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**Adaptive designs for clinical studies**- Not available.
**Agresti-Coull confidence interval for binomial probability**- BINOMIAL(AGRESTICOULL) option in TABLE statement of Base SAS
^{®}PROC FREQ. **Alpha (Cronbach's)**- ALPHA option in Base SAS PROC CORR and SAS
^{®}Viya^{®}PROC CORRELATION. **Alternating Logistic Regression (ALR)**- Use the LOGOR= option in the REPEATED statement in the SAS/STAT
^{®}PROC GENMOD, or (beginning in SAS 9.4 TS1M3) in PROC GEE. See "Generalized Estimating Equations" in this note. **Analysis of means**- SAS/QC
^{®}PROC ANOM. Also, in many modeling procedures in SAS/STAT, the DIFF=ANOM option in the LSMEANS statement. Beginning in SAS^{®}Studio 3.6, the Analysis of Means task. **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.
**Area under a curve, estimation of****Area under ROC curve (AUC)**- See ROC curve.
**Association analysis**- Answers questions like "If item A is purchased, what is the probability that item B is also purchased?" Can be done using the Association or Market Basket node in SAS
^{®}Enterprise Miner™. **Attributable (and Population attributable) rate or fraction**- INDIRECT(AF) or MH(AF) option in SAS/STAT PROC STDRATE (beginning in SAS 9.3 TS1M2). See the example in this note.
**Automatic Interaction Detector (AID)**- See CHAID below.
**Autoregressive Conditional Heteroscedasticity (ARCH)**- SAS/ETS
^{®}PROC AUTOREG. **Average treatment effect (ATE)**- Beginning in SAS 9.4 TS1M4, SAS/STAT PROC CAUSALTRT.
**Average treatment effect for the treated (ATT)**- Beginning in SAS 9.4 TS1M4, SAS/STAT PROC CAUSALTRT.
**Bagging (bootstrap aggregation), Boosting, Ensemble models**- SAS Enterprise Miner and, beginning in SAS 9.4, PROC HPFOREST in SAS High-Performance Data Mining. See Gradient boosting.
**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**- These replication methods are available via the VARMETHOD= option in the survey procedures in SAS/STAT software — SURVEYFREQ, SURVEYLOGISTIC, SURVEYMEANS, SURVEYPHREG, and SURVEYREG.
**Barnard's unconditional exact test for 2×2 tables**- BARNARD option in EXACT statement of SAS/STAT PROC FREQ.
**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 (homoscedasticity), sphericity**- See this note for testing homoscedasticity in PROC ANOVA and PROC GLM. See this note for testing sphericity in PROC FACTOR. Also, see Covariance matrices, testing the equality of.
**Bayesian Methods****Berkson estimation**- See Minimum chi-square estimation (Berkson)
**Beta-binomial model**- Specify DIST=BETABIN in the MODEL statement in SAS/STAT PROC FMM. See the example titled
*Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal*in the FMM documentation and this example. **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. **Binning (bucket, Winsorized, or quantile)**- Beginning in SAS 9.4, Base SAS PROC HPBIN can bin interval variables using equal-length (bucket), winsorized, or pseudo-quantile methods.
**Binomial cluster model**- Specify DIST=BINOMCLUS in the MODEL statement in SAS/STAT PROC FMM. The MODEL statement models the mean and the PROBMODEL statement models the mixing proportions. See the example
*Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal*in the FMM documentation. **Binomial probability, test of or confidence interval for****Binomial probabilities, comparing each to overall****Binomial probabilities, comparing two****Biplot****Biserial correlation**- BISERIAL macro. See also point biserial correlation.
**Bivariate data, generating**- See Multivariate data, generating.
**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 ANOVA, GLM, LIFETEST, MULTTEST, and procedures supporting the LSMEANS, ESTIMATE, or LSMESTIMATE statements with the ADJUST= option.
**Bootstrapping****Boschloo's unconditional exact test for 2×2 tables**- Not available.
**Box plot (or box-and-whisker plot)**SAS/STAT PROC BOXPLOT, SAS/IML**High-resolution:**^{®}Studio, SAS/GRAPH^{®}PROC GPLOT (I=BOX*xxx*option in SYMBOL statement). Also SAS Viya PROC SPC.SAS/QC PROC SHEWHART.**High- or low-resolution:**PLOTS option in Base SAS PROC UNIVARIATE.*Low-resolution:***Box-Behnken Designs**- SAS/QC ADX Interface.
**Box-Cox Transformation**- 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);

You can also use the BOXCOX option in the MODEL statement of SAS/ETS PROC QLIM. This option allows transformation of both dependent and independent variables. The SAS/QC ADX Interface and ADXTRANS macro provide the Box-Cox transformation. For an autoregressive model, use the BOXCOXAR macro in SAS/ETS. **Box-Tidwell power transformation for independent variables**- Not available. An alternative method for finding a suitable functional form for an independent variable is through the use of a spline smoother as can be done in the SAS/STAT GAM or GAMPL procedures or the GAMMOD procedure in SAS
^{ }Viya. See the example titled "Generalized Additive Model with Binary Data" in the GAM documentation. **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 or reliability**- This is a version of the average squared error when the response is discrete. Beginning in SAS 9.3, the Brier statistic can be obtained from the FITSTAT option in SCORE statement of SAS/STAT PROC LOGISTIC. Also produced by SAS/STAT PROC HPLOGISTIC when the PARTITION statement is specified. Otherwise,
*Logistic Regression Examples Using the SAS System*gives a formula, and it could be computed easily using predicted values from LOGISTIC, PROBIT, or GENMOD. **Causal analysis**- Beginning in SAS 9.4 TS1M4, SAS/STAT PROC CAUSALTRT estimates the average causal effect of a binary treatment variable on a continuous or discrete outcome. It can adjust for confounding by modeling the treatment assignment or the outcome or both. Beginning in SAS 9.4 TS1M5, SAS/STAT PROC CAUSALMED estimates causal mediation effects from observational data. Beginning in SAS Studio 3.6, the Causal Models task.
**Censored regression**- SAS/ETS PROC QLIM and (beginning in SAS 9.4) PROC HPQLIM. Also SAS Viya PROC CQLIM.
**CHAID (Chi-square Automatic Interaction Detector)**- SAS/STAT PROC HPSPLIT (beginning in SAS 9.4), or 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. **Circular (directional, spherical) statistics**- Not available.
**Clarke test to compare nonnested models****Classification and Regression Trees**- Beginning in SAS 9.4, SAS/STAT PROC HPSPLIT. Classification and regression tree modeling is available in SAS Enterprise Miner and in SAS Viya PROC TREESPLIT. Also, see Decision trees and CHAID.
**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**SAS/STAT procedures CLUSTER, FASTCLUS, MODECLUS. Beginning in SAS Studio 3.6, the Cluster Observations and K-Means Clustering tasks.*Of observations:*SAS/STAT procedures VARCLUS. Beginning in SAS Studio 3.6, the Cluster Variables task.*Of variables:*SAS/STAT PROC FASTCLUS. Beginning in SAS Studio 3.6, the K-Means Clustering task.*K-means clustering:*Use SAS/STAT PROC DISTANCE to compute a distance matrix using a selected metric and then analyze the matrix with the CLUSTER or MODECLUS procedure in SAS/STAT. See Distances. Also, you can select a metric and do an analysis using SAS Viya PROC KCLUS.*Of observations with categorical data:*SAS/STAT PROC TREE produces a tree diagram, or dendrogram, summarizing a cluster analysis. See also Classification and regression trees.*Tree diagram of:***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**- To compute the number of combinations or permutations, see this note. To produce a list enumerating the combinations or permutations, use the ALLCOMB and ALLPERM options (or the LEXCOMB and LEXPERM options) described in the SAS Language Reference: Dictionary. See also the COMB and PERM options in SAS/STAT PROC PLAN. Permuting the observations in a data set can be done using PROC PLAN or PROC MULTTEST.
**Competing-risks data**- Beginning in SAS 9.4 TS1M1, use the EVENTCODE= option in the MODEL statement of PROC PHREG. Also, beginning in SAS 9.4 TS1M3, use the EVENTCODE= option in the TIME statement of PROC LIFETEST. Beginning in SAS 9.4 TS1M5, the EVENTCODE(COX)= option applies the Cox model to the cause-specific hazard for each event type separately.
**Concordance index**- This is the area under the receiver operating characteristic (ROC) curve (AUC).
**Compound distribution model**- Estimates aggregate loss over time by modeling the severity (magnitude) of loss and the frequency (count) of loss separately. PROC HPCDM in SAS/ETS and PROC CCDM in SAS Viya.
**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**- Confidence ellipse plots about the mean or individual values are available in Base SAS PROC CORR using the PLOTS=SCATTER(ELLIPSE=MEAN) or PLOTS=SCATTER(ELLIPSE=PREDICTED) option. Prediction ellipses are also available in SAS/IML Studio (
**Analysis ⇒ Multivariate ⇒ Correlation Analysis**). See also the CONELIP macro. **Confidence interval**CLM, LCLM or UCLM options in Base SAS PROC MEANS. CIBASIC option in Base SAS PROC UNIVARIATE.*On a mean:*: CIBASIC option in Base SAS PROC UNIVARIATE. Alternatively, the VARTEST macro.*On a variance or standard deviation*: CIPCTLDF or the CIPCTLNORMAL option in Base SAS PROC UNIVARIATE.*On a percentile (for example the median)**On a binomial probability*: 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 difference between two binomial probabilities**On a relative potency**On odds ratios**On a rate*: See ROC (Receiver Operating Characteristic) curve.*On the area under an ROC curve (AUC)*: Use the RISKLIMITS option in the MODEL statement of SAS/STAT PROC PHREG. To save these to a data set, use the global ODS OUTPUT statement.*On hazard (or risk) ratios*: 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 normal regression parameters*: CLPARM= option in the MODEL statement of SAS/STAT PROC LOGISTIC. Use the LINK=PROBIT option to request a probit model. To save these to a data set, use the global ODS OUTPUT statement.*On logistic and probit regression parameters*: Known as inverse (or fiducial) confidence limits in a logistic or probit model. Use the INVERSECL option in SAS/STAT PROC PROBIT.*On the predictor value that produces a specified response probability***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*. **Constraint programming**- SAS/OR PROC CLP or the Constraint Programming Solver within PROC OPTMODEL (SOLVE WITH CLP). Also SAS Viya PROC CLP.
**Control Charts**- SAS/QC procedures SHEWHART, MACONTROL, CUSUM, and (beginning in SAS 9.4 TS1M3) RAREEVENTS. Beginning in SAS Studio 3.6, the Control Charts task. Also, SAS Viya PROC SPC.
**Cook's D**- SAS/STAT procedures REG and GLM (COOKD= options in the OUTPUT statement), RSREG (D option on MODEL statement), and LOGISTIC (C= option on the OUTPUT statement, but this value must be divided by the number of parameters in the model). A similar statistic can be computed for generalized linear models. Specify the COOKD= option in the OUTPUT statement of SAS/STAT PROC GENMOD. Also, see this example.
**Copulas**- Beginning in SAS 9.3, you can simulate realizations or estimate parameters of multivariate distributions using copulas in SAS/ETS PROC COPULA and HPCOPULA. Also, SAS Viya PROC CCOPULA. Normal, normal mixture, and t copulas are supported in SAS/ETS PROC MODEL with the COPULA= option in the SOLVE statement. For more information and examples, see this paper.
**Correlations**BISERIAL macro**Biserial:**

