Create a PERMANOVA design for an unlimited number of factors. Factors can be fixed, random, finite or correspond to a repeatedly measured subject or whole-plot from a split-plot design. Each factor can be specified as being nested within one or more other factors, or is treated as crossed. Build a priori contrasts among individual levels or groups of levels of any factor. Specify, remove, pool or change the order of fit for any/all individual terms from a list of all terms that are available (implied by your design), including all potential interactions among factors. Include one or more quantitative covariables in the model (via separate worksheet with matching sample labels). Treat sets of covariates in groups (specified by an indicator) to enable cyclical/seasonal (sin/cos) or other spatio-temporal (lat/long) models. Allow for heterogeneity of within-group dispersions, specifying the factor (or combination of factors) across which heterogeneity lies. Choose a partitioning based on Type I, Type II or Type III SS for unbalanced designs.

Analyse multivariate data in response to complex multi-factor experimental/sampling designs on the basis of a chosen resemblance matrix using permutational multivariate (or univariate) analysis of variance (PERMANOVA). Correct F-tests are constructed carefully by reference to expectations of mean squares (EMS) for the specified design. P-values are obtained using permutation algorithms for each term in the model using the correct permutable units and construction of appropriate residuals to account for other factors/terms in the model. Choose to do one of the following: the main (overall) tests (output in a PERMANOVA table) for all terms in the model; pair-wise tests to compare groups for specific factors, either a main effect or tests within levels of other factors to follow up significant interactions; or output a residual distance matrix after fitting the full model specified in the design file. Choose the number of permutations and to permute raw data, reduced-model residuals or full-model residuals. Optionally output Monte Carlo tests (useful for cases with few possible permutations) and/or histograms of values of the F statistic under permutation. PERMANOVA done on the basis of a Euclidean distance matrix calculated from one variable yields a permutational univariate ANOVA.

Generate a residual dissimilarity matrix after fitting a model using either PERMANOVA or DISTLM. Remove the effects of unwanted, nuisance or known-to-be-important factors or predictor variables. Visualise potential pattern/relationships with other/minor/remaining factors or covariables by doing ordination(s)of residual dissimilarities.

Principal Coordinate Analysis (PCO), an eigenvalue/eigenvector decomposition of the Gower-transformed dissimilarity matrix, showing % variation explained, with options to output: an ordination plot, PCO scores to a worksheet, scree plot, and further diagnostics such as Shepard diagrams and stress claculations for the 2D or 3D PCO ordination (for comparison with MDS outputs).

Fit a distance/dissimilarity-based linear model on the basis of a resemblance measure of choice (DISTLM), a form of multivariate multiple regression. Predictor variables can be quantitative, ordinal or binary but must be numeric and are provided in a separate worksheet (with matching sample names). Specify the variables to be included in the model and the ordering of the fit, or perform model selection by choosing a selection procedure (forward, backward, step-wise, or ‘best’) and a selection criterion (R^2, Adjusted R^2, AIC, AICc, or BIC). Do marginal tests (each variable alone) or sequential conditional tests, with p-values obtained using permutation of residuals under a reduced model and choose the number of permutations. Optionally group sets of predictor variables together using an indicator (e.g., to handle factors as binary codes or to fit 2D+ spatial or cyclical models). Optionally output a dbRDA plot associated with the final model fit, predictor variable correlations and/or a residual distance/dissimilarity matrix.

Canonical analysis of principal coordinates (CAP). Find linear combinations of unit-scaled PCO axes from a resemblance matrix that: (i) best discriminate groups (provided as a factor), (ii) best discriminate positions along a single gradient, or (iii) correlate best with linear combinations of some other set of variables (X). Do diagnostics to assess the appropriate number of PCO axes to include in the model (m) , with the option to output diagnostic plots. Specify m explicitly, or choose m to maximise leave-one-out % allocation success to groups (cross-validation) or to minimise the leave-one-out residual sum-of-squares for the CAP model. Optionally add new samples and predict their positions on CAP axes / group membership / gradient position. Optionally do a permutation test and/or output CAP scores to a worksheet, including predicted values/classifications for new samples. When based on a Euclidean distance measure, the CAP method corresponds to classical discriminant analysis (for groups) or canonical correlation analysis (for gradients), but with all tests by robust permutation.

