Beginning in SAS 9.1, high-resolution graphs can be produced using ODS graphics. Prior to 9.1, output the residuals and use SAS/GRAPH PROC GPLOT. Both are illustrated in the Influence Diagnostics section of the REG documentation.

Partially Balanced Incomplete Block Designs (PBIBDs)

See Balanced Incomplete Block Designs. No procedure creates these specifically, but SAS/QC PROC OPTEX may find such designs if they are optimal according to the criterion used.

Path analysis

SAS/STAT PROC CALIS.

Pearson correlation

See Correlations

Percentiles

See Quantiles

Perceptual mapping methods

This encompasses the following methods: See correspondence analysis, preference mapping, multidimensional preference analysis, and multidimensional scaling.

Permutations

See Combinations and permutations.

PERT

SAS/OR PROC CPM

Peto test

SAS/STAT PROC MULTTEST

Phi coefficient

Base SAS PROC FREQ (CHISQ option).

Piecewise Regression

PROC NLIN provides a method to estimate segmented models. PROC NLIN requires you to specify the functional form of your equation. See the example, Segmented Model, in the PROC NLIN documentation which illustrates fitting a continuous, smooth curve in two segments joined at an unknown point. PROC TRANSREG is another procedure that can fit a piecewise regression model via splines. The number and location of knots can be specified. See the example, Using Splines and Knots in the PROC TRANSREG documentation. Other procedures such as PROC LOESS, PROC TPSLINE, and PROC GAM can fit flexible, nonparametric models to data.

Point biserial correlations

See Correlations

Poisson regression

SAS/STAT PROC GENMOD (DIST=POISSON option in the MODEL statement).

Polychoric correlation coefficient

See Correlations

Polychoric correlation matrix

POLYCHOR macro.

Polyserial correlations

See Correlations

Portfolio optimization

SAS/OR PROC OPTQP or SAS/OR PROC OPTMODEL (use SOLVE WITH QP statement).

Positive predictive value

Power and sample size

Preference mapping

SAS/STAT PROC TRANSREG.

Prevalence Ratio

See Relative Risk.

Probability plots

Base SAS PROC UNIVARIATE and SAS/QC PROC CAPABILITY.

Project management

SAS/OR PROC CPM and PROJMAN menu system.

Projection pursuit

Not available.

Propensity scores, computing, matching on, analysis using

Proportion, test or confidence interval for

See Binomial Probability.

Q-mode factor analysis

QIC for GEE models

Quantiles

Base SAS procedures UNIVARIATE, MEANS, and SUMMARY can estimate quantiles and weighted quantiles. Beginning in SAS 9.2, if the weights are survey weights, use SAS/STAT PROC SURVEYMEANS.

Quantile regression

SAS/STAT PROC QUANTREG. See also Least Absolute Value regression.

Quartiles

See Quantiles

Queuing

Not available.

R-square

SAS/STAT procedures REG, GLM, RSREG, ORTHOREG, ROBUSTREG, SURVEYREG, TRANSREG, GLMSELECT, CALIS, LOGISTIC, SURVEYLOGISTIC, CANDISC, STEPDISC, CLUSTER, FASTCLUS, and VARCLUS. SAS/ETS procedures AUTOREG, PANEL, PDLREG, MDC, QLIM, SYSLIN, and TSCSREG.

R-square, partial

Random numbers, Generating

Use the RAND function to generate random values from any of a wide variety of theoretical univariate distributions. See details on the RAND function in the SAS Language Reference. Random samples from certain multivariate distributions can be generated using the RANDxxx modules in SAS/IML.

Random sampling

Rank Biserial Correlation

See Correlations

Rasch model

This is an item response model used to analyze the responses of subjects to items on a test. This model is not explicitly fit by any procedure currently.

Ratio analysis

The RATIO statement in SAS/STAT PROC SURVEYMEANS provides point estimates, confidence intervals, and tests for ratios of continuous or categorical variables. Beginning in SAS 9.2, the TEST=RATIO option in SAS/STAT PROC TTEST provides point estimates, confidence intervals, and tests of mean ratios for either normal or lognormal data.

Reduced major axis regression

This regression model minimizes the areas of the right triangles formed by the data points' vertical and horizontal deviations from the fitted line and the fitted line. Use SAS/OR PROC NLP with appropriate minimization criterion. For example:

   proc nlp;
      min area;
      parms b1=1, b0=1;
      area=(y - (b0 + b1*x))**2 / abs(b1);
      run;

Regression

Various types of regression are available in the following SAS/STAT procedures: REG, ORTHOREG, ROBUSTREG, QUANTREG, GLM, GLMSELECT, GAM, LOGISTIC, PROBIT, PHREG, LIFEREG, NLIN, RSREG, TRANSREG, GENMOD, SURVEYREG, SURVEYLOGISTIC, MIXED, GLIMMIX, HPMIXED. Other methods are available in SAS/QC PROC RELIABILITY and in these SAS/ETS procedures: AUTOREG, COUNTREG, MODEL, PDLREG, MDC, QLIM, ENTROPY, SYSLIN, and TSCSREG. See the many specific types of regression appearing in this list.

