SC contains over 1300 commands: what follows is not a list of everything you can do in SC, but a list of some of the standard statistical operations that can be done with a single command. Full information about all the commands, and references to the source material, are available online. Many statistical operations not listed here can be programmed in the SC language in a few statements.
(*) below denotes 'not in Real Mode DOS version'. Everything listed below is in both the Protected Mode DOS version of SC and Unix versions.
Anova: independent groups factorial (balanced, completely crossed, any number of factors); independent groups factorial (balanced, completely crossed, any number. of factors) using ranks (Shirley, 1987); 1 between- conditions factor (balanced or unbalanced); all possible mixed designs with 2 or 3 factors (balanced); repeated measures (balanced, any number of factors). Bartlett homogeneity of variance test. Box M statistics for equality and compound symmetry of covariance matrices. Cronbach alpha. Durbin test for balanced incomplete block designs (nonparametric). Geisser-Greenhouse epsilon estimate (compound symmetry), and its tail probability. Good (1994) permutation tests for Latin Square designs and 2-way factorials. Hodges-Lehmann k-sample test for blocked observations, using alignment. Repeated measures analysis by fitting polynomials to individual cases. Huynh & Feldt test of homogeneity of treatment difference variances. R-regression linear models (Hettmansperger), and aligned rank tests. There is also a general program for any balanced compact design which allows arbitrary miztures of fixed and random factors, can report the composition of Expected Mean Squares, and makes Simple Main Effect tests very easy. There is another even more general program that handles arbitrarily unbalanced designs, including designs with missing cells. See also k-sample comparisons and Multiple Regression
Dietz nonparametric M* and W* test for bivariate 1-sample location. Hoeffding (Blum) test for bivariate independence. Hollander test for bivariate symmetry. See also Correlation
Bootstrap tests of variance homogeneity (Boos & Brownie, 1989). Bootstrap version of Johnson's modified t procedure for skewed distributions. Bootstrap intervals for randomized assignments. Efron Bias-corrected BC(a) intervals. Efron's jack- knife-after-bootstrap. Jack-knife ratio estimates. Kaigh & Cheng (1991) quartile comparisons. DiCiccio & Efron's (1992) ABC non- randomized bootstrap. Miller's jack-knife test and intervals for the ratio of 2 variances. Balanced bootstrap and subsampling schemes. General-purpose bootstrap and jack-knife routines are built into SC: the only programming required to use them is to specify the function to be bootstrapped or jack-knifed. Population bootstrap tests and CIs. Also, other types of bootstrapping - e.g. smoothed bootstraps - can easily be set up using the replacement- sampling built-in routines. Multivariate bootstrap.
Goodman & Kruskal gamma correlation test and intervals. Jolliffe's runs test for dependence. Kendall tau(b) correlation test. Partial tau (with jack-knife confidence intervals), partial gamma. Pearson r correlation matrix as lower triangle. Pearson r correlation coefficient tests and intervals. Pitman r correlation test (permutation-based). Spearman rho correlation test and large-n approximate confidence intervals. Tetrachoric correlation. Exact partial correlation test using Kendall S. See also Trend.
Bivariate normal probabilities. Extreme value c.d.f. Extreme value distribution maximum likelihood parameter estimates, Menu-driven table- generation for binomial, hypergeometric, negative binomial, Poisson, and Kendall S distributions. Jonckheere J statistic. Logistic. Multiple R-square right tail. Distribution of the largest multinomial count. Pareto. Percentage points for linear rank statistics. Tables of critical depths for binomial confidence intervals for the median. Tables of critical depths for Mann-Whitney confidence intervals for difference in medians. Tables of critical values of Kendall S. Tables of the Mann-Whitney U distribution. Tables of the Spearman rho distribution. There are functions for looking up the c.d.f. and inverse c.d.f. for the following distributions: beta (central and non-central and Type II), binomial, bivariate normal, Cauchy, chisquare (central and non-central), F (central and non-central), hypergeometric, Kendall S, negative binomial, Poisson, Rayleigh, Spearman rho, Student t (central and non-central), studentized range. There is also a general-purpose routine for linear rank statistics via Cornish-Fisher expansions. There are routines for most standard densities as well as for their tail probabilities and inverses.