SAS/STAT PROC CANCORR and beginning in SAS Studio 3.6, the Canonical Correlation task.**Canonical:**

Base SAS PROC CORR (HOEFFDING option)**Hoeffding's D:**

See Intraclass correlation**Intraclass:**

SAS/STAT PROC LOGISTIC for assessing the correlation between observed responses and predicted probabilities**Kendall's tau-a:**

Base SAS procedures CORR (KENDALL option) and FREQ (MEASURES option)**Kendall's tau-b:**

Base SAS PROC CORR (PARTIAL statement), SAS/STAT PROC REG (PCORR1 and PCORR2 options), SAS/STAT PROC LOGISTIC (PCORR option), SAS/STAT PROC CANCORR (SQPCORR option)**Partial:**

Base SAS procedures CORR, HPCORR (beginning in SAS 9.4), and FREQ (MEASURES option). SAS Viya PROC CORRELATION.**Pearson:**

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**Point biserial:**

Base SAS PROC FREQ (PLCORR option). Beginning in SAS 9.3 TS1M2, the POLYCHORIC option in Base SAS PROC CORR. Beginning in SAS 9.4, the OUTPLC= option in Base SAS PROC CORR saves a matrix of polychoric correlations. Beginning in SAS 9.4 TS1M2, the POLYCHORIC option in SAS/STAT PROC IRT. Also, the POLYCHOR macro.**Polychoric:**

Beginning in SAS 9.3, the POLYSERIAL option in Base SAS PROC CORR. Beginning in SAS 9.4, the OUTPLS= option in Base SAS PROC CORR saves a matrix of polyserial correlations.**Polyserial:**

BISERIAL macro**Rank Biserial:**

SAS/STAT PROC REG (SCORR1, SCORR2 options), CANCORR (SPCORR and SQSPCORR options)**Semipartial:**

Base SAS procedures CORR (SPEARMAN option) and FREQ (MEASURES option)**Spearman:**