From a resemblance matrix, create an ordination showing the centroids for main effects (i.e., the centroids for each level of every factor) in the space of the chosen resemblance measure. Can be done for a single factor or for all factors specified in a PERMANOVA Design worksheet. Specify the ordination method (mMDS, tmMDS or nMDS). Optionally include the overall centroid and/or replicates in the plot as well. Distances among all points in the plot are also output as a new resemblance matrix.

From a resemblance matrix, create an ordination of centroids corresponding to all combinations of factor levels (cells) in a two-way or three-way design, given a PERMANOVA design worksheet, in the space of a chosen resemblance measure. Specify the ordination method (mMDS, tmMDS or nMDS). For a three-way design, the colours of symbols identify the levels of the first factor; the shapes of symbols identify the levels of the second factor, and the labels identify the levels of the third factor. For a two-way design, combined colours+symbols identify the levels of the first factor, and labels identify the levels of the second factor. Distances among all centroids in the plot are also output as a new resemblance matrix.

Classical multivariate control chart, using Hotelling’s T^2 criterion. From a data sheet, discern if a new sample point (e.g., in a monitoring context) is ‘in-control’ or ‘out-of-control’, by comparison with a reference set of previous (‘in-control’) observations. Choose the number of initial control-chart samples and the type of chart (progressive, fixed baseline or moving window). Specify the alpha-level and type of upper control-chart limit (non-parametric or parametric). Robust non-parametric limits are obtained from quantiles of a permutation distribution. Choose to apply shrinkage for high-dimensional systems. Produce a control-chart plot and a factor that identifies in-control/out-of-control samples.

From a resemblance matrix, implement a dissimilarity-based multivariate control chart. This utilises Hotelling’s T^2 criterion, but on a set of ordination axes that represent the information in the dissimilarity matrix. In addition to all of the options and features of the classical multivariate control chart, choose the ordination method and number of axes that shall be used to represent the resemblance marix for analysis (PCO, mMDS, or nMDS) and limit the ordination to a dimensionality that is fixed by the user, chosen to capture a certain percentage of the variation (PCO), or to achieve a certain matrix correlation with the original resemblance matrix (e.g., rho > 0.99).

Test the null hypothesis of no differences in multivariate dispersion (beta diversity) among groups based on a chosen resemblance matrix. Provide a factor identifying the groups to be compared, choose to obtain p-values from tables or using permutation of residuals and specify the number of permutations. Optionally output pair-wise tests as well, or individual deviation values of sample units to their own group centroid (and/or their means) to a worksheet.

Dissimilarity-based redundancy analysis (dbRDA) produces ordination axes to show the fitted variation from a DISTLM. This can be implemented as an option from the DISTLM routine for a given model specified there, or can be achieved directly from a specified predictor variable worksheet (with matching sample names). Options include provision of dbRDA scores to a worksheet or output of a residual distance matrix. The default plot shows the predictor variables as vectors on the dbRDA ordination. dbRDA on the basis of a Euclidean distance matrix produces an RDA.

Calculate distances among centroids corresponding to levels of a user-supplied factor. The factor can optionally be constructed as combinations of factors for multi-way designs (using Edit > Combine). The result is a resemblance matrix among centroids that is ready for ordination/plotting.

Open, Close, Save, Rename, Delete, Print, Exit any file within a PRIMER workspace, or the entire workspace file itself (*.pwk), with all of its component elements: data sheets, resemblance matrices, results files, graphics, and/or notes.

Toggle on or off from View: the Explorer tree, the Tool bar, the Status bar, or (for the Python add-on) the script Console window.

Keep track of all analyses and workflows in a single workspace. Use the Explorer tree to navigate files, analyses, graphics and results.

Add a Note anywhere in the Explorer tree. Keep track of ideas, trials, insights and lines of thought right inside the PRIMER workspace itself. Notes can contain text or graphics – anything you can copy and paste. Perfect for sharing analyses with mentors/students/collaborators.

Arrange the Windows in the PRIMER workspace: Cascade, Tile Horizontally, Tile Vertically, Arrange Icons, or Close All Windows.

Arrange multiple plots within a single Graphic. Specify the graphics to include and arrange them horizontally or vertically, specifying the number of columns or rows. Optionally suppress showing individual titles, sub-titles and/or keys. Customise the font scale and/or the symbol sizes.

Reverse deletions, name changes, etc. on the Explorer tree.

Rename the Levels of Factors/Indicators

Create a new: Workspace, Sample data sheet, Variable information file, Note, or Multi plot.