Anderson-Darling goodness-of-fit tests. Chisquare test. Correlation goodness-of-fit tests for Cauchy, exponential, extreme value, and logistic. D'Agostino's tests for non-normal skew and kurtosis. Dip test of unimodality (Hartigan, 1985). Fisher exact variance test for the Poisson distribution. Kolmogorov-Smirnov goodness-of-fit test and 1-sample confidence bands. Lilliefors test for normality. Martinez & Iglewicz non-Gaussian index. McWilliams (1990) runs test for symmetry. Michael's test for non-Normality. Nomination sampling c.d.f. estimation. Olmstead test for grouping. Shapiro & Francia W' test of normality. Sillitto skew and kurtosis indicators. Tukey g- and h- distributions for skew and shape.
Binomial p interval (exact and asymptotic). Biweight interval. Box-Andersen test (an approximation to a permutation test). Coefficient of variation confidence interval, Vangel (1996). Exact permutation test for raw scores, ranks, Normal Scores, winsorized Wilcxon scores, or other rank-transforms. Exact permutation-based confidence intervals. Fisher exact variance test for the Poisson distribution (dispersion index). Hollander-Proschan test for 'new-better-than-used' alternatives. Huber M-estimator interval. Interval for median using the Sign statistic, incl. Hettmansperger's interpolated intervals. Kornbrot's rank-difference test. Liu (1991) test based on a modified bipivot statistic. Markowski & Hettmansperger rank step scores confidence interval. Normal theory interval for the variance. Student t intervals and tests. Wilcoxon signed rank intervals and tests. Tukey & McLaughlin trimmed mean intervals. Wilcoxon rank-sum test for matched sets (with exact probabilities if required). Exact Wilcoxon-like test for comparing changes in an ordinal variable.
Bell-Doksum normal scores 2-group test. Berger & Boos (1994) test for the Behrens-Fisher problem. Blair & Thompson (1991) rank-like test for scale. Blair et al (1994) pFmax permutation test. Boos Linear Rank statistics (k-group test for shift, spread, skew, kurtosis). Box-Andersen variance ratio test (an approximation to a permutation test). Brownie et al (1990) modified F test. Chacko-Shorack trend test. Cramer - von Mises 2-group test. Dunn pairwise contrasts. Exact permutation-based confidence interval. Fligner & Policello modified Mann-Whitney U test (not assuming identical shape), and the associated confidence interval. Fung studentized Wilcoxon test. Good (1994)'s permutation test for equality of variance. Hettmansperger & Norton k-sample tests for patterned alternatives. Hollander test for extreme reactions (including exact version based on permutation). Isotonic regression for simple and umbrella orders. Jonckheere-Terpstra test (approximate and exact). Johnson modified t test and interval for skewed distributions. Logrank and Wilcoxon tests for (censored) survival times. Kaigh & Chang (1991) bootstrap intervals for quartile comparison, Klotz test for difference in spread. Kolmogorov-Smirnov 2-sample test (approximate & exact). Kruskal-Wallis test, approximate and exact. Mack & Wolfe test for umbrella (inverted-U) trends. Mann-Whitney (Wilcoxon) U test for 2 unrelated samples, with exact probabilities if required. Exact stratified Mann-Whitney test. Median test for 2 independent samples. Median test for k independent samples. Mood k-sample test. Mood test for difference in spread. Moses test for equal scale. Moses interval for 2 unrelated samples. Normal theory interval for the variance ratio. Permutation tests using the mean, trimmed means, or a user-supplied function. Permutation test for comparing changes in an ordinal variable. Rust & Fligner modified Kruskal-Wallis test (not assuming identical shape). Student t intervals and tests. Student t test for unequal variances. Van der Waerden normal scores k-sample test. Wilcox (1988,1995) 1-way Anovas for unequal variances. Yuen trimmed mean intervals. Exact tesst for comparing 2 sets and k sets of changes in an ordinal variable. Tukey MCA, Dunnett 1-sided MCC, Dunnett constrained MCB simultaneous confidence intervals. See also Analysis of Variance.
Doksum test. Cochran & Friedman tests (including exact version sbased on permutation). Kendall S trend test for k related samples. Hollander trend test for k related samples. Kendall W concordance. Page L test for k related conditions. Parametric and nonparametric analyses for crossover designs. Rosenthal & Ferguson multiple comparisons. Permutation-based repeated measures analysis of variance.
Fitting lines: least-squares, Tukey's iterative method, Sen, Siegel, least median of squares, L1-norm, Brown & Mood, Dodge adaptive L1/LSQS. Hollander test for parallelism of 2 regression lines, and confidence intervals. Least-squares confidence bands for mean response, and prediction (tolerance) intervals. Wald-Wolfowitz tests on residuals (Good, 1994) to see if quadratic (cubic,...) term is needed. See also Correlation.