Base SAS PROC FREQ (MEASURES option)**Stuart's tau-c:**

Same as Polychoric above.**Tetrachoric:****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. See also, the Market Research Application, and beginning in SAS Studio 3.6, the Correspondence Analysis task.
**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. See this example.
**Cox Regression**- SAS/STAT PROC PHREG and SAS Viya PROC PHSELECT.
**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**- Beginning in SAS 9.4, PROC HPSPLIT in SAS/STAT and PROC HPFOREST in SAS High-Performance Data Mining. Also, SAS Enterprise Miner and PROC FOREST in SAS
^{®}Visual Data Mining and Machine Learning. SAS/OR PROC DTREE for decision analysis. Also, see Classification and Regression Trees. **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. **Diebold-Mariano Test**- Not available. This test compares the forecast accuracy of two competing time series models fit to a given set of data.
**Difference in differences of means****Differential equations**- See ODE (Ordinary Differential Equations)
**Discrete Choice model****Discriminant analysis**- SAS/STAT PROC DISCRIM and beginning in SAS Studio 3.6, the Discriminant Analysis task.
**Distances**- SAS/STAT PROC DISTANCE and beginning in SAS Studio 3.6, the Compute Similarities and Distances task.
**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.
**Effect selection****Effect size**- See eta-squared and omega-squared below. Use the EFFECTSIZE option in the MODEL statement in SAS/STAT PROC GLM.
**Elastic net selection**- Beginning in SAS 9.4 TS1M1, SAS/STAT PROC GLMSELECT with option SELECTION=ELASTICNET in the MODEL statement. Also, using SAS/STAT PROC NLMIXED as described in this note
**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. Available in SAS/STAT PROC IRT for estimating item response models. Used in SAS/Genetics
^{™}PROC HAPLOTYPE to generate maximum likelihood estimates of haplotype frequencies. **E**_{max}or Hill model**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 (and noninferiority, superiority) tests**EQUIV, NONINF, and SUP suboptions of BINOMIAL and RISKDIFF options in Base SAS PROC FREQ.**For binomial proportion and difference in proportions:**TOST option in SAS/STAT PROC TTEST provides Schuirman's two one-sided test (TOST) for normal or lognormal data.**For mean, mean ratio, or mean difference:**SAS/STAT PROC POWER for test of binomial proportion or difference of proportions in one-, two-, or paired-sample situations. Also for one-sample test of mean for normal or lognormal data, and for two- or paired-sample tests for mean difference of normal data or for mean ratio of lognormal data.**Power and sample size:****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 OPTMODEL. Alternatively, see this paper for a macro implementing Deming regression, or 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 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**- EXACT statement in SAS/STAT PROC LOGISTIC. See also the EXACTOPTIONS option in the PROC LOGISTIC statement. Also the EXACT statement in PROC GENMOD with the DIST=BINOMIAL option in the MODEL statement. See also the EXACTOPTIONS statement. A stratified exact analysis is provided if the STRATA statement is also specified in either procedure.
**Exact Poisson regression**- EXACT statement in PROC GENMOD along with the DIST=POISSON option in the MODEL statement. A stratified exact analysis is provided if the STRATA statement is also specified.
**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**- SAS/STAT FACTOR and CALIS procedures, and beginning in SAS Studio 3.6, the Factor Analysis task.
**Factor analysis, Q-mode****Factorial**- Use the Base SAS FACT function. For example, FACT(7) computes 7! ("seven factorial"). The Base SAS GAMMA function can also be used. The factorial of an integer, x, is returned by GAMMA(x+1).
**Factorization machines**- PROC FACTMAC in SAS
^{®}Visual Data Mining and Machine Learning. **Fiducial (inverse confidence) limits**- INVERSECL option in SAS/STAT PROC PROBIT.
**Fieller's theorem**- The INVERSECL option in SAS/STAT PROC PROBIT uses Fieller's theorem to provide confidence intervals for response rates in a binary response model. This note discusses using Fieller's theorem and the delta method to provide confidence intervals for a ratio of linear combinations of model parameters in generalized linear models.
**Finite Mixture Models**- SAS/STAT PROC FMM.
**Firth's penalized maximum likelihood estimation method**- FIRTH option in the MODEL statement of SAS/STAT PROC LOGISTIC (for logit-linked models only) or PROC PHREG. Beginning in SAS 9.4 TS1M5, the FIRTH option is available with all links in PROC LOGISTIC. Firth's method is useful in cases of nonconvergence due to separation in logistic regression or monotone likelihood in the Cox model. Firth's method reduces bias in the parameter estimates. In logistic regression, such bias can occur when modeling a rare event resulting 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 and PROC LOGISTIC using the STRATA statement.
**Fixed effects Poisson regression**- This model conditions out the strata (clusters, panels) parameters. Beginning in SAS 9.4 TS1M1, fit this model using the ERRORCOMP=FIXED option in the MODEL statement and the GROUPID= option in the PROC COUNTREG statement of SAS/ETS PROC COUNTREG. Also, SAS Viya PROC CNTSELECT using the same syntax. For small data sets, exact methods can be used by specifying the EXACT and STRATA statements in SAS/STAT PROC GENMOD. It can also be fit using SAS/STAT PROC NLMIXED by specifying the conditional log likelihood function. However, note that 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, SAS/ETS PROC COUNTREG, SAS Viya PROC GENSELECT or PROC CNTSELECT, or beginning in SAS 9.4, in SAS/STAT PROC HPGENSELECT or SAS/ETS PROC HPCOUNTREG 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****Four- or 5-parameter logistic model****Fractional Factorial Designs**- SAS/QC PROC FACTEX and the ADX Interface.
**Fractional logistic (or logit) model****Fractional polynomials**- This method of adaptive regression analysis is not available, but see this paper.
**Frailty model**- Specifying the RANDOM statement in SAS/STAT PROC PHREG allows you to fit a shared frailty model for clustered data resulting in correlated failure times. Beginning in SAS 9.3 TS1M2, adding the BAYES statement requests a Bayesian frailty model. See the discussion and example in the PHREG documentation.
**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 Row Mean Scores Differ CMH statistic is Friedman's test if there is only one response per treatment-block combination. See the example titled "Friedman's Chi-Square Statistic" in the FREQ documentation. 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. The LSMEANS statement with the PDIFF option provides 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. Beginning in SAS 9.3, METHOD=FIML option in SAS/STAT PROC CALIS.
**Gage (or gauge) repeatability and reproducibility (R&R)**- 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).
**Gail-Simon Test for Qualitative Interaction**- For binary response data in stratified 2x2 tables, use the CMH(GAILSIMON) option in the TABLES statement of Base SAS PROC FREQ. For continuous response, see the GAILSIMON macro presented in the book
*Analysis of Clinical Trials Using SAS: A Practical Guide*by Dmitrienko et. al. **Gains chart****GAMs (Generalized Additive Models)**- SAS/STAT PROC GAM or, beginning in SAS 9.4 TS1M3, PROC GAMPL. Also SAS Viya PROC GAMMOD.
**GARCH (Generalized Autoregressive Conditional Heteroscedasticity)**- SAS/ETS PROC AUTOREG. Also, SAS/ETS PROC MODEL with the H.
*var*specification. See the examples here of estimating GARCH models. **Gatekeeping strategies for multiple endpoints**- These multiple testing strategies are not directly available, but gatekeeping procedures and macros implementing them are presented in the book
*Analysis of Clinical Trials Using SAS: A Practical Guide*by Dmitrienko, et. al. (SAS Institute, 2005). **Geary's c**- AUTOCORR option in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.
**GEE (Generalized Estimating Equations)**- First-order GEE (GEE1): Use the REPEATED statement in SAS/STAT PROC GENMOD or (beginning in SAS 9.4 TS1M2) PROC GEE. For multinomial responses: use GEE or GENMOD for an ordinal response, use GEE for a nominal response. Also, SAS/STAT PROC GLIMMIX with the EMPIRICAL option and RANDOM _RESIDUAL_ statement with subject variable in the SUBJECT= option. Second-order GEE (GEE2): Can be done using GLIMMIX or SAS/STAT NLMIXED by treating the response as normally distributed, regardless of its true distribution. See Vonesh (2012). See also, Weighted GEE.
**Generalized (Non)Linear (Mixed) Models**- SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, and beginning in SAS 9.4 HPGENSELECT and HPNLMOD. Also, SAS Viya procedures GENSELECT, CQLIM, and NLMOD. Beginning in SAS Studio 3.6, the Mixed Models task. Also, beginning in SAS 9.4 TS1M4, SAS/ETS PROC QLIM fits logit and probit models, optionally with random effects. Particular models in this class are also fit by other procedures. For example, logistic models (with no random effects) can also be fit with SAS/STAT PROC LOGISTIC and probit models by SAS/STAT PROC PROBIT.
**Generalized Poisson regression****Genetic algorithms**- SAS/OR PROC OPTLSO. See 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 9.4 TS1M2, the GEOMEAN option in the OUTPUT statement of Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY provides a point estimate. The DIST=LOGNORMAL option in SAS/STAT PROC TTEST provides a point estimate and confidence interval. Beginning in SAS 9.3 TS1M2, the ALLGEO option in SAS/STAT PROC SURVEYMEANS provides a standard error estimate as well as a point estimate and confidence interval. To compute the geometric mean of values across variables within an observation, use the Base SAS function GEOMEAN or GEOMEANZ.
**Gini index (of diagnostic test performance)**- This is a measure of logistic model fit related to the area under the ROC curve (AUC), c, by Gini = 2c-1. The Gini index is provided by SAS/STAT PROC LOGISTIC as Somers' D.
**Gini's mean difference**- ROBUSTSCALE option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. Also available in SAS/IML Studio. This is a robust estimate of the population standard deviation.
**Goodness-of-fit test**- See Distribution Fitting.
**Gradient boosting**- Gradient boosting node in SAS Enterprise Miner and PROC GRADBOOST in SAS
^{®}Visual Data Mining and Machine Learning. **Granger causality test**- CAUSAL statement in PROC VARMAX. Also, see the example here 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 mean**- You can obtain a nonparametric estimate of the harmonic mean of values in an observation using the Base SAS function HARMEAN or HARMEANZ. A maximum likelihood estimate can be obtained using PROC NLMIXED as described in this note.