Open/Import 3-column or rectangular Data matrices, triangular Resemblance matrices or Image files. Can read in: any PRIMER file format (version 4, 5, 6, 7 or 8); Text files (*.txt, *.csv), Excel files (*.xls, *.xlsx, *.xlsb, *.xlsm); Rich text files (*.rtf); or Image files (*.jpg, *.jpeg, *.png, *.bmp, *.tif, *.gif, *.emf).

Highlight, Cut, Copy, Paste or Delete individual values; Highlight, Add, Insert, Delete, Move or Sort rows or columns; Edit Labels on rows or columns (Variable/Sample names).

Changes to data entries can be (multiply) reversed.

Edit Data Properties, including Data type (abundance, biomass, environmental or unknown/other), specify Samples as either Columns or Rows, and add/remove a Description (meta-data).

Edit Resemblance matrix Properties, including Resemblance type (similarity, dissimilarity, distance, distance^2, correlation, ANOSIM R-statistic, or rank), and add/remove a Description (meta-data).

Edit Variable Information sheet Properties, including Data type (taxa, traits, scores, or unknown/other), and add/remove a Description (meta-data).

Add, Duplicate, Combine, Rename Delete or Import Factors/Indicators associated with Data or Resemblance matrices. Optionally choose to Fill Values or Patterns to auto-complete manual entry of new Factor/Indicator levels. Edit the Levels of Factors/Indicators.

Create ordered groups from a continuous variable. These can be: (i) a given number of groups with equal sample sizes or at equally-space intervals; (ii) a given number of groups obtained by minimising the within-group sum-of-squares (SS) or mean-absolute-deviation (MAD), or the sum of average rank distances within groups; (iii) specified by user-entered breaks or quantiles; (iv) specified by a choosing a common within-group sample size.

Split a Data sheet into multiple sheets according to group identified by either a Factor or a Variable.

Summarise Variables or Samples (either overall or separately within groups specified by a Factor or Indicator) with any combination of the following statistics: average, median, sum, minimum, maximum, quantiles (uer-specified), range, inter-quartile range (IQR), standard deviation, variance, sample size, standard error, symmetry, skewness, kurtosis, number of zeros, number of singletons, number of doubletons, number of non-zeros (frequency), smallest number above a user-specified threshold value, largest number below a user-specified threshold.

Aggregate data according to a taxonomic or other hierarchy (e.g., to analyse at the genus, family, or other level of your choice), via an Aggregation file (Variable Information sheet).

Average data across Samples according to the levels of a Factor, or across Variables according to the levels of an Indicator

Check Data matrices for: missing values, duplicate samples, all-zero samples, estimated values, negative values, duplicate variables, and/or all-zero variables.

Duplicate an item (data sheet, resemblance matrix, graphic, etc.) in the PRIMER workspace

Expand a Data sheet so it can be matched with one that is sampled more finely.

Merge two data sheets together, with separate join and merge options for Samples and Variables.

Replace missing values with zeros or with an estimated value, using an expectation-maximisation (EM) algorithm, which assumes a multivariate normal distribution model for the data.

Rank each variable individually (largest numerical value has rank = 1).

Sum data across Samples according to the levels of a Factor, or across Variables according to the levels of an Indicator

Transpose (swaps columns and rows) of a data sheet to a create a new one. The properties of thematrix do not change (i.e, sample/variable orientation is also switched to correspond to the new orientation of the matrix).

Create a Resemblance matrix (e.g., as a preamble to a RELATE test) corresponding to a model of: Seriation (with a numeric Factor specifying distances), Cyclicity (with a numeric Factor specifying fractional positions along a circle), Euclidean 2D spatial distances (two Factors are used to specify the position of the sample in a 2D plane), or Unordered groups (with a Factor specifying the groups).

Average Resemblance values across all samples within groups identified by a Factor.

Check Resemblance matrices for: undefined values, out of bounds values, or duplicate labels.

Convert Similarities to Dissimilarities (and vice versa)

Duplicate a Resemblance matrix in the PRIMER workspace

Expand a Resemblance matrix so it can be matched with one that is sampled more finely.

Rank the values in a resemblance matrix (highest similarity / smallest dissimilarity has rank = 1).

Transform highlighted values according to a user-specified mathematical expression (using a format that is the same as the BASIC computer language).

Sequentially ‘unwind’ a resemblance matrix into a single column of values.

Display hierarchical (e.g., taxonomic) data as a cascading tree of entries.