Relative potency estimate and confidence interval

Isn't directly computed by any procedure, but can be obtained using results from LOGISTIC. See Categorical Data Analysis Using the SAS System.

Relative Risk

The RELRISK and MEASURES options in Base SAS PROC FREQ compute the relative risk for a 2x2 table and for each strata in a stratified 2x2 tables. For stratified 2x2 tables, an estimate of the common (across strata) relative risk is provided by the CMH option. SAS/STAT PROC GENMOD can be used to model the relative risk.

Reliability coefficient

Base SAS PROC CORR, ALPHA option. See also, Intraclass correlation.

Repeated measures analysis

SAS/STAT procedures GLM, MIXED, CATMOD, GENMOD, GLIMMIX.

Repeated measures multiple comparisons

See Multiple comparisons (repeated measures).

Risk ratios

See Hazards ratios.

Robust estimators

Of location: Trimmed mean or Winsorized mean.

Of scale (variability): Includes Gini's mean difference, interquartile range and MAD (Median Absolute Deviation).

Of R²: SAS/STAT PROC ROBUSTREG.

Of model parameter standard errors: See White empirical ("sandwich") variance estimator and standard errors.

Robust (or Resistant) Regression

Includes such methods as median or quantile regression, kernel regression, thin-plate splines, loess, MARS, wavelets, least absolute value (LAV) or L₁ regression, Least Median of Squares (LMS), and Least Trimmed Squares (LTS). SAS/STAT PROC ROBUSTREG (see the METHOD= option) provides Huber M estimation, high breakdown value estimation (LTS and S methods), and combinations of the two (MM method). See also the SAS/IML functions LAV, LMS, and LTS.

ROC (Receiver Operating Characteristic) curve

Creating an ROC curve:  Beginning in SAS 9.1, use ODS graphics to plot the ROC curve for a binary-response model as shown in this usage note. Prior to SAS 9.1, use the ROCPLOT macro or use the OUTROC= option in SAS/STAT PROC LOGISTIC to output the data for the ROC curve, then plot the sensitivity variable (_SENSIT_) against the 1-specificity variable (_1MSPEC_). The ROCPLOT macro can be used to label points on the ROC curve with predictor values or statistic values from the OUT= or OUTROC= data set. A bias-adjusted estimate of the ROC curve based on an approximate leave-one-out crossvalidation method can be obtained by plotting sensitivity against 1-specificity using the data set created by the ODS OUTPUT CLASSIFICATION=<data-set-name>; statement.

Area under the ROC curve:  Is estimated by the c statistic (known as the concordance index) reported by SAS/STAT PROC LOGISTIC. Beginning in SAS 9.2, you can use the ROC and ROCCONTRAST statements to obtain point- and confidence interval estimates of the area under the ROC curve and to test that the area under the ROC curve is different from 0.5. Prior to SAS 9.2, this can be done as shown in an example of using the ROC macro. Examples of using the ROCPLOT macro illustrate displaying the value of the area under the curve in a plot of the ROC curve. A bias-adjusted estimate of the area based on an approximate leave-one-out crossvalidation method can be obtained by applying the ROC macro to the event probabilities estimated by crossvalidation which are available from PROC LOGISTIC via the PREDPROBS=CROSSVALIDATE option in the OUTPUT statement. Specify the variable containing these estimates in the VAR= parameter of the ROC macro (for example, VAR=XP_1).

Comparing areas under several ROC curves:  Beginning with SAS 9.2, use the ROC and ROCCONTRAST statements. Prior to SAS 9.2, the ROC macro performs a nonparametric comparison of areas under correlated ROC curves. See the example which plots several ROC curves separately, produces a comparative plot, and uses the ROC macro to test the equality of the areas under the ROC curves.

ROC curve for survival models:  Not available. See the discussion in Analyzing Receiver Operating Characteristic Curves with SAS.

Runs or Wald-Wolfowitz test

Runs test or Western Electric Rules

SAS/QC PROC SHEWHART (TESTS= option).

Sample selection models

Beginning in SAS 9, SAS/ETS PROC QLIM fits the Heckman selection model via maximum likelihood. Two-step estimation of the Heckman model can be done using this user-contributed program.

Scheffe multiple comparisons

SAS/STAT procedures GLM and ANOVA.

Seasonal Kendall's test

Not available.

Seemingly unrelated regression

SAS/ETS procedures SYSLIN and MODEL.