**Hausman specification test**- HAUSMAN option in the FIT statement in SAS/ETS PROC MODEL. 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*. **Hazard ratios**- By default, SAS/STAT PROC PHREG produces hazard ratio estimates for predictors not involved in interactions. The RISKLIMITS option in the MODEL statement provides confidence intervals. 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****Hidden Markov model**- SAS Viya PROC HMM fits the Gaussian hidden Markov model.
**Hierarchical Linear Models (HLMs)**- Use SAS/STAT PROC MIXED or PROC GLIMMIX with RANDOM statements. HLMs are also commonly called multilevel models or random coefficients models. See this usage note for more.
**Hodrick-Prescott filter**- TRANSFORM= option in the CONVERT statement of SAS/ETS PROC EXPAND.
**Hoeffding's D**- See Correlations:Hoeffding's D
**Hollander-Proschan New Better than Used in Expection (NBUE) test**- Not available.
**Homogeneity of Variance, tests of****Hotelling's T-square**- See SAS System for Linear Models
**Huber-White Sandwich Estimator**- See White's empirical ("sandwich") variance estimator and robust standard errors
**Hurdle models**- PROC FMM beginning in SAS 9.3. See this example.
**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.
**Information value (IV)**- WOE option in Base SAS PROC HPBIN (beginning in SAS 9.4).
**Integration**- SAS/IML (CALL QUAD). Beginning in SAS 9.4 TS1M3, specify CALL QUAD in SAS/STAT PROC MCMC to use a general integration function enabling the procedure to fit models, such as marginal likelihood models, that require integration. 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, and SAS/IML Studio.
**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 (fiducial) confidence limits**- INVERSECL option in SAS/STAT PROC PROBIT.
**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**- PROC IRT beginning in SAS 9.4 TS1M1.
**Jackknifing****Jeffreys confidence interval for binomial probability**- BINOMIAL(JEFFREYS) option in TABLE statement of Base SAS PROC FREQ.
**Joint modeling**- SAS/STAT PROC GLIMMIX can be used for joint modeling of multivariate outcomes. See the example in the GLIMMIX documentation.
**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)**- AGREE option in Base SAS PROC FREQ or (beginning in SAS 9.4 TS1M1) SAS/STAT PROC SURVEYFREQ.
**Kappa for Multiple raters**- MAGREE macro
**Kendall's Coefficient of Concordance**- MAGREE macro
**Kendall correlation**- Base SAS PROC CORR (KENDALL option).
**Kendall's Tau**- See Correlations.
**Kernel Density Estimation**- In Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY, use the KERNEL option in the HISTOGRAM statement (or in the COMPHISTOGRAM statement in PROC CAPABILITY). Beginning in SAS 9.3, SAS/ETS PROC SEVERITY can plot the kernel estimate in plots of the PDF or CDF. In SAS/STAT procedures KDE and DISCRIM, use the KERNEL= and R= options. In SAS/IML Studio, select
**Analysis ⇒ Distribution Analysis ⇒ Descriptive Statistics**. **Kernel Regression (scatter plot or surface smoothing)**- In SAS IML/Studio, use
**Graph ⇒ Scatter Plot...**, then right click on the scatter plot, select**Fit Curves...**and use the Kernel tab. **Kolmogorov-Smirnov test**- In SAS/STAT PROC NPAR1WAY, the EDF option in the PROC NPAR1WAY statement provides an asymptotic test. The EDF or KS option in the EXACT statement provides an exact test.
**Kriging**- SAS/STAT PROC KRIGE2D.
**Kruskal-Wallis test**- In SAS/STAT PROC NPAR1WAY, the WILCOXON option in the PROC NPAR1WAY statement provides an asymptotic test. The WILCOXON option in the EXACT statement provides an exact test.
**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.
**L**_{1}and L_{2}penalties for regression- These penalties constrain, or regularize, the regression parameters. L
_{1}regularization is known as LASSO. L_{2}regularization is known as ridging. Elastic net uses a combination of L_{1}and L_{2}penalties. See Penalized regression methods. See also Least absolute value regression. **Latent Class, Profile, or Transition Analysis**- Not available. See this note regarding user-written procedures not supported by SAS Institute.
**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**- INVERSECL option in SAS/STAT PROC PROBIT. See this note which illustrates estimating the LD50 and obtaining a confidence interval using both Fieller's theorem and the delta method.
**LD50, Comparing across groups****LASSO (Least Absolute Shrinkage and Selection Operator), group lasso, and adaptive lasso selection**- The lasso method is available in SAS/STAT PROC GLMSELECT and (beginning in SAS 9.3 TS1M2) in PROC QUANTSELECT with option SELECTION=LASSO in the MODEL statement. Beginning in SAS 9.4, also in PROC HPREG with option METHOD=LASSO in the SELECTION statement. Beginning in SAS 9.4 TS1M1, also in SAS/ETS PROC COUNTREG with option SELECT=PEN in the MODEL statement. The adaptive lasso method is available in PROC GLMSELECT and (beginning in SAS 9.3 TS1M2) in PROC QUANTSELECT with option SELECTION=LASSO(ADAPTIVE) in the MODEL statement. Beginning in SAS 9.4 TS1M3, the group lasso method is available in PROC GLMSELECT with option SELECTION=GROUPLASSO in the MODEL statement and in PROC HPGENSELECT with option METHOD=LASSO in the SELECTION statement. In SAS Viya , lasso methods are available in several procedures including LOGSELECT, GENSELECT, REGSELECT, and PHSELECT.
**Least Angle Regression (LAR)**- Available for normal-response models in SAS/STAT PROC GLMSELECT. Beginning in SAS 9.4, in SAS/STAT HPREG. Also, SAS Viya PROC REGSELECT.
**Least Absolute Value (LAV, L**_{1}, or median) regression- LAV regression minimizes the absolute values of the residuals. This is the default model fit by SAS/STAT PROC QUANTREG. Alternatively, use CALL LAV in SAS/IML.
**Levene's test of equal variances****Lift chart****Likelihood Ratio test for model comparison****Likelihood ratio chi-square**- Base SAS PROC FREQ (CHISQ option).
**Linear programming (optimization)**- SAS/OR PROC OPTMODEL and PROC OPTMILP.
**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/STAT procedures LOESS, GAM or, beginning in SAS 9.4 TS1M3, GAMPL. Also, SAS/IML Studio.
**Loglinear models**- DIST=POISSON option in SAS/STAT PROC GENMOD, SAS/ETS PROC COUNTREG, or in SAS Viya, in the CNTSELECT or GENSELECT procedures. Beginning in SAS 9.4, DIST=POISSON options in PROC HPGENSELECT or SAS/ETS PROC HPCOUNTREG. Also, using the LOGLIN statement in SAS/STAT PROC CATMOD.
**Longitudinal data analysis**- See Repeated measures analysis
**M estimation**- See Robust Regression
**MAD (Median Absolute Deviation)**- ROBUSTSCALE option in Base SAS PROC UNIVARIATE, SAS/IML function MAD, SAS/STAT procedures DISTANCE, ROBUSTREG, and STDIZE.
**Mahalanobis distances**- The Mahalanobis distances from each observation to the mean 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. See this note for an example which also shows computing Mahalanobis distances from each of a set of observations to a reference point and distances between each pair of observations. The SAS/IML function MVE can also be used to compute Mahalanobis distances.
**Major axis regression**- See Errors-in-variables regression
**Mann-Whitney U Test**- Equivalent to the Wilcoxon rank sum test.
**Mantel-Fleiss criterion for Mantel-Haenszel chi-square approximation**- CMH(MANTELFLEISS) option in the TABLES statement of Base SAS PROC FREQ.
**Mantel-Haenszel chi square**- Base SAS PROC FREQ (CHISQ and CMH options).
**Marginal effects**- The Margins macro can estimate and test marginal effects for predictors in generalized linear models and GEE models. For binary or ordinal logit or probit models, point estimates of marginal effects for predictors not involved in interactions can be obtained from the MARGINAL option in the OUTPUT statement of SAS/ETS PROC QLIM. This note discusses and illustrates the estimation of 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.
**Marginal model plots**- These plots, proposed by Cook and Weisberg (1997) and discussed by Fox and Weisberg (2011), display the marginal relationship between the response and each predictor in a model. See this paper for discussion and examples.
**Margins, predictive**- The Margins macro can estimate and test predictive margins for predictors in generalized linear models and GEE models.
**Market basket analysis**- See Association analysis.
**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. See also these Market Research papers and tools.