Check Variable Information sheet for: missing values, duplicate species, or inconsistent taxa (incorrect nesting in the hierarchy)

Duplicate a Variable Information sheet in the PRIMER workspace

Standardise Samples (or Variables) by dividing each value in a given Sample (or Variable) by the total sum or the maximum value of that Sample (or Variable). Further options include: standardising separately wtihin levels of an Indicator/Factor; expressing the results as either direct or cumulative percentages or proportions.

Transform all of the Variables in a Data sheet to one of: none, square root, fourth root, log(x+1) or presence/absence.

Transform highlighted variables in a Data sheet according to a user-specified mathematical expression (using a format that is the same as the BASIC computer language)

Cumulatively sum the values of each sample. The order of cumulation is either the same as the variable order in the Data sheet or is specified by a numeric Indicator.

Each of the Variables in a Data sheet is weighted by values given by a numeric indicator.

Down-weight species (or taxa), based on their degree of clustering (estimated variance/mean ratio) as per a Generalised Poisson model of over-dispersed counts.

Variables are individually down-weighted depending on their variability according to: pooled standard deviation, averaged standard deviation, averaged range or averaged inter-quartile range.

Values for each Variable have their mean subtracted and are divided by their standard deviation.

Principal Component Analysis (PCA), an eigenvalue/eigenvector decomposition of the covariance matrix (so normalised data should be input), showing % variation explained, with options to output: an ordination plot, PCA scores to a worksheet, scree plot, and further diagnostics such as Shepard diagrams and stress claculations for the 2D or 3D PCA ordination (for comparison with MDS outputs). The PCA ordination plot, by default, also shows base variables as labeled vectors (eigenvectors within a unit circle).

Univariate non-parametric Wilcoxon signed rank test to compare two levels of a (first) factor in a paired design, based on the ranks of paired differences. A (second) factor identifying pairs must also be provided and the alternative hypothesis (two-tailed or one-tailed) must be specified. A p-value is achieved using permutations of values across the two levels of the first factor, separately within each pair. Options include: to perform the test separately within levels of another (third) factor; to output values of the test-statistic under permutation to a worksheet and/or histogram; and to output box plot(s) of paired differences.

Univariate non-parametric Mann-Whitney U test to compare two levels of a factor, based on the ranks of the combined set of sample values (both groups). The alternative hypothesis (two-tailed or one-tailed) must be specified. A p-value is achieved using permutations of values across the two levels. Options include: to perform the test separately within levels of another (second) factor; to output values of the test-statistic under permutation to a worksheet and/or histogram; and/or to output box plot(s) to visually compare the two groups.

Univariate non-parametric Kruskal-Wallis test to compare two or more levels (groups) of a factor, based on the ranks of the combined set of sample values (all groups). A p-value is achieved using permutations of values across the groups. Options include: to perform pairwise comparisons of groups and (optionally) output results to a worksheet; to perform the test separately within levels of another (second) factor; to output values of the test-statistic under permutation to a worksheet and/or histogram; and/or to output box plot(s) to visually compare the groups.

Non-paramertric Kolmogorov-Smirnov test to compare two distributions of a continuous variable (two-sample test). Rejection of the null hypothesis indicates that the shape/position of the two distributions differ from one another in some way (location, dispersion, skewness, etc.). A p-value is achieved using permutations of values across the groups. Options include: to perform the test separately within levels of another (second) factor; to output values of the test-statistic under permutation to a worksheet and/or histogram; and/or to output cumulative empirical distribution plot(s) to visually compare the groups.

Non-parametric bivariate test of association between two variables obtained from the same set of sampling units. The alternative hypothesis must be specified: (two-tailed or one-tailed with expectation of either a positive or a negative association). A permutation test (randomizing the ordering of the samples for one variable while the ordering for the other variable stays constant), is used to calculate a p-value. The test can be based on one of the following measures: Pearson correlation, Spearman rank correlation, Weighted Spearman rank correlation, Kendall’s tau, or the Index of Association. Options include: to perform the test separately within levels of a specified factor; to output values of the test-statistic under permutation to a worksheet and/or histogram; and/or to output scatter plot(s) to visually examine patterns.

Obtain a Resemblance matrix by calculating measures of association (similarity, correlation, dissimilarity or distance) between all pairs of Samples or Variables in a Data sheet on the basis of 49+ resemblance measures: Bray-Curtis, Euclidean, Index of Association, Jaccard, Sørensen, Hellinger, Mod. Gower, Canberra, Minkowski, Binomial deviance, Chi-squared, Czekanowksi, Manhattan, Pearson, Spearman, Kendall, and more. Provide a taxonomic hierarchy or dissimilariy matrix among variables to calculate Taxonomic (Gamma+), Functional or Phylogenetic (Theta+) resemblances. Option to add a dummy variable (present in all samples) to calculate the adjusted Bray-Curtis (or other) measure. Resemblance calculations will all now operate in the presence of missing data entries.