Semi-partial correlations

See Correlations

Sensitivity

Can be computed by Base SAS PROC FREQ. In the context of binary-response models, SAS/STAT PROC LOGISTIC (CTABLE and OUTROC= options).

Sensitivity Analysis

Sequential methods, design and testing

Beginning in SAS 9.2, SAS/STAT procedures SEQDESIGN and SEQTEST.

Simulated annealing

Not available.

Simultaneous Equations

For estimation of a linear system of simultaneous equations using either two- or three-stage least squares, use SAS/ETS PROC SYSLIN with the 2SLS or 3SLS option in the PROC SYSLIN statement. For estimation of a nonlinear system of simultaneous equations using either two- or three-stage least squares, use the SAS/ETS PROC MODEL with the 2SLS or 3SLS option in the FIT statement. To solve a system of simultaneous equations involving N equations and N unknowns, use PROC MODEL with a SOLVE statement as illustrated in this example. SAS/STAT PROC CALIS for constrained and unconstrained problems in simultaneous equation models with reciprocal causation.

Simultaneous logistic equations

Not available.

Simulation

SOLVE statement in SAS/ETS PROC MODEL or use the random number functions in the DATA step.

Skewness

Base SAS procedures UNIVARIATE and MEANS; SAS/QC PROC CAPABILITY; SAS/INSIGHT

Somer's d

Includes Somer's d_XY and d_YX. See the MEASURES option in Base SAS PROC FREQ.

Spatial prediction or modeling

SAS/STAT procedures KRIGE2D and VARIOGRAM.

Spearman correlation

See Correlations

Spearman-Karber estimate of LD50

Not available. See LD50 for other estimation methods.

Specificity

Can be computed by Base SAS PROC FREQ. In the context of binary-response models, SAS/STAT PROC LOGISTIC (CTABLE and OUTROC= options).

Standard deviation, Test and Confidence Interval of

See Variance (one-sample), Test and Confidence Interval

Standardizing data

Base SAS PROC STANDARD, SAS/STAT PROC STDIZE (prior to SAS 8 use the STDIZE macro), SAS/STAT PROC DISTANCE (beginning in SAS 9.1).

Stochastic Frontier Models

FRONTIER option in the ENDOGENOUS statement of SAS/ETS PROC QLIM beginning in SAS 9.2.

Stuart-Maxwell test

Bhapkar's test is asymptotically equivalent to the Stuart-Maxwell test for marginal homogeneity.

Student-Newman-Keuls test

SAS/STAT procedures GLM and ANOVA.

Student's t-test

One sample: Base SAS procedures UNIVARIATE, MEANS, and SUMMARY.

Two independent samples: SAS/STAT procedures TTEST and MULTTEST.

Two independent samples using summary statistics: See ANOVA on summary statistics.

More than two independent samples (multiple comparisons): SAS/STAT procedures ANOVA, GLM, MIXED, and MULTTEST.

Two dependent (paired) samples: Base SAS procedures UNIVARIATE, MEANS, and SUMMARY; SAS/STAT PROC TTEST.

Sum of squares

Corrected and uncorrected sum of squares are available for single samples in Base SAS procedures UNIVARIATE, MEANS, and SUMMARY, SAS/QC PROC CAPABILITY, and in SAS/INSIGHT. In the context of analysis of variance: SAS/STAT procedures ANOVA and GLM.

Summary statistics, ANOVA on

See ANOVA on summary statistics above.

Superiority test for binomial proportion or difference in proportions

See Equivalence tests.

Survey sample methods (sample selection and data analysis)

Symmetry, test of in 2-way table

AGREE option in Base SAS PROC FREQ.

System of logistic equations

Not available.

t-test

See Student's t-test.

Taguchi designs

SAS/QC ADX Interface. See Getting Started with the SAS ADX Interface for Design of Experiments.

Tau-a (Kendall's)

See Correlations

Tau-b (Kendall's)

See Correlations

Tau-c (Stuart's)

See Correlations

Tetrachoric correlation matrix

POLYCHOR macro.

Tetrachoric correlations

See Correlations

Thin-plate smoothing spline

SAS/STAT procedures TPSPLINE and GAM

Three-stage least squares (3SLS)

SAS/ETS procedures SYSLIN and MODEL.

Tobit analysis

SAS/STAT PROC LIFEREG and SAS/ETS PROC QLIM.

Tolerance intervals

SAS/QC PROC CAPABILITY.

Trend test for ordered alternatives

For binary responses: Cochran-Armitage test in Base SAS PROC FREQ (TREND option in TABLES statement); SAS/STAT PROC MULTTEST (CA option in TEST statement); score test in SAS/STAT PROC LOGISTIC (equivalent to the Cochran-Armitage test).

