Authors and copyright

The characters used to form Genstat statements are a subset of those available on most computers. For the Genstat language they are classified as brackets, digits, letters, punctuation symbols, simple operators, or special symbols.

A comment consists of any series of characters that the computer can represent, enclosed by double quotes ("); comments are ignored and can appear anywhere in a Genstat program.

These are used to store information within Genstat, such as numbers, character strings or even identifiers of other data structures. Directives known as declarations are available to form each of the available types.

is a data structure that stores the diagonal elements of a square matrix whose other values are all zero. Diagonal matrices can be declared using the DIAGONALMATRIX directive.

is a standard form of instruction in the Genstat language requesting a particular action or analysis. All Genstat 5 directives have the same syntax.

is an arithmetic expression consisting of lists and functions separated by operators. An expression data structure stores a Genstat expression, and can be declared using the EXPRESSION directive.

is a data structure that specifies an allocation of the units into groups. It is thus a vector that, unlike the variate or the text, takes only a limited set of values, one for each group. The groups are referred to by numbers known as levels; you can also define textual labels. Factors can be declared using the FACTOR directive.

is a model formula of lists and operators defining the list of model terms involved in an analysis. A formula data structure stores a Genstat formula, and can be defined using the FORMULA directive.

denotes a standard operation in an expression or formula, with the form "function-name (sequence of lists and/or expressions separated by ;)". The function-name is a system word and may be abbreviated to four characters; if characters 5-8 are given, they must match the standard form. A wide range of functions are available, for operations ranging from transformations to the calculation of summary statistics.

is the name given to a particular data structure within a Genstat program. The first character of an identifier must be a letter; any others can be either letters or digits. Only the first eight characters are significant; subsequent characters are ignored. The directive SET allows you to specify whether or not the case of the letters (small or capital) is to be significant; e.g. whether LENGTH is the same as Length.

Letters in Genstat are the upper-case (capital) letters A to Z, the lower-case letters a to z, the underline symbol (_), and the percent character (%).

is a compound data structure storing latent roots and vectors, mainly used in multivariate analysis. They can be declared using the LRV directive.

is a Genstat text structure containing a section of a Genstat program. The text must have an unsuffixed identifier. It can be substituted into the program, by giving its identifier, preceded by a contiguous pair of substitution symbols (##). The substitution takes place as soon as Genstat reads the pair of hashes. (However, Genstat also has the EXECUTE directive, which allows a text containing a list of statements to be executed for example within a loop or procedure.)

is a data structure that stores a rectangular array of numbers. Matrices can be declared using the MATRIX directive.

is denoted within a Genstat program by one asterisk (*). When reading data, a series of contiguous asterisks or an asterisk followed by letters or digits is treated as a missing value too, and other characters can also be defined to represent missing values.

allows repetive lists to be specified concisely. A multiplier may be a number, or the substitution symbol (#) followed by a single-valued numerical data structure.

is a sequence of digits, optionally containing a decimal point (.). The sequence can be preceded by a sign (+ or -) and can be followed by an exponent: i.e. the letter E or D (in upper or lower case) optionally followed by spaces, then a sequence of digits optionally preceded by a sign.

is a symbol or symbols denoting an operation in an expression or formula:

Options specify arguments that are global within a Genstat statement: i.e. they apply to all the items in the parameter list(s). Often, but not always, options have default values and so need not be specified.

Parameters specify parallel lists of arguments for a statement: i.e. the statement (with its option settings) operates for the first item in each list, then the second, and so on. The number of times that this happens is determined by the length of the parameter list that is first in the prescribed order for the directive or procedure concerned. Subsequent lists are recycled if they are shorter than the first list.

is a data structure that stores a series of identifiers, pointing to other data structures. Pointers can be declared using the POINTER directive.

This is a structure that contains Genstat statements, and fulfils the role of the subroutine in the Genstat language. The use of a procedure looks just like the use of a Genstat directive. All data structures within the procedure are local (i.e. they cannot be referenced, or confused, with data structures outside the procedure); input and output structures for the procedure are defined by option and parameter settings in the procedure call.

The Genstat Procedure Library contains procedures contributed not only by the writers of Genstat but also by knowledgeable Genstat users from many application areas and countries. The Library is controlled by an Editorial Board, who check that the procedures are useful and reliable, and maintain standards for the documentation. It is regularly extended and updated, independently to the releases of Genstat itself, and these revised versions are distributed automatically to all supported Genstat sites. Information about the Library is available using procedures in the help module of the Library. Other modules cover, for example, manipulation, graphics and various types of statistical analysis. These procedures are all accessed automatically by Genstat, when required. Instructions for authors of procedures can be obtained using procedure NOTICE. You can also form your own procedure libraries using the STORE directive.

is a series of statements, ending with the statement STOP.

Lists of numbers ascending or descending with equal increments can be specified succinctly using the form "number, number ... number" where the first two numbers define the first two elements in the list (and thus the increment) and the list ends with the value beyond which the third number would be passed. For lists with an increment of plus or minus one, the second number can be omitted, to give the form "number ... number".