Calculate Caswell’s V statistic under ‘neutral model’ assumptions.

Calculate a suite of diversity indices for species-by-sample data. Options include: total species (S), total individuals (N), Margalef’s species richness, Pielou’s evenness (J’), Brillouin (H), Fisher’s alpha, Shannon (H’), Simpson’s evenness/dominance, Hill’s diversity numbers, rarefaction (estimated number of species in samples of user-specified sizes), taxonomic diversity (delta), taxonomic distinctness (delta*), average taxonomic distinctness (AvTD, Delta+), total taxonomic distinctness (TTD), variation in taxonomic distinctness (VarTD, Lambda+), average phylogenetic diversity (Phi+), Total phylogenetic diversity (PD).

Calculate differences between k-dominance plot curves for all pairs of samples, with an option to log-transform the species rank axis.

Similarity Percentages (SIMPER) to assess the contributions of individual species (or taxa) to Bray-Curtis similarity, or variable contributions to Euclidean distance. Can be done for one-way or two-way crossed designs. Calculates the average contribution of a species to all pair-wise similarities within a group and (optionally) average contributions of a species to all pair-wise dissimilarities between samples occuring in different groups (separately for each pair of groups).

Similarity Profile (SIMPROF) tests for cluster-type structures in samples or correlation/association-type structures in variables for a set of data. Sample (or Variable) similarities are ordered and plotted against their ranks to produce a profile. This profile for the data set is compared with the mean profile calculated from a distribution of profiles obtained under permutation, using the sum of absolute differences (the ‘pi’ statistic) to create a test of the null hypothesis of ‘No structure’.

Hierarchical agglomerative cluster analysis with a choice of cluster mode (single linkage, complete linkage, group average or flexible beta linkage). Options include the ability to: identify clusters with ‘significant structure’ remaining within them via SIMPROF tests performed at every node; create a factor based on the SIMPROF results; and/or to create a cophenetic distance matrix. Dendrogram plots in the output can be further customised. Specify factors or indicators for labels and/or symbols. Change the orientation of the plot (up, right, down or left). Rotate the leaves of the dendrogram (click horizontal lines). Simplify by collapsing leaves within any branch (click vertical lines). Use Zoom-in/Zoom-out tools to focus on particular parts of a dendrogram. Show a ‘slice’ through the dendrogram at a particular similarity/dissimilarity value and create a factor from this.

Divide a set of multivariate observations (species or samples) into groups so as to maximise the ANOSIM R-statistic using binary top-down splits to yield a divisive hierarchical tree. Nominate the minimum group size and/or split size. Optionally identify clusters with ‘significant structure’ remaining within them via SIMPROF tests performed at every node; create a factor based on the SIMPROF results; and display vertical positions of nodes using either equally spaced (A%) or split quality (B%) criteria.

Non-parametric classification based on divisive top-down binary splits chosen to maximise the ANOSIM R statistic (like UNCTREE) while also being constrained by one or more other variables in a secondary set of data (e.g., spatial/environmental). More specifically, the constraints require that a split can only be made that simultaneously corresponds to a split in the rank-ordered values of one more more variables in the other (secondary) data set. Optionally identify clusters with ‘significant structure’ remaining within them via SIMPROF tests performed at every node; create a factor based on the SIMPROF results; display vertical positions of nodes using either equally spaced (A%) or split quality (B%) criteria; and replace variable names in the information pane of the plot with the levels of an indicator or factor.

Divide a set of multivariate observations (species or samples) into a given number (k) of clusters/groups to maximise a given criterion – either the ANOSIM R statistic or the average rank within groups – using an iterative technique. Chose a single value for k, or perform the analysis for a range of k values. For the latter the lowest k is chosen so that a SIMPROF test shows no significant structure remains within the clusters. Output is a factor identifying the k groups.

