Basic and nonparametric statistics

Many simple statistical operations, including calculation of summary statistics, t-tests, one- and two-way analysis of variance and non-parametric tests are provided by procedures in the Library:

`DESCRIBE`	calculates summary statistics for variates
`TALLY`	forms a simple tally table of the distinct values in a vector
`VSUMMARY`	Summarizes a variate, with classifying factors, into a data matrix of variates and factors
`TTEST`	performs a one- or two-sample t-test
`A2WAY`	performs analysis of variance of a balanced or unbalanced design with up to two treatment factors
`A2DISPLAY`	provides further output following an analysis of variance by `A2WAY`
`A2KEEP`	copies information from an `A2WAY` analysis into Genstat data structures
`AONEWAY`	provides one-way analysis of variance
`BLANDALTMAN`	produces Bland-Altman plots to assess the agreement between two variates
`CHISQUARE`	calculates chi-square statistics for one- and two-way tables
`CHIPERMTEST`	performs a random permutation test for a two-dimensional contingency table
`BNTEST`	calculates one- or two-sample binomial tests
`PNTEST`	calculates one- or two-sample Poisson tests
`FCORRELATION`	forms the product moment correlation matrix for a list of variates, and tests whether the correlations are zero
`PRCORRELATION`	calculates probabilities for product moment correlations
`CDESCRIBE`	calculates summary statistics and tests of circular data
`CASSOCIATION`	calculates measures of association for circular data
`CCOMPARE`	tests whether samples from circular distributions have a common mean direction or have identical distributions
`FRIEDMAN`	performs Friedman’s nonparametric analysis of variance
`GSTATISTIC`	calculates the gamma statistic of agreement for ordinal data
`HCOMPAREGROUPINGS`	calculates the Rand index, adjusted Rand index or Jaccard index to compare groupings defined by two factors
`KAPPA`	calculates a kappa coefficient of agreement for nominally scaled data
`KCONCORDANCE`	calculates Kendall’s Coefficient of Concordance (synonym `CONCORD`)
`KOLMOG2`	performs a Kolmogorov-Smirnoff two-sample test
`KRUSKAL`	carries out a Kruskal-Wallis one-way analysis of variance
`KTAU`	calculates Kendall’s rank correlation coefficient τ
`LCONCORDANCE`	calculates Lin’s concordance correlation coefficient
`MANNWHITNEY`	performs a Mann-Whitney U test
`MCNEMAR`	performs McNemar’s test for the significance of changes
`MCOMPARISON`	performs pairwise multiple comparison tests within a table of means
`QCOCHRAN`	performs Cochran’s Q test for differences between related-samples
`CATRENDTEST`	calculates the Cochran-Armitage chi-square test for trend
`CMHTEST`	performs the Cochran-Mantel-Haenszel test
`RUNTEST`	performs a test of randomness of a sequence of observations
`SIGNTEST`	performs a one or two sample sign test
`SPEARMAN`	calculates Spearman’s rank correlation coefficient
`STEEL`	performs Steel’s many-one rank test
`TEQUIVALENCE`	performs equivalence, non-inferiority and non-superiority tests
`WILCOXON`	performs a Wilcoxon Matched-Pairs (Signed-Rank) test
`STTEST`	calculates the sample size for t-tests (including equivalence tests)
`SBNTEST`	calculates the sample size for binomial tests
`SCORRELATION`	calculates the sample size to detect specified correlations
`SLCONCORDANCE`	calculates the sample size for Lin’s concordance coefficient
`SMANNWHITNEY`	calculates sample sizes for the Mann-Whitney test
`SMCNEMAR`	calculates sample sizes for McNemar’s test
`SPRECISION`	calculates the sample size to obtain a specified precision
`SSIGNTEST`	calculates the sample size for a sign test

There are also facilities for fitting or assessing statistical distributions:

`DISTRIBUTION`	estimates the parameters of continuous and discrete distributions
`BBINOMIAL`	estimates the parameters of the beta binomial distribution
`EDFTEST`	performs empirical-distribution-function goodness-of-fit tests
`ELPOISSON`	calculates expected values of the lower parts of Poisson distributions
`EUPOISSON`	calculates expected values of the upper parts of Poisson distributions
`FDRMIXTURE`	estimates false discovery rates using mixture distributions
`KERNELDENSITY`	uses kernel density estimation to estimate a sample density
`NORMTEST`	performs tests of univariate and/or multivariate Normality
`PRCORRELATION`	calculates probabilities for product moment correlations
`PRDOUBLEPOISSON`	calculates the probability density for the double Poisson distribution
`PRMANNWHITNEYU`	calculates probabilities for the Mann-Whitney U statistic
`PRSPEARMAN`	calculates probabilities for Spearman’s rank correlation statistic
`PRWILCOXON`	calculates probabilities for the Wilcoxon signed-rank statistic
`RFFAMOUNT`	fits harmonic models to mean rainfall amounts for a Markov model
`RFFPROBABILITY`	fits harmonic models to rainfall probilities for a Markov model
`RFSUMMARY`	forms summaries for a Markov model from rainfall data
`WSTATISTIC`	calculates the Shapiro-Wilk test for Normality

Updated on February 7, 2023

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