Design matrix generation. Fourier transforms. Gauss-Legendre quadrature, integration. Generation of many types of subsets: combinations, permutations, partitions, etc. Generating model matrices, e.g. for log-linear models. Left Kronecker vector/matrix product. Mahalanobis distances, and Penny (1996) revised critical values. Matrix editing: selecting subsets of rows/columns, re-ordering rows/columns, horizontal or vertical joins of matrices, etc.. Matrix eigenstructure and rank. Householder, QL, LU, Cholesky and singular value matrix decompositions. Latin Square generator. Minimization (4 methods). Moore-Penrose generalised matrix inverse. Multiply-restrained partitions. Numerical approximation of first derivatives and Hessian matrix. Derivaties up to order 5 for a function of 1 variable). Polynomial interpolation. Projection matrices. Required sample size calculations for 2 unrelated samples (t) and for cohort studies (Breslow & Day). Savage rank-scores. Sample size calculations for 2 unrelated sample tests. Signal detection theory model fitting by maximum likelihood. Trace of a square matrix. Urn model probabilities. Wilkinson SWEEP and Beaton SWP matrix operations.
Bounded-influence Welsh regression (M-estimators with Mallows weights). Condition number, condition index, Hat matrix, variance inflation factors, and other multicollinearity diagnostics. Anscombe/Godfrey/Koenker heterescedacity test. L1-norm regression. Least median of squares regression (with reweighted least-squares as follow-up); Stromberg's (1991) exact LMS. Least squares regression. Least-squares polynomial fit (tests and intervals). Probit, and Poisson regression. Logistic regression: exact tests for a single parameter and maximum likelihood. Minimum volume ellipsoid leverage. Rank regression (Hettmansperger). Robust regression using M-estimators (Andrews sine, Huber, biweight). General multi-stage re-weighted least-squares routine, allowing several weighting schemes and termination criteria to be applied in series (Andres, biweight, Cauchy, fair, Huber, logistic, Talworth, Welsch weighting functions). There are 5 regression-report routines, which screen data for signs of collinearity, unnoted structure among the carriers, a small number of significant digits, etc.. Partial Least Squares regression.
Blair et al (1994) step-down permutation tests for several related samples. Canonical correlation. CART (cross-classification and regression trees): the routines allow binary, nominal, ordinal, or continuous response variables, and can be used with exact permutation tests to choose splits. Dietz & Killeen nonparametric multivariate test for monotone trend. Canonical analysis of skew-symmetry. Discriminant functions. Guttman scale analysis. Hotelling 1-sample and 2-sample T-square; 2 group permutation tests using T-square or Boyett & Schuster's statistic. Hutchinson NETSCAL scaling. Likelihood-ratio statistic for comparing multivariate samples. m nearest-neighbour multivariate smooth (Taylor & Thopson, 1992). Minimum spanning trees (*). Multivariate runs test using minimum spanning tree (*). Oja bivariate median. The mediancentre. Principle components. Minimum volume ellipsoid mean and covariance estimator, and robust distances. Puri & Sen's multivariate median and rank-sum tests (also a permutation-based version of their rank-sum test). Single-linkage cluster analysis + dendrogram. Van Valen statistics for multivariate tests for equal variability. There are general routines that give complete distributions or tail probabilities under permutation of cases across groups, for any user-supplied multivariate statistic.
Atkinson forward-selection Mahalanobis method. Bradu & Hawkins tetrads for 2-way layouts. Atkinson's (1993) forward selection Mahalanobis method.
Autocorrelation plot. Average shifted histogram plot (Scott). Barplots. Boxplots. EQQ plots. Fence displays (outliers). Histograms. Index plots. Letter-value displays. Normal and half- normal plots. One-way Anova plot (Levin et al). Plots of binomial, Kendall S, Poisson distributions. Quantile plots. Stem-and-leaf plots. Tallies. Tukey 5-number summary. x-y plots.
There are routines to generate publication-quality Postscript versions of the following plots in cooperation with the Unix tools grap, pic, and troff : note that the Gnu groff versions of the pic/troff tools are supplied free with Unix and MSODS Protected Mode executable versions of sc, augmented by a homespun grap-substitute called ggrap. Atkinson stalactite plots, barplots, barplot matrices, boxplots (schematic plots), bubble plots, confidence interval or error-bar plots, coplots (covariance plots), correspondence analysis plots, density traces, density traces with Silverman test graphs, dot plots, dot-dash plots, dot-dash plot matrices, effect and residual plots after analysis of variance, EQQ plots, event-series plots, function (including density function) plots, histograms, interaction plots of means after analysis of variance, interference plots, m-d plots, parallel coordinate plots, rectangle plots, TQQ plots (e.g. Chi-square, Normal, and Normal plots augmented with Michael's tolerance limits), wire-frame 3-d plots, x-y plots, matrices of x-y plots, x-y-z plots, x-y-z plots with all 2- and 1-dimensional marginals. Event charts. Time-series plots (raw, smooth, and residuals).