These may occur in a list of identifiers to define subsets of the values of a data structure. The form is "identifier $ qualifier", where the qualifier is a sequence of identifier lists enclosed in square brackets. For factors, variates, and texts, the qualifier has a single list, each element of which defines a subset of the vector concerned. For matrices there are two lists running in parallel, one for each dimension. For a symmetric matrix, there can be either one or two lists, depending on whether or not its two dimensions are to be subsetted in the same way. For a diagonal matrix there is a single list. Tables cannot be qualified. The elements of the qualifier lists can be scalars, numbers, variates, quoted strings, or texts.

is a data structure that stores a single number. Scalars can be declared using the SCALAR directive.

is a compound data structure storing sums of squares and products, means and ancillary information for use in regression and multivariate analysis. SSPMs can be declared using the SSPM directive.

is a sequence of characters forming one unit (or line) of a Genstat text structure. In most contexts, the string must be quoted: i.e. enclosed in single quotes ('). Quoted strings may contain any of the characters available on the computer. However, if single quote ('), double quote ("), or the continuation symbol (\) are required as characters within a quoted string, they must each be typed twice to distinguish this use from their action in, respectively, terminating the string, introducing a comment within the string, or indicating continuation. Newline within a quoted string is taken to terminate the current (quoted) string and begin another one, unless the newline is within a comment or preceded by an (unduplicated) continuation symbol (\), or unless directive SET has specified that newline is to be ignored. Unquoted strings can occur in unnamed texts, or in option or parameter settings where you have to specify a particular string from a prescribed set of alternatives; an unquoted string must have a letter as its first character and contain only letters or digits.

An identifier list can contain qualified identifiers, each defining a list of subsets of the values of the data structure concerned.

is a data structure that stores the lower triangle (including the diagonal) of a symmetric square matrix.

is a letter followed by letters and/or digits with a special meaning within the Genstat language, e.g. directive, option, parameter, or function names. The case of the letters (small/capital) is not significant; the abbreviation rules vary according to context.

is a compound data structure storing a model for use in Box-Jenkins modelling of time series. TSMs can be declared using the TSM directive.

An identifier list may contain unnamed variates, scalars, texts, pointers, expressions, or formulae. An unnamed structure consists of an exclamation mark, followed by the type code, and then the values contained in round brackets. The type code is E for expression, F for formula, P for pointer, S for scalar, T for text, or V for variate. If no code is given, variate is assumed by default.

is a data structure that stores a series of numbers. Variates can be declared using the VARIATE directive.

is a series of values, notionally arranged in a column. Genstat has three different types of vector: factors, texts, and variates.

ADD adds extra terms to a linear, generalized linear, generalized additive, or nonlinear model.

ADDPOINTS adds points for new objects to a principal coordinates analysis.

ADISPLAY displays further output from analyses produced by ANOVA.

AKEEP copies information from an ANOVA analysis into Genstat data structures.

ANOVA analyses y-variates by analysis of variance according to the model defined by earlier BLOCKSTRUCTURE, COVARIATE, and TREATMENTSTRUCTURE statements.

ASSIGN sets elements of pointers and dummies.

AXES defines the axes in each window for high-resolution graphics.

BLOCKSTRUCTURE defines the blocking structure of the design and hence the strata and the error terms.

BREAK suspends execution of the statements in the current channel or control structure and takes subsequent statements from the channel specified.

CALCULATE calculates numerical values for data structures.

CASE introduces a "multiple-selection" control structure.

CATALOGUE displays the contents of a backing-store file.

CLOSE closes files.

CLUSTER forms a non-hierarchical classification.

COLOUR defines the red, green and blue intensities to be used for the Genstat colours with certain graphics devices.

COMBINE combines or omits "slices" of a multi-way data structure (table, matrix, or variate).

CONCATENATE concatenates and truncates lines (units) of text structures; allows the case of letters to be changed.

CONTOUR produces contour maps of two-way arrays of numbers (on the terminal/printer).

COPY forms a transcript of a job.

CORRELATE forms correlations between variates, autocorrelations of variates, and lagged cross-correlations between variates.

COVARIATE specifies covariates for use in subsequent ANOVA statements.

CVA performs canonical variates analysis.

DCLEAR clears a graphics screen.

DCONTOUR draws contour plots on a plotter or graphics monitor.

DDISPLAY redraws the current graphical display.

DEBUG puts an implicit BREAK statement after the current statement and after every NSTATEMENTS subsequent statements, until an ENDDEBUG is reached.

DECLARE declares one or more customized data structures.

DELETE deletes the attributes and values of structures.

DEVICE switches between (high-resolution) graphics devices.

DGRAPH draws graphs on a plotter or graphics monitor.

DHISTOGRAM draws histograms on a plotter or graphics monitor.

DIAGONALMATRIX declares one or more diagonal matrix data structures.

DISPLAY prints, or reprints, diagnostic messages.

DISTRIBUTION estimates the parameters of continuous and discrete distributions.

DKEEP saves information from the last plot on a particular device.

DPIE draws a pie chart on a plotter or graphics monitor.

DREAD reads the locations of points from an interactive graphical device.

DROP drops terms from a linear, generalized linear, generalized additive, or nonlinear model.

DSURFACE produces perspective views of a two-way arrays of numbers.

DUMMY declares one or more dummy data structures.

DUMP prints information about data structures, and internal system information.

DUPLICATE forms new data structures with attributes taken from an existing structure.

D3HISTOGRAM produces three-dimensional histograms.

EDIT edits text vectors.

ELSE introduces the default set of statements in block-if or in multiple-selection control structures.

ELSIF introduces a set of alternative statements in a block-if control structure.

ENDBREAK returns to the original channel or control structure and continues execution.

ENDCASE indicates the end of a "multiple-selection" control structure.

ENDDEBUG cancels a DEBUG statement.

ENDFOR indicates the end of the contents of a loop.

ENDIF indicates the end of a block-if control structure.

ENDJOB ends a Genstat job.

ENDPROCEDURE indicates the end of the contents of a Genstat procedure.

ENQUIRE provides details about files opened by Genstat.

EQUATE transfers data between structures of different sizes or types (but the same modes i.e. numerical or text) or where transfer is not from single structure to single structure.

ESTIMATE estimates parameters in Box-Jenkins models for time series.

EXECUTE executes the statements contained within a text.

EXIT exits from a control structure.

EXPRESSION declares one or more expression data structures.

FACROTATE rotates factor loadings from a principal components or canonical variates analysis according to either the varimax or quartimax criterion.