**MARS**^{Note}(Multivariate Adaptive Regression Splines)- Beginning in SAS 9.3 TS1M2, SAS/STAT PROC ADAPTIVEREG fits multivariate adaptive regression splines, a nonparametric regression technique.
**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
**Mediation analysis**- Beginning in SAS 9.4 TS1M5, SAS/STAT PROC CAUSALMED. Also, see this note.
**Mills ratio**- 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 and SAS Viya PROC CQLIM.
**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 procedures MI, MIANALYZE, and (beginning in SAS 9.4 TS1M3) SURVEYIMPUTE. Beginning in Base SAS 9.4, PROC HPIMPUTE. Beginning in SAS Studio 3.6, the Replace Missing Values task. SAS/STAT PROC STDIZE (see the MISSING=, REPLACE, and REPONLY options). Base SAS PROC STANDARD (REPLACE option) replaces missing values with the mean or a constant. 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*. **Model selection**- Several methods for selecting a final model from among a list of candidate effects are available in many procedures. Methods include forward, backward, stepwise, best subset, R-square-based, least angle regression (LAR), LASSO (including adaptive LASSO and group LASSO), and elastic net selection methods. The procedures offering some of these methods are listed in this note which also discusses grouping of effects for entry or removal from the model.
**Modified Park test**- For selecting a suitable response distribution in log-linked generalized linear models, based on the mean-variance relationship. See this note.
**Monte Carlo estimation of exact p-values**- See Exact and Monte Carlo methods
**Monte Carlo Simulation**- See Simulation.
**Moran's I**- AUTOCORR option in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.
**Mosaic plots**- Available for two- or multi-way tables in Base SAS PROC FREQ and SAS/STAT PROC SURVEYFREQ when specifying the PLOTS=MOSAICPLOT option.
**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, the Market Research Application, and beginning in SAS Studio 3.6, the Multidimensional Preference Analysis task.
**Multidimensional scaling**- SAS/STAT PROC MDS and Market Research Application.
**Multinomial cluster model**- Beginning in SAS 9.4 TS1M2, specify DIST=MCLUS in the MODEL statement in SAS/STAT PROC FMM. The MODEL statement models the mean and the PROBMODEL statement models the mixing proportions. See the example
*Modeling Multinomial Overdispersion: Town and Country*in the FMM documentation. **Multinomial Logit model****Multinomial Probit model**- SAS/ETS PROC MDC
**Multiple comparisons of means**- See Student's t-test. In the context of generalized linear models, the NLMeans macro.
**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 or confidence interval adjustment for**- Many adjustment methods are available in SAS/STAT PROC MULTTEST (Bonferroni, Sidak, Holm, Hochberg, Hommel, Stouffer-Liptak, false discovery rate (FDR), Fisher combination, adaptive methods, step-up and step-down methods, and resampling methods using bootstrap or permutation). MULTTEST does not provide adjusted confidence intervals. Adjustment of p-values and confidence intervals is available via the ADJUST= option in the LSMEANS or LSMESTIMATE statement in many SAS/STAT procedures (STRATA statement in PROC LIFETEST). Also see SAS/Genetics PROC PSMOOTH.
**Multivariate GARCH models**- GARCH statement in SAS/ETS PROC VARMAX.
**Multivariate logit model****Multivariate data, generating**- Use the RANDxxx function modules in SAS/IML to generate samples from multivariate normal, multivariate t, Wishart (generalization of gamma), Dirichlet (generalization of beta), multinomial (generalization of binomial) distributions. SAS/STAT PROC SIMNORMAL can perform conditional and unconditional simulation for a set of correlated normal random variables.
**Multivariate normality, Test of**- See Normality, test of.
**Multivariate probit models**- SAS/ETS PROC QLIM
**Negative binomial regression**- SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or beginning in SAS 9.4, HPGENSELECT, HPNLMOD. Also, SAS Viya procedures GENSELECT, CNTSELECT, and NLMOD. SAS/ETS PROC COUNTREG, or beginning in SAS 9.4, PROC HPCOUNTREG. A version of the negative binomial with linear variance function is also available with the DIST=NEGBIN(P=1) option in COUNTREG, HPCOUNTREG, or CNTSELECT.
**Negative predictive value****Nested Logit models****Network optimization**- See Optimization.
**Neural Networks**- Neural node in SAS Enterprise Miner or PROC HPNEURAL beginning in SAS 9.4 of SAS High-Performance Data Mining. Also, PROC NNET in SAS
^{®}Visual Data Mining and Machine Learning. **Newey-West standard error correction**- SAS/ETS PROC MODEL with KERNEL= option in the FIT statement with GMM estimator. See this note for discussion and examples. Beginning in SAS 9.3 TS1M2, SAS/ETS PROC AUTOREG with COVEST=NEWEYWEST option in the MODEL statement (see available suboptions). Not available in SAS/STAT PROC REG.
**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*. Base SAS PROC UNIVARIATE provides tests for location (median).**One sample:**SAS/STAT PROC NPAR1WAY provides tests for location and scale differences.**Two or more independent samples:**Beginning with SAS 9.3 TS1M2, specify the DSCF option in PROC NPAR1WAY.**Multiple comparisons for more than two independent samples:**Base SAS PROC UNIVARIATE provides tests for location (median). Base SAS PROC FREQ provides McNemar's test.**Two dependent samples:**Friedman's test in Base SAS PROC FREQ**More than two dependent samples:**See Nonparametric, Robust (or Resistant) Regression**Regression:**Base SAS procedures CORR and FREQ. See Correlations.**Correlation:**The Jonckheere-Terpstra test is a nonparametric test of trend.**Trend:**See Kernel Density Estimation**Density estimation:**SAS/STAT PROC DISCRIM with METHOD=NPAR option and either the K= (nearest neighbor) or the R= (kernel density estimation) option.**Discriminant Analysis:****Nonparametric, Robust (or Resistant) Regression**- Includes such methods as median or quantile regression, kernel regression, adaptive regression, thin-plate splines, loess, radial smoothing, wavelets, least absolute value (LAV) or L
_{1}regression, Least Median of Squares (LMS), Least Trimmed Squares (LTS), Minimum Covariance Determinant (MCD), and Minimum Volume Ellipsoid (MVE). SAS/STAT PROC ADAPTIVEREG fits multivariate adaptive regression splines. 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), and employs a generalized MCD algorithm in leverage point analysis. See also the SAS/IML functions LAV, LMS, LTS, MCD, and MVE. **Normality, test of**- Univariate tests of normality are provided in the Base SAS PROC UNIVARIATE, SAS/QC PROC CAPABILITY, and SAS/IML Studio. Tests of multivariate normality can be obtained using the MULTNORM macro and the NORMAL option in the FIT statement of SAS/ETS PROC MODEL.
**Number needed to treat****ODE (Ordinary Differential Equations), solving**- SAS/ETS PROC MODEL. SAS/IML CALL ODE. Beginning in SAS 9.4 TS1M3, specify CALL ODE in SAS/STAT PROC MCMC to use an ordinary differential equation (ODE) solver enabling the procedure to fit models that contain differential equations such as pharmacokinetic models.
**Omega-squared**- EFFECTSIZE option in the MODEL statement in SAS/STAT PROC GLM.
**Odds Ratios**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. 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, GLIMMIX, or SURVEYLOGISTIC 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. When GLM parameterization of CLASS variables is used in the LOGISTIC, GENMOD, GLIMMIX, or SURVEYLOGISTIC procedures, you can also use the EXP option in the LSMESTIMATE statement, or the DIFF and EXP options in the LSMEANS and SLICE statements.*Model-based 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.*Nonmodeling methods:***Optimization**- SAS/OR procedures OPTMODEL, OPTLP, OPTQP, and OPTMILP and SAS/ETS PROC MODEL. Also, see the linear and nonlinear optimization subroutines in SAS/IML. Beginning in SAS Studio 3.6, the Network Optimization task.
**Ordered (or ordinal) logistic or probit models**- SAS/STAT procedures LOGISTIC, PROBIT, GENMOD, and beginning in SAS 9.4 HPLOGISTIC. SAS/ETS PROC QLIM. Also, SAS Viya procedures LOGSELECT, GENSELECT, CQLIM, and NLMOD.
**Orthogonal regression**- See Errors-in-variables regression
**Outlier detection**- In the context of regression, see the DIAGNOSTICS and LEVERAGE options in the MODEL statements of SAS/STAT procedures ROBUSTREG and QUANTREG. MVE function in SAS/IML. See also 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
**Panel data analysis**- Panel data occurs when time series and cross-sectional data are combined. SAS/ETS PANEL, HPPANEL, and TSCSREG procedures fit econometric models to such data. Also, SAS Viya PROC CPANEL and PROC CNTSELECT. See also Repeated measures analysis.
**Pareto charts**- SAS/QC PROC PARETO and SQC Menu System. Beginning in SAS Studio 3.6, the Pareto Analysis task.
**Partial correlation**- See Correlations
**Partial least squares**- SAS/STAT PROC PLS, SAS Viya PROC PLSMOD, and beginning in SAS Studio 3.6, the Partial Least Squares task.
**Partial Proportional Odds Model****Partial regression leverage plots**- PARTIAL option in the MODEL statement of SAS/STAT PROC REG. Also available in SAS/IML Studio (select
**Analysis ⇒ Model Fitting ⇒ Linear Regression**). **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.
**Passing-Bablok regression**- Not available, but see Errors-in-variables regression.
**Path analysis**- SAS/STAT PROC CALIS
**Path diagrams**- Beginning in SAS 9.4 TS1M1, PROC CALIS. Beginning in SAS 9.4 TS1M2, PROC FACTOR.
