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# 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 forms a simple tally table of the distinct values in a vector Summarizes a variate, with classifying factors, into a data matrix of variates and factors performs a one- or two-sample t-test performs analysis of variance of a balanced or unbalanced design with up to two treatment factors provides further output following an analysis of variance by `A2WAY` copies information from an `A2WAY` analysis into Genstat data structures provides one-way analysis of variance produces Bland-Altman plots to assess the agreement between two variates calculates chi-square statistics for one- and two-way tables performs a random permutation test for a two-dimensional contingency table calculates one- or two-sample binomial tests calculates one- or two-sample Poisson tests forms the product moment correlation matrix for a list of variates, and tests whether the correlations are zero calculates probabilities for product moment correlations calculates summary statistics and tests of circular data calculates measures of association for circular data tests whether samples from circular distributions have a common mean direction or have identical distributions performs Friedman’s nonparametric analysis of variance calculates the gamma statistic of agreement for ordinal data calculates the Rand index, adjusted Rand index or Jaccard index to compare groupings defined by two factors calculates a kappa coefficient of agreement for nominally scaled data calculates Kendall’s Coefficient of Concordance (synonym `CONCORD`) performs a Kolmogorov-Smirnoff two-sample test carries out a Kruskal-Wallis one-way analysis of variance calculates Kendall’s rank correlation coefficient τ calculates Lin’s concordance correlation coefficient performs a Mann-Whitney U test performs McNemar’s test for the significance of changes performs pairwise multiple comparison tests within a table of means performs Cochran’s Q test for differences between related-samples calculates the Cochran-Armitage chi-square test for trend performs the Cochran-Mantel-Haenszel test performs a test of randomness of a sequence of observations performs a one or two sample sign test calculates Spearman’s rank correlation coefficient performs Steel’s many-one rank test performs equivalence, non-inferiority and non-superiority tests performs a Wilcoxon Matched-Pairs (Signed-Rank) test calculates the sample size for t-tests (including equivalence tests) calculates the sample size for binomial tests calculates the sample size to detect specified correlations calculates the sample size for Lin’s concordance coefficient calculates sample sizes for the Mann-Whitney test calculates sample sizes for McNemar’s test calculates the sample size to obtain a specified precision 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 estimates the parameters of the beta binomial distribution performs empirical-distribution-function goodness-of-fit tests calculates expected values of the lower parts of Poisson distributions calculates expected values of the upper parts of Poisson distributions estimates false discovery rates using mixture distributions uses kernel density estimation to estimate a sample density performs tests of univariate and/or multivariate Normality calculates probabilities for product moment correlations calculates the probability density for the double Poisson distribution calculates probabilities for the Mann-Whitney U statistic calculates probabilities for Spearman’s rank correlation statistic calculates probabilities for the Wilcoxon signed-rank statistic fits harmonic models to mean rainfall amounts for a Markov model fits harmonic models to rainfall probilities for a Markov model forms summaries for a Markov model from rainfall data calculates the Shapiro-Wilk test for Normality

Updated on February 7, 2023