FACTOR declares one or more factor data structures.

FCLASSIFICATION forms a classification set for each term in a formula, breaks a formula up into separate formulae (one for each term), and applies a limit to the number of factors and variates in the terms of a formula.

FILTER filters time series by time-series models.

FIT fits a linear, generalized linear, generalized additive, or generalized nonlinear model.

FITCURVE fits a standard nonlinear regression model.

FITNONLINEAR fits a nonlinear regression model or optimizes a scalar function.

FKEY forms design keys for multi-stratum experimental designs, allowing for confounded and aliased treatments.

FLRV forms the values of LRV structures.

FOR introduces a loop; subsequent statements define the contents of the loop, which is terminated by the directive ENDFOR.

FORECAST forecasts future values of a time series.

FORMULA declares one or more formula data structures.

FOURIER calculates cosine or Fourier transforms of real or complex series.

FPSEUDOFACTORS determines patterns of confounding and aliasing from design keys, and extends the treatment model to incorporate the necessary pseudo-factors.

FRAME defines the positions of windows within the frame of a high-resolution graph. The positions are defined in normalized device coordinates ([0,1]´ [0,1]).

FSIMILARITY forms a similarity matrix or a between-group-elements similarity matrix or prints a similarity matrix.

FSSPM forms the values of SSPM structures.

FTSM forms preliminary estimates of parameters in time-series models.

FVARIOGRAM forms auto variograms for individual variates or cross variograms for pairs of variates.

GENERATE generates factor values for designed experiments: with no options set, factor values are generated in standard order; the options allow treatment factors to be generated using the design-key method, or pseudo-factors to be generated to describe the confounding in a partially balanced experimental design.

GET accesses details of the "environment" of a Genstat job.

GETATTRIBUTE accesses attributes of structures.

GRAPH produces scatter and line graphs on the terminal or line printer.

GROUPS forms a factor (or grouping variable) from a variate or text, together with the set of distinct values that occur.

HCLUSTER performs hierarchical cluster analysis.

HDISPLAY displays results ancillary to hierarchical cluster analyses: matrix of mean similarities between and within groups, a set of nearest neighbours for each unit, a minimum spanning tree, and the most typical elements from each group.

HELP prints details about the Genstat language and environment.

HISTOGRAM produces histograms of data on the terminal or line printer.

HLIST lists the data matrix in abbreviated form.

HSUMMARIZE forms and prints a group by levels table for each test together with appropriate summary statistics for each group.

IF introduces a block-if control structure.

INPUT specifies the input file from which to take further statements.

INTERPOLATE interpolates values at intermediate points.

JOB starts a Genstat job.

KRIGE calculates kriged estimates using a model fitted to the sample variogram.

LIST lists details of the data structures currently available within Genstat.

LRV declares one or more LRV data structures.

MARGIN forms and calculates marginal values for tables.

MATRIX declares one or more matrix data structures.

MDS performs non-metric multidimensional scaling.

MERGE copies subfiles from backing-store files into a single file.

MODEL defines the response variate(s) and the type of model to be fitted for linear, generalized linear, generalized additive, and nonlinear models.

MONOTONIC fits an increasing monotonic regression of y on x.

OPEN opens files.

OPTION defines the options of a Genstat procedure with information to allow them to be checked when the procedure is executed.

OR introduces a set of alternative statements in a "multiple-selection" control structure.

OUTPUT defines where output is to be stored or displayed.

OWN does work specified in Fortran subprograms linked into Genstat by the user.

PAGE moves to the top of the next page of an output file.

PARAMETER defines the parameters of a Genstat procedure with information to allow them to be checked when the procedure is executed.

PASS does work specified in subprograms supplied by the user, but not linked into Genstat. This directive may not be available on some computers.

PCO performs principal coordinates analysis, also principal components and canonical variates analysis (but with different weighting from that used in CVA) as special cases.

PCP performs principal components analysis.

PEN defines the properties of "pens" for high-resolution graphics.

POINTER declares one or more pointer data structures.

PREDICT forms predictions from a linear or generalized linear model.

PRINT prints data in tabular format in an output file, unformatted file, or text.

PROCEDURE introduces a Genstat procedure.

QUESTION obtains a response using a Genstat menu.

RANDOMIZE randomizes the units of a designed experiment or the elements of a factor or variate.

RCYCLE controls iterative fitting of generalized linear, generalized additive, and nonlinear models, and specifies parameters, bounds etc for nonlinear models.

RDISPLAY displays the fit of a linear, generalized linear, generalized additive, or nonlinear model.

READ reads data from an input file, an unformatted file, or a text.

RECORD dumps a job so that it can later be restarted by a RESUME statement.

REDUCE forms a reduced similarity matrix (referring to the GROUPS instead of the original units).

RELATE relates the observed values on a set of variates to the results of a principal coordinates analysis.

REML fits a variance-components model by residual (or restricted) maximum likelihood.

RESTRICT defines a restricted set of units of vectors for subsequent statements.

RESUME restarts a recorded job.

RETRIEVE retrieves structures from a subfile.

RETURN returns to a previous input stream (text vector or input channel).

RFUNCTION estimates functions of parameters of a nonlinear model.

RKEEP stores results from a linear, generalized linear, generalized additive, or nonlinear model.

ROTATE does a Procrustes rotation of one configuration of points to fit another.

SCALAR declares one or more scalar data structures.

SET sets details of the "environment" of a Genstat job.

SETOPTION sets or modifies defaults of options of Genstat directives or procedures.

SETPARAMETER sets or modifies defaults of parameters of Genstat directives or procedures.

SKIP skips lines in input or output files.

SORT sorts units of vectors according to an index vector.

SPREADSHEET allows interactive entry or editing of data (available in only some implementations).

SSPM declares one or more SSPM data structures.