**Pearson correlation**- See Correlations
**Penalized regression methods**- Methods include LASSO (including group and adaptive LASSO), ridging, and elastic net and are available in several SAS/STAT and SAS/ETS procedures. The LASSO method is useful for model selection. These penalized regression methods can also be implemented in SAS/STAT PROC NLMIXED by specifying the likelihood function and including the appropriate penalty term as described in this note. See also the Firth method.
**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**- The Peto mortality-prevalence test is available in SAS/STAT PROC MULTTEST. The Peto-Peto and modified Peto-Peto test for comparing survival curves is available in SAS/STAT PROC LIFETEST.
**Pharmacokinetics (PK) compartment model**- Beginning in SAS 9.4 TS1M5, the CMPTMODEL statement in SAS/STAT PROC NLMIXED and PROC MCMC enables you to fit one-, two-, and three-compartment models. Also, see ODE.
**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 SAS/STAT procedures such as LOESS, TPSLINE, GAM, and GAMPL can fit flexible, nonparametric models to data. Also see Spline effects in models. **Point biserial correlations**- See Correlations
**Poisson regression**- SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or beginning in SAS 9.4, HPGENSELECT, HPNLMOD. Also, SAS Viya procedures GENSELECT, CNTSELECT, and NLMOD, SAS/ETS PROC COUNTREG, or beginning in SAS 9.4, PROC HPCOUNTREG.
**Polychoric correlation**- See Correlations
**Polychotomous logit model****Polyserial correlation**- See Correlations
**Population attributable rate (PAR) or fraction**- INDIRECT(AF) or MH(AF) option in SAS/STAT PROC STDRATE (beginning in SAS 9.3 TS1M2). See the example in this note.
**Portfolio optimization**- SAS/OR PROC OPTQP or SAS/OR PROC OPTMODEL (use SOLVE WITH QP statement).
**Positive predictive value****Power and sample size**- In SAS/STAT, the POWER and GLMPOWER procedures, the Power and Sample Size Application, and beginning in SAS Studio 3.6, the Power and Sample Size task all perform prospective power and sample size analyses. Also, see the sample programs for computing sample size or the power of chi-square tests that compare two proportions or testing independence in RxC tables and this discussion on computing power in contingency tables.
**Prediction intervals**- For normally distributed data, prediction intervals are available via options in the OUTPUT statements of the REG, GLM, NLIN, and HPMIXED procedures, and in the MODEL statement of the TRANSREG procedure in SAS/STAT software. The SCORE statement in SAS/STAT PROC PLM can also produce prediction intervals, but only for regression models on normally distributed data with identity link. The GLMPI macro can produce prediction intervals for generalized linear models on normal or nonnormal data with various links.
**Preference mapping**- SAS/STAT PROC TRANSREG.
**Prevalence Ratio**- See Relative Risk.
**Principal Components Analysis (PCA)**- SAS/STAT PRINCOMP, FACTOR, and (beginning in SAS 9.4 TS1M1) HPPRINCOMP. Also, SAS Viya PROC PCA, and beginning in SAS Studio 3.6, the Principal Components Analysis task.
**Probability plots**- Base SAS PROC UNIVARIATE and SAS/QC PROC CAPABILITY.
**Project management**- SAS/OR PROC CPM.
**Projection pursuit**- Not available.
**Propensity score analysis**- Beginning in SAS 9.4 TS1M4, SAS/STAT PROC PSMATCH can compute propensity scores (PSMODEL statement) or import propensity scores (PSDATA statement), and can match observations based on those scores (MATCH statement) using one of three methods. The balance of the resulting matched data can be assessed (ASSESS statement). Creation of strata (STRATA statement) or weights (OUTPUT statement) is also available for use in outcome analysis done in other procedures.
**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. If the weights are survey weights, use SAS/STAT PROC SURVEYMEANS.
**Quantile regression**- SAS/STAT procedures QUANTREG, QUANTLIFE, and QUANTSELECT. Also, SAS Viya PROC QTRSELECT. See also Least Absolute Value regression.
**Quartiles**- See Quantiles
**Queuing**- Not available.
**R-square**- An R-square statistic based on sums of squares is provided in several SAS/STAT regression procedures (REG, ORTHOREG, ROBUSTREG, GLM, GLMSELECT, etc.) and clustering and multivariate procedures (CLUSTER, DISCRIM, FASTCLUS, VARCLUS). Several likelihood-based R-square measures are available in SAS/STAT procedures that use maximum likelihood estimation such as LOGISTIC, HPLOGISTIC, SURVEYLOGISTIC as well as in several SAS/ETS procedures (AUTOREG, QLIM, etc.). An R-square measure based on the squared length of the variance function for models like generalized linear models and generalized additive models is available using the RsquareV macro.
**R-square, partial****Radial smoothing**- SAS/STAT PROC GLIMMIX with TYPE=RSMOOTH and KNOTMETHOD= options in the RANDOM statement.
**Random forests**- Beginning in SAS 9.4, PROC HPFOREST in SAS High-Performance Data Mining. Also, PROC FOREST in SAS
^{®}Visual Data Mining and Machine Learning. **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*. Also, random samples from many univariate and multivariate distributions can be generated using the RANDxxx modules in SAS/IML. **Random sampling**- SAS/STAT PROC SURVEYSELECT provides several methods for selecting probability-based random samples. Beginning in SAS 9.4, Base SAS PROC HPSAMPLE performs simple random sampling or stratified sampling. Beginning in SAS Studio 3.6, the Random Sampling task. Random sampling can also be done in the DATA step.
**Rank Biserial Correlation**- See Correlations
**Rasch model**- See Item Response Theory
**Ratio analysis**- The RATIO statement in SAS/STAT PROC SURVEYMEANS provides point estimates, confidence intervals, and tests for ratios of continuous or categorical variables. 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. In the context of a generalized linear model which uses a link function involving the log (such as logistic or count models), ratios of means, rates, or log odds can be estimated and tested using the DIFF and EXP option in the LSMEANS, SLICE, or ESTIMATE statement. See also the NLMeans macro.
**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**- A wide range of regression models is available in many SAS/STAT and SAS/ETS procedures as well as PROC RELIABILITY in SAS/QC. See the SAS/STAT, SAS/ETS, and SAS/QC User's Guides for details and examples. See also procedures in SAS Viya.
**Regularization methods for regression**- Regularization methods constrain the regression parameters by applying a penalty. See Penalized regression methods.
**Relative potency estimate and confidence interval**- See this note which illustrates using the delta method in SAS/STAT PROC NLMIXED and using Fieller's theorem in SAS/IML. This is also illustrated in Categorical Data Analysis Using the SAS System.
**Relative Risk**- Also known as the risk ratio. 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 provide a model-based estimate of the relative risk.
**Reliability coefficient**- Base SAS PROC CORR, ALPHA option. See also, Intraclass correlation.
**Repeated measures analysis**- For normally distributed responses, use SAS/STAT procedures GLM or MIXED. For other response distributions (and normal distributions), use SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or (beginning in SAS 9.4 TS1M2) PROC GEE. Beginning in SAS 9.4 TS1M1, SAS/ETS PROC COUNTREG can be used for repeated count responses (panel data). Beginning in SAS 9.4 TS1M2, SAS/ETS PROC HPCOUNTREG is also available for repeated count responses. Also SAS Viya PROC CNTSELECT.
**Repeated measures multiple comparisons**- See Multiple comparisons (repeated measures).
**Ridge regression**- RIDGE= option in SAS/STAT PROC REG. See also Penalized regression methods.
**Risk difference (difference in proportions) for multiway tables**- Beginning with SAS 9.4 TS1M1, the RISKDIFF(COMMON) option (and beginning with SAS 9.4 TS1M5, the COMMONRISKDIFF option) in the TABLES statement of PROC FREQ provides the common (overall) risk difference for multiway 2x2 tables. The risk difference can also be estimated when fitting a categorical response model as discussed in this note.
**Risk ratio**- Also known as the Relative Risk. Also see Hazard ratios.
**Robust estimators**Trimmed mean or Winsorized mean.*Of location:*Includes Gini's mean difference, interquartile range and MAD (Median Absolute Deviation).*Of scale (variability):*SAS/STAT PROC ROBUSTREG.*Of R-square:*SAS/STAT PROC ROBUSTREG.*Of AIC and BIC:*See White empirical ("sandwich") variance estimator and robust standard errors.*Of model parameter standard errors:***ROC (Receiver Operating Characteristic) curve**Binary response data is required. For a model fit in SAS/STAT PROC LOGISTIC, use an ROC statement, the PLOTS=ROC option, or the OUTROC= option. See the examples in the Examples section of the LOGISTIC documentation. Given predicted event probabilities from any model or method, use the PRED= option in the ROC statement as shown in this note. Beginning in SAS 9.3 TS1M2, use the PLOTS=ROC(ID= ) option to label points in the ROC curve with predictor (requires an ID statement) or statistic values. The ROCPLOT macro also plots and labels points on the ROC curve with additional capabilities. A bias-adjusted estimate of the ROC curve based on an approximate leave-one-out crossvalidation method can be obtained as discussed in this note. Beginning in SAS 9.4 TS1M3: For a decision tree model on binary data, use PLOTS=ROC in SAS/STAT PROC HPSPLIT.**Plot the ROC curve:**Beginning in SAS 9.3, use the ROCPLOT macro.