There are about 45 routines to dirve the gnuplot software, supplied with exectuable versions of sc for DOS and Unix. gnuplot supports numerous screen drivers (e.g. EGA, VGA, SVGA in 800x600 or 1024x768 resolution, X11, etc.) and numerous printers (postscript, Deskjet, Laserjet, Paintjet, etc.). For DOS, both real mode and protected mode versions of gnuplot are provided: the latter is a full 32-bit program using up to 128 Mbyte of RAM and 128 Mbyte of virtual memory on disk. The plot-types provided include most of those listed above for the grap/pic/troff software, except that some multi-part display (e.g. coplots) are not provided, and their are additional gnuplot routines, e.g. for plotting densities (Beta, Chisquare, F, Gumbel, Nomal, Pareto, t, etc.), wire-frame 3-d plots with projected contours, etc..
There are fast high-quality built-in generators for: uniform (3 types), random beta, random binomial, random bits, random Cauchy, random exponential, random gamma, random integers, random Poisson, random combinations of integers, random permutations, replacement and non-replacement sampling from vectors and matrices. Numerous other generators are implemented as external routines: e.g.filling vectors with binomial, chisquare, double exponential, exponential, F, gamma, normal, Poisson, Student t, or uniform random numbers (menu driven); random contaminated normal samples; random correlated normal variates; random dipole variates; random Dirichlet vectors; random geometric variates; random multinomials; random multivariate normal, log-normal, or arcsinh-normal vectors; random uniform order statistics; random Wishart matrices (or covariance matrices from a multivariate normal random sample).
Adaptive kernel density estimates. Bootstrap bump-hunting (Silverman): tests for multi-modality based on density estimation (*). Cleveland & Kleiner (1975) scatterplot smooth. Gaussian kernel density estimates (*). Hardle smoothing using M-estimators and Fourier transforms. Kernel x-y smoothing. Least squares cross-validation choice of window width for density estimation (*). Lowess and loess (locally weighted robust regression, as implemented by Cleveland). m nearest- neighbour multivariate smooth (Taylor & Thopson, 1992). Piecewise monotonic regression. Remedian curve estimate. Scott's Average Shifted Histogram. Sheather & Jones (1991) bandwidth selection for density estimates. Simonoff (1995) bivariate adaptive density estimate based on conditional densities. Spliced robust smoothing (Gebski & McNeil, 1984). Tukey running-median smoothers (8 types). Wilcox (1995) regression smoothers for resistant measures of centre and scale.
In the 32-bit versions only, there are facilities for storing sparse vectors and matrices economically, and all arithmetic, logical, and comparison operators work with sparse structures .
Chisquare dispersion test; Hopkins' test
Mean, median, biweight, Huber M-estimate, Hampel tanh, Hampel X84, Hodges-Lehmann 1- and 2-sample estimates, weighted median, trimean, remedian centre estimate, percentiles, minimum, maximum, standard deviation, variance, fourth-spread, interquartile range, biweight scale estimator, Gini mean difference, Sillitto skew and kurtosis indices, shortest fraction scale estimators, Harrel-Davis quantile estimators, Rousseeuw & Croux S(n).
Absolute deviations about the median. John & Draper modulus transform. Letter value displays under a set of power/log transforms. Matched transformation for symmetry (EDA method). Normal and half-normal transforms, winsorized rank transforms. Normal to Johnson transformations, and vice versa. Power (log) transform, folded power (log) transform. Savage scores. Standardizing, trimming, winsorizing. Transforming for equal-spread, linearity, or symmetry (iterative EDA methods using diagnostic plots), Also, numerous transformations are possible by applying one of the built-in functions.
Autocorrelation function. Durbin-Watson statistic. Exact Wald- Wolfowitz test for serial dependence. Odds-ratio comovement statistic; permutation tests for comovement between lagged autocorrelated sequences.
Cox-Stuart trend test, and Cox-Stuart test for trend in variability. Fligner-Verducci nonparametric test for temporal bias. Gap test. Runs test for independence, and the Wald-Wolfowitz runs test.