STEP selects terms to include in or exclude from a linear, generalized linear, or generalized additive model according to the ratio of residual mean squares.

STOP ends a Genstat program.

STORE to store structures in a subfile of a backing-store file.

STRUCTURE defines a compound data structure.

SUSPEND suspends execution of Genstat to carry out commands in the operating system. This directive may not be available on some computers.

SVD calculates singular value decompositions of matrices i.e. ( LEFT *+ SINGULAR *+ TRANSPOSE(RIGHT) ).

SWITCH adds terms to, or drops them from a linear, generalized linear, generalized additive, or nonlinear model.

SYMMETRICMATRIX declares one or more symmetric matrix data structures.

TABLE declares one or more table data structures.

TABULATE forms summary tables of variate values.

TDISPLAY displays further output after an analysis by ESTIMATE.

TERMS specifies a maximal model, containing all terms to be used in subsequent linear, generalized linear, generalized additive, and nonlinear models.

TEXT declares one or more text data structures.

TKEEP saves results after an analysis by ESTIMATE.

TRANSFERFUNCTION specifies input series and transfer function models for subsequent estimation of a model for an output series.

TREATMENTSTRUCTURE specifies the treatment terms to be fitted by subsequent ANOVA statements.

TRY displays results of single-term changes to a linear, generalized linear, or generalized additive model.

TSM declares one or more TSM data structures.

TSUMMARIZE displays characteristics of time series models.

UNITS defines an auxiliary vector of labels and/or the length of any vector whose length is not defined when a statement needing it is executed.

VARIATE declares one or more variate data structures.

VCOMPONENTS defines the variance-components model for REML.

VDISPLAY displays further output from a REML analysis.

VKEEP copies information from a REML analysis into Genstat data structures.

VPEDIGREE generates an inverse relationship matrix for use when fitting animal or plant breeding models by REML.

VSTATUS prints the current model settings for REML.

VSTRUCTURE defines a variance structure for random effects in a REML model

WORKSPACE accesses private data structures for use in procedures.

ABIVARIATE produces graphs and statistics for bivariate analysis of variance.

AFALPHA generates alpha designs.

AFCYCLIC generates block and treatment factors for cyclic designs.

AFORMS prints data forms for an experimental design.

AFUNITS forms a factor to index the units of the final stratum of a design.

AGALPHA forms alpha designs by standard generators for up to 100 treatments.

AGBIB generates balanced incomplete block designs.

AGBOXBEHNKEN generates Box Behnken designs.

AGCENTRALCOMPOSITE generates central composite designs.

AGCYCLIC generates cyclic designs from standard generators.

AGDESIGN generates generally balanced designs.

AGFRACTION generates fractional factorial designs.

AGHIERARCHICAL generates orthogonal hierarchical designs.

AGMAINEFFECT generates designs to estimate main effects of two-level factors.

AGNEIGHBOUR generates neighbour-balanced designs.

AGRAPH plots one- or two-way tables of means from ANOVA.

AKAIKEHISTOGRAM prints histograms with improved definition of groups.

AKEY generates values for treatment factors using the design key method.

ALIAS finds out information about aliased model terms in analysis of variance.

AMERGE merges extra units into an experimental design.

ANTMVESTIMATE estimates missing values in repeated measurements.

ANTORDER assesses order of ante-dependence for repeated measures data.

ANTTEST calculates overall tests based on a specified order of ante-dependence.

AONEWAY provides one-way analysis of variance for inexperienced users.

APLOT plots residuals from an ANOVA analysis.

APPEND appends a list of vectors of the same type.

APRODUCT forms a new experimental design from the product of two designs.

ARANDOMIZE randomizes and prints an experimental design.

AREPMEASURES produces an analysis of variance for repeated measurements.

ASTATUS provides information about the settings of ANOVA models and variates.

ASWEEP performs sweeps for model terms in an analysis of variance.

AUDISPLAY produces further output for an unbalanced design (after AUNBALANCED).

AUNBALANCED performs analysis of variance for unbalanced designs.

A2PLOT plots effects from two-level designs with robust s.e. estimates.

BANK calculates the optimum aspect ratio for a graph.

BARCHART plots a bar chart using line-printer or high-resolution graphics.

BIPLOT produces a biplot from a set of variates.

BJESTIMATE fits an ARIMA model, with forecast and residual checks.

BJFORECAST plots forecasts of a time series using a previously fitted ARIMA.

BJIDENTIFY displays time series statistics useful for ARIMA model selection.

BOOTSTRAP produces bootstrapped estimates, standard errors and distributions.

BOXPLOT draws box-and-whisker diagrams or schematic plots.

CANCOR does canonical correlation analysis.

CENSOR pre-processes censored data before analysis by ANOVA.

CHECKARGUMENT checks the arguments of a procedure.

CHISQUARE calculates chi-square statistics for one- and two-way tables.

CINTERACTION clusters rows and columns of a two-way interaction table.

CLASSIFY obtains a starting classification for non-hierarchical clustering.

CONCORD calculates Kendall's Coefficient of Concordance.

CONVEXHULL finds the points of a single or a full peel of convex hulls.

CORRESP does correspondence analysis, or reciprocal averaging.

CUMDISTRIBUTION fits frequency distributions to accumulated counts.

CVAPLOT plots the mean and unit scores from a canonical variate analysis.

CVASCORES calculates scores for individual units in canonical variate analysis.

DAPLOT plots residuals from ANOVA with interactive identification of outliers.

DAYCOUNT converts a date to a daycount, or vice versa.

DAYLENGTH calculates daylengths at a given period of the year.

DBARCHART produces barcharts for one or two-way tables.

DDENDROGRAM draws dendrograms with control over structure and style.

DDESIGN plots the plan of an experimental design.

DECIMALS sets the number of decimals for a structure, using its round-off.

DESCRIBE saves and/or prints summary statistics for variates.