**Find optimal cutpoints on the ROC curve:**Estimated by the**Area under the ROC curve (AUC):****c**statistic (known as the*concordance index*) reported by SAS/STAT procedures LOGISTIC and (beginning in SAS 9.4) HPLOGISTIC. Given predicted event probabilities from any model or method, use the PRED= option in the ROC statement as shown in this note. Use the ROCCI option in the MODEL statement (beginning in SAS 9.4 TS1M3) or specify the ROC and ROCCONTRAST statements in PROC LOGISTIC to obtain point and confidence interval estimates of the AUC as shown in this note, which also shows how to test if the AUC differs from 0.5. Also available using the ROC macro. A bias-adjusted estimate and confidence interval for the area based on either validation data or on an approximate leave-one-out crossvalidation method can be obtained as discussed in this note. Beginning in SAS 9.4 TS1M3: For a decision tree model on binary data, use SAS/STAT PROC HPSPLIT.Use the ROC and ROCCONTRAST statements in SAS/STAT PROC LOGISTIC to perform a nonparametric comparison of areas under correlated ROC curves. Also available using the ROC macro. To compare independent ROC curves, see this note.**Comparing areas under several ROC curves:**Beginning in SAS 9.4 TS1M4, ROC statement in SAS/STAT PROC PHREG. See also the CONCORDANCE, PLOTS=ROC | AUC | AUCDIFF, and ROCOPTIONS options in the PROC PHREG statement.**ROC curve for survival models:****Runs or Wald-Wolfowitz test****Runs test or Western Electric Rules**- SAS/QC PROC SHEWHART (TESTS= option). Also SAS Viya PROC SPC.
**Sample selection models**- SAS/ETS PROC QLIM fits the Heckman selection model via maximum likelihood or the two-step estimation method (HECKIT option).
**Scheffe multiple comparisons**- SAS/STAT procedures ANOVA, GLM, LIFETEST, and procedures supporting the LSMEANS, ESTIMATE, and LSMESTIMATE statements with the ADJUST= option.
**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**- SAS/STAT procedures SEQDESIGN and SEQTEST.
**Shrinkage methods for regression**- The use of a penalty shrinks the regression parameters towards zero. See Penalized regression methods.
**Simulated annealing**- Not available as a general search algorithm, but it is available in SAS/Genetics PROC HTSNP specifically for fast identification of an optimal subset of SNPs without mining through all possible combinations of SNPs.
**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.
**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, and SAS/IML Studio.
**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. Beginning in SAS 9.4 TS1M4, SAS/ETS PROC SPATIALREG. Also SAS Viya PROC CSPATIALREG.
**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).
**Spline effects in models**- The EFFECT statement supports truncated power function, B-spline, and (beginning in SAS 9.3) natural cubic spline bases in many SAS/STAT procedures. For more information, see EFFECT Statement in the Shared Concepts and Topics chapter of the SAS/STAT User's Guide and this note. See also this note which discusses how predicted values are computed in models with splines. The EFFECT statement is also available in many procedures in SAS Viya. Also see Thin-plate smoothing or regression splines, Piecewise Regression, and GAMs (Generalized Additive Models). SAS/STAT PROC TRANSREG also can fit linear models with splines of various types.
**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, SAS/STAT PROC DISTANCE.
**Standardized mortality (or morbidity) ratio (SMR)**- SAS/STAT PROC STDRATE (beginning in SAS 9.3 TS1M2).
**Standardized rates and risks**- Beginning in SAS 9.3 TS1M2, SAS/STAT PROC STDRATE provides direct or indirect standardization methods for rates and risks (proportions).
**Stochastic Frontier Models**- FRONTIER option in the ENDOGENOUS statement of SAS/ETS PROC QLIM and (beginning in SAS 9.4) PROC HPQLIM. Also SAS Viya PROC CQLIM.
**Structural Equation Modeling**- SAS/STAT PROC CALIS.
**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**SAS/STAT PROC TTEST using the VAR statement, or Base SAS procedures UNIVARIATE, MEANS, or SUMMARY.**One sample:**SAS/STAT PROC TTEST with CLASS and VAR statements, or SAS/STAT PROC MULTTEST (primarily when adjusting for multiple tests).**Two independent samples:**See ANOVA on summary statistics.**Two independent samples using summary statistics:**SAS/STAT PROC TTEST using the PAIRED statement. Or use Base SAS procedures UNIVARIATE, MEANS, or SUMMARY to test that the mean of the difference of paired values is zero.**Two dependent (paired) samples:**Use the MEANS or LSMEANS statement with DIFF option in most SAS/STAT modeling procedures. See also the STRATA statement in SAS/STAT PROC LIFETEST and the TEST MEAN statement in SAS/STAT PROC MULTTEST.**More than two independent samples (multiple comparisons):****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 SAS/IML Studio. 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.
**Support vector machines**- PROC SVMACHINE in SAS
^{®}Visual Data Mining and Machine Learning. **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**- See Correlations
**Tetrachoric correlation matrix**- OUTPLC= option in Base SAS PROC CORR. Also, see the POLYCHOR macro. For two binary variables, the polychoric correlation is the tetrachoric correlation.
**Thin-plate smoothing or regression splines**- SAS/STAT procedures TPSPLINE, GAM, and beginning in SAS 9.4 TS1M3, GAMPL. Also, PROC GAMMOD in SAS Viya.
**Three-stage least squares (3SLS)**- SAS/ETS procedures SYSLIN and MODEL.
**Tobit analysis**- SAS/STAT PROC LIFEREG. Also SAS/ETS PROC QLIM and (beginning in SAS 9.4) PROC HPQLIM.
**Tolerance intervals**- SAS/QC PROC CAPABILITY.
**Trend test for ordered alternatives**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 responses:**Jonckheere-Terpstra test in Base SAS PROC FREQ (JT option in the TABLES statement).**For binary or multilevel 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).**For continuous responses:****Trimmed mean**- TRIMMED= option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. In SAS/IML Studio, select
**Analysis ⇒ Distribution Analysis ⇒ Location and Scale Statistics**. **Truncated negative binomial model****Truncated Poisson model****Truncated regression**- SAS/ETS PROC QLIM and PROC HPQLIM (beginning in SAS 9.4) fit the truncated normal model. Beginning in SAS 9.3, SAS/STAT PROC FMM and SAS/ETS PROC SEVERITY (and PROC HPSEVERITY beginning in SAS 9.4) can fit truncated models using various distributions. Also SAS Viya PROC CQLIM and SEVSELECT.
**Tukey's range test**- SAS/STAT procedures ANOVA, GLM, LIFETEST, and procedures supporting the LSMEANS statement with the ADJUST= option.
**TURF (Total Unreplicated Reach and Frequency) analysis**- Not available.
**Tweedie model**- In SAS/STAT, DIST=TWEEDIE option in PROC HPGENSELECT (beginning in SAS 9.4) , PROC GENMOD (beginning in SAS 9.4 TS1M1), and PROC GAMPL (beginning in SAS 9.4 TS1M5). Also SAS Viya procedures GENSELECT, GAMMOD, and SEVSELECT. Two parameterizations of the Tweedie distribution are available in SAS/ETS PROC SEVERITY beginning in SAS 9.3, in SAS/ETS PROC HPSEVERITY beginning in SAS 9.4, and in SAS Viya PROC SEVSELECT. See also the Ratemaking node in SAS Enterprise Miner 7.1 or later for modeling pure premium.
**Two-stage least squares (2SLS)**- SAS/ETS procedures SYSLIN and MODEL.
**van Elteren test****Variable selection****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**- SAS/ETS PROC VARMAX
**Vuong test to compare nonnested models****Wald confidence interval for binomial probability**- BINOMIAL(WALD) option in TABLE statement of Base SAS PROC FREQ.
**Wald-Wolfowitz or Runs test****Wavelets**- WAV
*xxx*functions in SAS/IML. **Weight of evidence (WOE)**- WOE option in Base SAS PROC HPBIN (SAS 9.4 or later).
**Weighted Generalized Estimating Equations (WGEE)**- Beginning in SAS 9.4 TS1M2, SAS/STAT PROC GEE. The GEE method for longitudinal analysis assumes data missing completely at random (MCAR). WGEE extends this to situations in which data are missing at random (MAR).
**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 robust standard errors**WHITE option in the MODEL statement of SAS/STAT PROC REG displays White standard errors and tests based on them.*In ordinary regression:*This is the default variance estimator used when the REPEATED statement is specified in SAS/STAT PROC GENMOD or (beginning in SAS 9.4 TS1M2) PROC GEE, and parameter tests are based on it. Note that repeated measurements are not required in order to use the REPEATED statement.*In generalized linear 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 mixed 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.*In econometric models:***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**- 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/IML Studio, select
**Analysis ⇒ Distribution Analysis ⇒ Location and Scale Statistics**. **Yule's Q for 2x2 tables**- Same as Gamma statistic in Base SAS PROC FREQ (CHISQ option)
**Zelen's Exact Test for Equal Odds Ratios**- ZELEN option in the EXACT statement of Base SAS PROC FREQ.
**Zero-inflated models**- The most common are zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models. Zero-inflated models are often used to account for overdispersion. ZIP and ZINB models are available in SAS/STAT PROC GENMOD. SAS/ETS PROC COUNTREG and SAS Viya PROC CNTSELECT also fit ZIP and ZINB models. Beginning in SAS 9.3, SAS/STAT PROC FMM can add zero-inflation to any of the wide range of models it can fit which includes ZIP and ZINB models. Beginning in SAS 9.4, ZIP and ZINB models can be fit in SAS/STAT PROC HPGENSELECT and SAS/ETS PROC HPCOUNTREG. PROC HPGENSELECT allows for selection of effects in both the mean and zero-inflation parts of the model. These models can also be fit using SAS/STAT PROC NLMIXED. See the example in this note and the example here of zero-inflated count models, and this note for an example of a zero-inflated binomial model.