For binary or multilevel responses: Jonckheere-Terpstra test in Base SAS PROC FREQ (JT option in the TABLES statement).

For continuous responses: Use Base SAS PROC CORR with KENDALL option. The p-value for the Kendall statistic is equivalent to the two-tailed p-value for the Jonckheere statistic. The one-tailed p-value is half this p-value. If the number of distinct response values is small, Base SAS PROC FREQ with the JT option can also be used. In small sample situations, an exact test is available (use the EXACT JT; statement).

Trimmed mean

TRIMMED= option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. In SAS/INSIGHT, from the Distribution(Y) window, click Tables ⇒ Trimmed/Winsorized Mean.

Tree diagram

SAS/STAT PROC TREE

Truncated regression

SAS/ETS PROC QLIM beginning in SAS 8.2

Tukey's range test

SAS/STAT procedures GLM and ANOVA.

TURF (Total Unreplicated Reach and Frequency) analysis

Not available.

Two-stage least squares (2SLS)

SAS/ETS procedures SYSLIN and MODEL.

van Elteren test

Base SAS PROC FREQ with CMH2 and SCORES=MODRIDIT options. TABLES statement should look like:

   TABLES blocks*treatments*response / CMH2 SCORES=MODRIDIT;

The second CMH statistic gives a two-tailed, asymptotic test of treatment differences. If the response is continuous, the NOPRINT option may be desired. See this sample program.

Variance (one-sample), Test and Confidence Interval

Base SAS PROC UNIVARIATE (CIBASIC option) provides one- and two-sided confidence intervals for the standard deviation and variance. SAS/STAT PROC TTEST provides a confidence interval for the standard deviation using either of two methods. The VARTEST macro provides a two-sided confidence interval for the standard deviation and variance and can optionally test the hypothesis that the standard deviation or variance equals a value versus an alternative hypothesis that the value is exceeded. Robust estimators of scale are also available.

Variances (k samples), test of equality

Vector autoregressive models

Beginning in SAS 8.2, SAS/ETS PROC VARMAX

Wald confidence interval for binomial probability

Beginning in SAS 9.2, BINOMIAL(WALD) option in TABLE statement of Base SAS PROC FREQ.

Wald-Wolfowitz or Runs test

Wavelets

SAS/IML beginning in SAS 8.2. See the WAVxxx functions.

Weighted means

Base SAS procedures MEANS, SUMMARY, and UNIVARIATE with WEIGHT statement (for estimates). SAS/STAT PROC GLM with WEIGHT statement (for test comparing weighted means). SAS/STAT PROC SURVEYMEANS (if weights are from a complex survey design).

Weighted quantiles (percentiles, quartiles, deciles)

See Quantiles

Western Electric Rules

See Runs test

Westgard Rules

Use the TESTS=T and TESTS=M chart statement options in SAS/QC PROC SHEWHART to specify custom T-pattern and M-pattern tests.

White's empirical ("sandwich") variance estimator and standard errors

In ordinary regression: Beginning in SAS 9.2, WHITE option in the MODEL statement of SAS/STAT PROC REG displays White standard errors and tests based on them. Prior to SAS 9.2, ACOV option in the MODEL statement displays White variance estimate. Must also specify TEST statements to obtain tests based on White standard errors.

In generalized linear models: This is the default variance estimator used when the REPEATED statement is specified in SAS/STAT PROC GENMOD and parameter tests are based on it. Note that repeated measurements are not required in order to use the REPEATED statement.

In mixed models: EMPIRICAL option in the PROC statements of SAS/STAT PROC MIXED, PROC GLIMMIX, and PROC NLMIXED displays White standard errors and tests based on them.

In econometric models: HCCME= option in the FIT statement of SAS/ETS PROC MODEL and in the MODEL statement of SAS/ETS PROC PANEL displays White standard errors and tests based on them.

Wilcoxon Rank Sum Test

SAS/STAT PROC NPAR1WAY, WILCOXON option. Base SAS PROC FREQ, CMH option.

Wilcoxon Signed Rank Test

Base SAS PROC UNIVARIATE

Wilson (score) confidence interval for binomial probability

Beginning in SAS 9.2, BINOMIAL(WILSON) option in TABLE statement of Base SAS PROC FREQ.

Winsorized mean

WINSORIZED= option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. In SAS/INSIGHT, from the Distribution(Y) window, click Tables ⇒ Trimmed/Winsorized Mean.

Yule's Q for 2x2 tables

Same as Gamma statistic in Base SAS PROC FREQ (CHISQ option)

Zero-inflated poisson (ZIP) and negative binomial (ZINB) models

Beginning in SAS 9.2, SAS/STAT PROC GENMOD (for ZIP models); SAS/ETS PROC COUNTREG (for ZIP and ZINB models).

Operating System and Release Information