DESIGN helps to select and generate effective experimental designs.

DIALLEL analyses full and half diallel tables with parents.

DILUTION calculates Most Probable Numbers from dilution series data.

DISCRIMINATE performs discriminant analysis.

DMST gives a high resolution plot of an ordination with minimum spanning tree.

DOTPLOT produces a dot-plot using line-printer or high-resolution graphics.

DPARALLEL displays multivariate data using parallel coordinates.

DPOLYGON draws polygons using high-resolution graphics.

DPTMAP draws maps for spatial point patterns using high-resolution graphics.

DPTREAD adds points interactively to a spatial point pattern.

DREPMEASURES plots profiles and differences of profiles for repeated measures data.

DRPOLYGON reads a polygon interactively from the current graphics device.

DSCATTER produces a scatter-plot matrix using high-resolution graphics.

DSHADE produces a pictorial representation of a data matrix.

EXTRABINOMIAL fits the models of Williams (1982) to overdispersed proportions.

FACAMEND permutes the levels and labels of a factor.

FACPRODUCT forms a factor with a level for every combination of other factors.

FDESIGNFILE forms a backing-store file of information for AGDESIGN.

FEXACT2X2 does Fisher's exact test for 2´ 2 tables.

FIELLER calculates effective doses or relative potencies.

FILEREAD reads data from a file.

FITMULTIVARIATE performs multivariate linear regression with accumulated tests.

FITNONNEGATIVE fits a generalized linear model with nonnegativity constraints.

FITPARALLEL carries out analysis of parallelism for nonlinear functions.

FITSCHNUTE fits a general 4 parameter growth model to a non-decreasing Y-variate.

FLIBHELP forms a help information file for use by LIBHELP &c.

FRESTRICTEDSET forms vectors with the restricted subset of a list of vectors.

FTEXT forms a text structure from a variate.

GEE fits models to longitudinal data by generalized estimating equations.

GENPROC performs a generalized Procrustes analysis.

GETDATA recovers data and information previously stored by SAVEDATA.

GINVERSE calculates the generalized inverse of a matrix.

GLM analyses non-standard generalized linear models.

GLMM fits a generalized linear mixed model.

GRANDOM generates pseudo-random numbers from probability distributions.

GRLABEL randomly labels two or more spatial point patterns.

GRTHIN randomly thins a spatial point pattern.

GRTORSHIFT performs a random toroidal shift on a spatial point pattern.

HANOVA does hierarchical analysis of variance/covariance for unbalanced data.

HEATUNITS calculates accumulated heat units of a temperature dependent process.

IFUNCTION estimates implicit and/or explicit functions of parameters.

INSIDE determines whether points lie within a specified polygon.

JACKKNIFE produces Jackknife estimates and standard errors.

KAPLANMEIER calculates the Kaplan-Meier estimate of the survivor function.

KAPPA calculates a kappa coefficient of agreement for nominally scaled data.

KOLMOG2 performs a Kolmogorov-Smirnoff two-sample test.

KRUSKAL carries out a Kruskal-Wallis one-way analysis of variance.

LATTICE analyses square and rectangular lattice designs.

LIBEXAMPLE accesses examples and source code of library procedures.

LIBFILENAME supplies the names of information files for library procedures.

LIBHELP provides help information about library procedures.

LIBINFORM prints information about the contents of the Procedure Library.

LIBMANUAL prints a "Manual" containing information about library procedures.

LIBVERSION provides the name of the current Genstat 5 Procedure Library.

LINDEPENDENCE finds the linear relations associated with matrix singularities.

LRVSCREE prints a scree diagram and/or a difference table of latent roots.

LVARMODEL analyses a field trial using the Linear Variance Neighbour model.

MANNWHITNEY performs a Mann-Whitney U test.

MANOVA performs multivariate analysis of variance and covariance.

MENU initiates a menu system.

MPOWER forms integer powers of a square matrix.

MULTMISS estimates missing values for units in a multivariate data set.

MVARIOGRAM fits models to an experimental variogram.

NLCONTRASTS fits nonlinear contrasts to quantitative factors in ANOVA.

NORMTEST performs tests of univariate and/or multivariate normality.

NOTICE gives access to the Genstat Notice Board (news, errors &c).

ORTHPOL calculates orthogonal polynomials.

PAIRTEST performs t-tests for pairwise differences.

PCOPROC performs a multiple Procrustes analysis.

PDESIGN prints or stores treatment combinations tabulated by the block factors.

PERCENT expresses the body of a table as percentages of one of its margins.

PERIODTEST gives periodogram-based tests for white noise in time series.

PLS fits a partial least squares regression model.

PPAIR displays results of t-tests for pairwise differences in compact diagrams.

PREWHITEN filters a time series before spectral analysis.

PROBITANALYSIS fits probit models allowing for natural mortality and immunity.

PTBOX generates a bounding or surrounding box for a spatial point pattern.

PTCLOSEPOLYGON closes open polygons.

PTDESCRIBE gives summary and second order statistics for a point process.

PTREMOVE removes points interactively from a spatial point pattern.

QUANTILE calculates quantiles of the values in a variate.

RANK produces ranks, from the values in a variate, allowing for ties.

RCHECK checks the fit of a linear or generalized linear regression.

RGRAPH draws a graph to display the fit of a regression model.

RIDGE produces ridge regression and principal component regression analyses.

RJOINT does modified joint regression analysis for variety-by-environment data.

ROBSSPM forms robust estimates of sum-of-squares-and-products matrices.

RPAIR gives t-tests for all pairwise differences of means from a regression or GLM.

RPROPORTIONAL fits the proportional hazards model to survival data as a GLM.

RSURVIVAL models survival times of exponential, Weibull or extreme-value distributions.

RUGPLOT draws "rugplots" to display the distribution of one or more samples.