MARS^{®} is a trademark of Jeril, Inc. and is licensed exclusively to Salford Systems.

Product Family | Product | System | SAS Release | |

Reported | Fixed* | |||

SAS System | SAS/STAT | z/OS | ||

OpenVMS VAX | ||||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

OS/2 | ||||

Windows | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

WINDOWS/NTSV | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

ABI+ for Intel Architecture | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

IRIX | ||||

Linux | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

Solaris | ||||

Tru64 UNIX | ||||

SAS System | SAS/QC | z/OS | ||

OpenVMS VAX | ||||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

OS/2 | ||||

Windows | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

WINDOWS/NTSV | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

ABI+ for Intel Architecture | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

IRIX | ||||

Linux | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

Solaris | ||||

Tru64 UNIX | ||||

SAS System | SAS/ETS | z/OS | ||

OpenVMS VAX | ||||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

OS/2 | ||||

Windows | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

WINDOWS/NTSV | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

ABI+ for Intel Architecture | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

IRIX | ||||

Linux | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

Solaris | ||||

Tru64 UNIX | ||||

SAS System | SAS/IML | z/OS | ||

OpenVMS VAX | ||||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

OS/2 | ||||

Windows | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

WINDOWS/NTSV | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

ABI+ for Intel Architecture | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

IRIX | ||||

Linux | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

Solaris | ||||

Tru64 UNIX | ||||

SAS System | SAS/OR | z/OS | ||

OpenVMS VAX | ||||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

OS/2 | ||||

Windows | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

WINDOWS/NTSV | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

ABI+ for Intel Architecture | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

IRIX | ||||

Linux | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

Solaris | ||||

Tru64 UNIX | ||||

SAS System | SAS/Genetics | z/OS | ||

Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||

Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||

Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||

Microsoft Windows XP 64-bit Edition | ||||

Microsoft® Windows® for x64 | ||||

Microsoft Windows 95/98 | ||||

Microsoft Windows 2000 Advanced Server | ||||

Microsoft Windows 2000 Datacenter Server | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows NT Workstation | ||||

Microsoft Windows Server 2003 Datacenter Edition | ||||

Microsoft Windows Server 2003 Enterprise Edition | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows XP Professional | ||||

Windows Millennium Edition (Me) | ||||

Windows Vista | ||||

64-bit Enabled AIX | ||||

64-bit Enabled HP-UX | ||||

64-bit Enabled Solaris | ||||

AIX | ||||

HP-UX | ||||

HP-UX IPF | ||||

Linux | ||||

Linux for x64 | ||||

Linux on Itanium | ||||

OpenVMS Alpha | ||||

OpenVMS on HP Integrity | ||||

Solaris | ||||

Solaris for x64 | ||||

Tru64 UNIX |

FASTats: Frequently Asked-For Statistics

Type: | Usage Note |

Priority: | |

Topic: | Analytics |

Date Modified: | 2018-10-18 11:25:23 |

Date Created: | 2007-10-09 17:17:13 |