RUNTEST performs a test of randomness of a sequence of observations.

SAMPLE samples from a set of units, possibly stratified by factors.

SAVEDATA saves all the current data and information for use in a future run.

SIGNTEST performs a one or two sample sign test.

SKEWSYMM provides an analysis of skew-symmetry for an asymmetric matrix.

SMOOTHSPECTRUM forms smoothed spectrum estimates for univariate time series.

SPEARMAN calculates Spearman's Rank Correlation Coefficient.

SPLINE calculates a set of basis functions for M-, B- or I-splines.

STANDARDIZE standardizes columns of a data matrix to have mean zero and variance one.

STEM produces a simple stem-and-leaf chart.

SUBSET forms vectors containing subsets of the values in other vectors.

TTEST performs a one- or two-sample t-test.

VEQUATE equates across numerical structures.

VFUNCTION calculates functions of variance components from a REML analysis.

VHOMOGENEITY tests homogeneity of variances and variance-covariance matrices.

VINTERPOLATE performs linear & inverse linear interpolation between variates.

VORTHPOL calculates orthogonal polynomial time-contrasts for repeated measures.

VPLOT plots residuals from a REML analysis.

VREGRESS performs regression across variates.

VTABLE forms a variate and set of classifying factors from a table.

WADLEY fits models for Wadley's problem, allowing alternative links and errors.

WILCOXON performs a Wilcoxon Matched-Pairs (Signed-Rank) test.

XOCATEGORIES performs analyses of categorical data from crossover trials.

ABS(x) the absolute value of x: |x|.

ANGULAR(p) or ANG(p) the angular transformation: for a percentage p (0 <p < 100), forms x = (180/pi) ´  arcsin(sqrt(p/100)).

ARCCOS(x) inverse cosine of x, where -1 <= x <= 1.

ARCSIN(x) inverse sine of x, where -1 <= x <= 1.

AREA(y;x) numerically integrates the curve running through the points specified by variates y and x.

CED(p;s) the chi-square equivalent deviate for probability p (0 < p < 1) with s degrees of freedom (synonym of EDCHI).

CHARACTERS(g) returns a variate giving the length of each line of the text g.

CHISQ(x;s) the chi-square probability of t < x with s degrees of freedom (synonym of CLCHI).

CHOLESKI(x) the Choleski decomposition of a symmetric matrix x: such that x = LL' where L is square with upper off-diagonal elements zero.

CIRCULATE(x;s) shifts the values of x, treating x as a circular stack. If s is omitted, values are shifted one to the right, as for s=1.

CLBETA(x;a;b) cumulative lower probability for a beta distribution with parameters a and b.

CLBINOMIAL(j;n;p) probability of x or fewer successes out of n binomial trials with probability of success p.

CLBVARIATENORMAL(x;y;r) cumulative lower probability for a bivariate normal distribution with means 0, variances 1, and correlation r.

CLCHISQUARE(x;df) cumulative lower probability for a chi-square distribution with df degrees of freedom.

CLF(x;df1;df2) cumulative lower probability for an F distribution with df1 and df2 degrees of freedom.

CLGAMMA(x;a;b) cumulative lower probability for a gamma distribution with index parameter a and shape parameter b.

CLHYPERGEOMETRIC(j;l;m;n) probability of x or fewer positive samples out of a total sample of size m from a population of size n of which l are positive (hypergeometric distribution).

CLLOGNORMAL(x) cumulative lower probability for a lognormal distribution corresponding to a normal distribution with mean 0 and variance 1.

CLNORMAL(x) cumulative lower probability for a normal distribution with mean 0 and variance 1.

CLOGLOG(p) takes the complementary log-log transformation of the percentages p (0 < p < 100%).

CLPOISSON(j;m) probability of value of x or less for a poisson distribution with mean m.

CLT(x;df) cumulative lower probability for a t distribution with df degrees of freedom.

CONSTANTS(g) or C(g) provides the value of various constants, according to the contents of g: e (for a string of 'e' or 'E'), P ('pi' or 'PI'), or missing value ('*').

CORRELATION(x;y) or CORRMAT(x;y) if both x and y are specified, returns a scalar giving the correlation between the values of x and y; if y is omitted, forms a correlation matrix from a symmetric matrix x.

COS(x) cosine of x, for x in radians.

COVARIANCE(x;y) returns a scalar giving the covariance between the values of x and y.

CUBETA(x;a;b) cumulative upper probability for a beta distribution with parameters a and b.

CUBINOMIAL(j;n;p) probability of more than x successes out of n binomial trials with probability of success p.

CUBVARIATENORMAL(x;y;r) cumulative upper probability for a bivariate normal distribution with means 0, variances 1, and correlation r.

CUCHISQUARE(x;df) cumulative upper probability for a chi-square distribution with df degrees of freedom.

CUF(x;df1;df2) cumulative upper probability for an F distribution with df1 and df2 degrees of freedom.

CUGAMMA(x;a;b) cumulative upper probability for a gamma distribution with index parameter a and shape parameter b.

CUHYPERGEOMETRIC(j;l;m;n) probability of more than x positive samples out of a total sample of size m from a population of size n of which l are positive (hypergeometric distribution).

CULOGNORMAL(x) cumulative upper probability for a lognormal distribution corresponding to a normal distribution with mean 0 and variance 1.

CUMULATE(x) or CUM(x) forms the cumulative sum of the values of x; i.e. x₁, x₁+x₂, x₁+x₂+x₃, and so on.

CUNORMAL(x) cumulative upper probability for a normal distribution with mean 0 and variance 1.

CUPOISSON(j;m) probability of a value greater than x for a poisson distribution with mean m.

CUT(x;df) cumulative upper probability for a t distribution with df degrees of freedom.

DETERMINANT(x), DET(x) or D(x) the determinant of a square or symmetric matrix.

DIFFERENCE(x;s) forms the differences of x, i.e. x_i-x_i-s; if s is omitted, first differences are formed, as for s=1

EDBETA(p;a;b) equivalent deviate corresponding to cumulative lower probability p for a beta distribution with parameters a and b.

EDCHISQUARE(p;df) equivalent deviate corresponding to cumulative lower probability p for a chi-square distribution with df degrees of freedom.

EDF(p;df1;df2) equivalent deviate corresponding to cumulative lower probability p for an F distribution with df1 and df2 degrees of freedom.

EDGAMMA(p;a;b) equivalent deviate corresponding to cumulative lower probability p for a gamma distribution with index parameter a and shape parameter b.

EDLOGNORMAL(p) equivalent deviate corresponding to cumulative lower probability p for a lognormal distribution corresponding to a normal distribution with mean 0 and variance 1.

EDNORMAL(p) equivalent deviate corresponding to cumulative lower probability p for a normal distribution with mean 0 and variance 1.

EDT(p;df) equivalent deviate corresponding to cumulative lower probability p for a t distribution with df degrees of freedom.

ELEMENTS(x;e1;e2) forms a sub-structure of x. If x is a vector or a diagonal matrix, then only e1 should be specified; this then indicates the selected elements of x. If x is a rectangular matrix, then both e1 and e2 should be given, to specify respectively the selected rows and columns of x. For a symmetric matrix x, if the same rows and columns are to be selected (giving a symmetric matrix) then only e1 should be specified; otherwise both e1 and e2 should be given (and the result is a matrix).

EXP(x) exponential: e^x.

EXPAND(x;s) forms a variate of length s, containing zeroes and ones; if s is omitted and the length cannot be determined from the context, the length of the current units structure, if any, is taken. The values in x specify the numbers of the units that are to contain the value 1.

FED(p;s1;s2) the F-distribution equivalent deviate for probability p (0 < p < 1) and (s1,s2) degrees of freedom (synonym of EDF).

FPROBABILITY(x;s1;s2) or FRATIO(x;s1;s2) the F-ratio probability of t < x with (s1,s2) degrees of freedom (synonym of CLF).

GETFIRST(g) gives a variate containing the position of the first non-space character in each string of the text g.

GETLAST(g) gives a variate containing the position of the last non-space character in each string of the text g.

GETPOSITION(g1;g2;x) for each unit, if the string in the text g2 occurs as a substring of the string in the text g1, this returns the position at which the substring starts; otherwise it returns the value zero. The text g2 may contain a single string (to be checked against every string of g1). The structure x (scalar or variate) supplies a logical value to indicate whether to ignore the case of any letters; if x is omitted, thelogical is assumed to be false (case not ignored).

IANGULAR(x) gives the inverse of the angular transformation (result in percentages).

ICLOGLOG(x) gives the inverse of the complementary log-log transformation (result in percentages).

ILOGIT(x) gives the inverse of the logit transformation (result in percentages).

INTEGER(x) or INT(x) integer part of x: [x].

INVERSE(x) or INV(x) or I(x) the inverse of a non-singular square or symmetric matrix x.

LLBINOMIAL(x;n;p) or LLB(x;n;p) log-likelihood function for the Binomial distribution; n is the sample size and p the mean proportion (or the probability).

LLGAMMA(x;a;b) or LLG(x;a;b) log-likelihood function for the Gamma distribution with index parameter a and shape parameter b.

LLNORMAL(x;m;v) or LLN(x;m;v) log-likelihood function for the Normal distribution; m is the mean and v the variance.

LLPOISSON(x;m) or LLP(x;m) log-likelihood function for the Poisson distribution; m is the mean.

LOG(x) natural logarithm of x, for x > 0.

LOG10(x) logarithm to base 10 of x, for x > 0.

LOGIT(p) takes the logit transformation log(p/(100-p)) of the percentages p (0 < p < 100%).

LTPRODUCT(x;y) left transposed product of x and y: a more efficient way of calculating TRANSPOSE(x)*+y.

MAXIMUM(x) or MAX(x) finds the maximum of the values in x.

MEAN(x) forms the mean of the values of x.

MEDIAN(x) or MED(x) finds the median of the values in x.

MINIMUM(x) or MIN(x) finds the minimum of the values in x.

MODULO(x;y) Form modulus of x to base y.

MVINSERT(x;y) replaces values in x by missing value wherever the second identifier stores a non-zero value (logical .TRUE.).

MVREPLACE(x;y) replaces missing values in x with the values in the corresponding units of y.

NCOLUMNS(x) gives the number of columns of x.

NED(p) gives the Normal equivalent deviate: that is the value x that leaves a proportion p (0 < p < 1) to the left of it under the standard Normal curve (synonym of EDNORMAL).

NEWLEVELS(f;x) forms a variate from the factor f; the variate x defines a value for each level and should be the same length as the number of levels of the factor.

NLEVELS(f) gives the number of levels of factor f.

NMV(x) counts the number of missing values in x.

NOBSERVATIONS(x) counts the number of observations (that is non-missing values) in x.

NORMAL(x) the Normal probability integral: gives the probability that a random variable with a standard Normal N(0,1) distribution is less than x (synonym of CLNORMAL).

NROWS(x) gives the number of rows of x.

NVALUES(x) gives the number of values, including missing values, of x (that is the length of x).

POSITION(x;y) finds the position, within the vector y, of each value of x.

PRBETA(x;a;b) probability density function for a beta distribution with parameters a and b.

PRBINOMIAL(x;n;p) probability of x successes out of n binomial trials with probability of success p.

PRCHISQUARE(x;df) probability density function for a chi-square distribution with df degrees of freedom.

PRF(x;df1;df2) probability density function for an F distribution with df1 and df2 degrees of freedom.

PRGAMMA(x;a;b) probability density function for a gamma distribution with index parameter a and shape parameter b.

PRHYPERGEOMETRIC(j;l;m;n) probability of x successes out of a sample of m from a population of size n of which l are positive (hypergeometric distribution).

PRLOGNORMAL(x) probability density function for a lognormal distribution corresponding to a normal distribution with mean 0 and variance 1.

PRNORMAL(x) probability density function for a normal distribution with mean 0 and variance 1.

PRODUCT(x;y) forms the matrix product of x and y (that is x *+ y).

PRPOISSON(j;m) probability of the value x for a poisson distribution with mean m.

PRT(x;df) probability density function for a t distribution with df degrees of freedom.

QPRODUCT(x;y) forms the quadratic product of x and y (that is x *+ y *+ TRANSPOSE(x)), where x is a rectangular matrix or variate and y is a symmetric or diagonal matrix or a scalar.

RESTRICTION(x) forms a variate with the value 1 in the units to which x is currently restricted.

REVERSE(x) reverses the values of x.

ROUND(x) rounds the values of x to the nearest integer.

RTPRODUCT(x;y) forms the right transposed product of x and y (that is x *+ TRANSPOSE(y)).

SHIFT(x;s) shifts the values of x by s places (to the right or left according to the sign of s). This is not a circular shift, so some positions lose their values and are given missing values.

SIN(x) sine of x, for x in radians.

SOLUTION(x;y) finds the solution b of the set of simultaneous linear equations x *+ b = y.

SORT(x;y) sorts the elements of x into the order that would put the values of y into ascending order; if y is omitted, the values of x are sorted.

SQRT(x) gives the square root of x (x ³ 0).

SUBMAT(x) forms sub-triangles or sub-rectangles of a rectangular or symmetric matrix. The rows and columns to be included are determined by matching the pointers indexing the resultant matrix with the pointers indexing x. (SUBMAT does not allow for indexing by variates or texts.)

SUM(x) forms the sum of the values in x (synonym TOTAL).

TMAXIMA(t) forms margins of maxima for table t.

TMEANS(t) forms margins of means for table t.

TMEDIANS(t) forms margins of medians for table t.

TMINIMA(t) forms margins of minima for table t.

TNMV(t) forms margins counting the numbers of missing values in table t.

TNOBSERVATIONS(t) forms margins counting the numbers of observations (non-missing values) in table t.

TNVALUES(t) forms margins counting the numbers of values (missing or non-missing) in table t.

TOTAL(x) forms the total of the values in x (synonym SUM).

TRACE(x) calculates the trace of the square, diagonal, or symmetric matrix x (that is the sum of all its diagonal elements).

TRANSPOSE(x) or T(x) forms the transpose of a rectangular matrix x.

TTOTALS(t) or TSUMS(t) forms margins of totals for table t.

TVARIANCES(t) forms margins of between-cell variances for table t.

UNSET(d) returns a scalar logical value according to whether or not the dummy d is set.

URAND(seed;s) provides s uniform pseudo-random numbers in the range (0,1). If s is not supplied and URAND cannot determine the length of the result from the context of the expression, the length of the current units structure (if any) is taken. Scalar seed initializes the generator. If zero in the first use of URAND in a job, the system clock is used to provide a seed; subsequent calls may use zero to continue the sequence of random numbers.

VARIANCE(x) or VAR(x) gives the variance of the values in x.

VCORRELATION(p1;p2) gives the correlation, at every unit, between the values of the corresponding structures in the pointers p1 and p2.

VCOVARIANCE(p1;p2) gives the covariance, at every unit, between the values of the corresponding structures in the pointers p1 and p2.

VMAXIMA(p) finds the maximum of the values in each unit over the variates in pointer p.

VMEANS(p) gives the mean of the non-missing values in each unit over the variates in pointer p.

VMEDIANS(p) finds the median of the values in each unit over the variates in pointer p.

VMINIMA(p) finds the minimum of the values in each unit over the variates in pointer p.

VNMV(p) counts the number of missing values in each unit over the variates in pointer p.

VNOBSERVATIONS(p) counts the number of observations (non-missing values) in each unit over the variates in pointer p.

VNVALUES(p) gives the number of values in each unit over the variates in pointer p (that is the number of values of p).

VTOTALS(p) or VSUMS(p) gives the total of the non-missing values in each unit over the variates in pointer p.

VVARIANCES(p) gives the variance of the non-missing values in each unit over the variates in pointer p.

COMPARISON(f;s;m) calculates the comparisons amongst the levels of factor f specified by the first s rows of the matrix m (TREATMENT formulae only).

POL(f;s;v) indicates that the effects of factor f are to be partitioned into polynomial components (linear, quadratic etc) up to order s, where s is a scalar containing an integer between 1 and 4; variate v defines a numerical value for each level of the factor; if omitted, the factor levels themselves are used; in regression models POL(v;s) can be used to fit simple polynomials of a variate v up to order s.

POLND(f;s;v) has the same effect as POL, except that no Dev components are fitted for factor f in interactions (TREATMENT formulae only).

REG(f;s;m) indicates that the effects of factor f are to be partitioned into the regression contrasts specified by the first s rows of the matrix m. In TREATMENT formulae scalar s must lie between 1 and 7. In regression models REG(v;s;m) can be used to fit a set of associated variates stored in the rows of a matrix; if m is omitted orthogonal polynomial contrasts are constructed for either f or v (in regression models contrasts are otherwise not orthogonalised).

REGND(f;s;m) has the same effect as REG, except that no Dev components are fitted for factor f in interactions (TREATMENT formulae only).

SSPLINE(v;s;p) or S(v;s;p) indicates that the effect of a variate v is to be fitted by a smoothing spline with approximately s degrees of freedom or using "smoothing parameter" p (regression models only).