Non-metric multi-dimensional scaling (create a configuration of inter-point distances to match rank-order dissimilarities) using an iterative algorithm from multiple initial random configurations to identify a global lowest-stress solution. Choose: the number of dimensions for the configuration(s) (2 to 3, or user-specified range of dimensions) and the number of restarts (random initial random configurations). There are options to choose the Kruskal fit scheme (1 or 2), animate the configuration plot, output Shepard diagrams and/or scree plots, send configuration coordinates to a worksheet, or ‘fix’ a potential ‘collapsed’ configuration by ‘mixing’ in a specified proportion of a metric MDS solution in the stress equation.

Metric multi-dimensional scaling (create a configuration of inter-point distances to match dissimilarities linearly) using an iterative algorithm from multiple initial random configurations to identify a global lowest-stress solution. Choose: the number of dimensions for the configuration(s) (2 to 3, or user-specified range of dimensions), and the number of restarts (random initial random configurations). There are options to animate the configuration plot, output Shepard diagrams and/or scree plots, or send configuration coordinates to a worksheet.

Threshold metric multi-dimensional scaling (create a configuration of inter-point distances to match dissimilarities linearly, but relax the intercept to a non-zero value) using an iterative algorithm from multiple initial random configurations to identify a global lowest-stress solution. Choose: the number of dimensions for the configuration(s) (2 to 3, or user-specified range of dimensions), and the number of restarts (random initial random configurations). There are options to animate the configuration plot, output Shepard diagrams and/or scree plots, or send configuration coordinates to a worksheet.

Minimises an equal mixture of stress functions from two nMDS ordinations, which has potential application to produce a consensus view of among-sample relationships for two sets of variables which cannot be merged into a single matrix – perhaps needing different resemblance measures (e.g. biotic and abiotic; motile organism counts and colonial species areas, etc.).

Analysis of similarities (ANOSIM), a non-parametric test using the R statistic to rigorously test the null hypothesis of no differences among groups of multivariate samples (levels of a factor) in any specified design up to three factors having crossed and/or nested relationships among them. P-values are all achieved using rigorous permutation methods, including appropriate constraints or choice of permutable units for any given factor within the context of the full design. Choose a maximum number of permutations. For multiway tests with no replciation, choose the correlation method (Spearman, Weighted Spearman or Kendall). Optionally output pairwise tests values of R and/or their associated significance levels to worksheet(s), histogram plots or worksheets showing the distribution of test-statistic values under permutation.

Select a set of variables (from a ‘Fitted data’ worksheet) that will generate a distance (or dissimilarity) matrix (based on a chosen resemblance measure) that ‘best matches’ the patterns of relationships among samples in a given (target) resemblance matrix. This is an exhaustive search. Often used to find (say) environmental (or other) variables that, taken together, match patterns in biotic (species) dissimilarities. Choose the matrix correlation method (Spearman, weighted Spearman, Pearson, or Kendall). Optionally, keep fitted data variables together in groups specified by an indicator, do the analysis within levels of a factor, or do a permutation test for a significant ‘match’ that also carefully accommodates the ‘search’ beaing done through the fitted variables (computer intensive). Examine a chosen number of best overall results as well as the best results for a given number of fitted variables.

Select a set of variables (from a ‘Fitted data’ worksheet) that will generate a distance (or dissimilarity) matrix (based on a chosen resemblance measure) that ‘best matches’ the patterns of relationships among samples in a given (target) resemblance matrix. This is not an exhaustive search, but rather begins with either a fixed set of variables or a specified number of random trial variables, followed by a stepwise (forward/backward) selection method to improve the fit. Useful for identifying indicator and/or redundant species sets. Choose a stopping criterion (e.g., rho > 0.95) and tolerance (e.g., delta rho < 0.001) for the fit; all other options are similar to BIOENV.

Calculate an index of multivariate dispersion, based on the rank dissimilarities among replicates within groups.

Calculate a matrix correlation (using Spearman’s rho, weighted Spearman’s rho, Pearson’s correlation or Kendall’s tau) and test the null hypothesis of no significant association (no relationship in multivariate patterns) between two resemblance matrices. The second resemblance matrix can be a user-generated resemblance matrix or a model matrix (e.g., for trend or cyclicity). P-values are obtained via permutation of sampling units. Equivalent to a Mantel test when Pearson’s measure of matrix correlation is used. Choose the maximum number of permutations. Optionally perform the test within levels of a factor. Optionally output a histogram or a worksheet showing the distribution of values of the test-statistic under permutation.

Calculate the matrix correlation (using Spearman’s rho, weighted Spearman’s rho, Pearson’s correlation or Kendall’s tau) between all pairs of two or more resemblance matrices. The resulting matrix correlations are output into a new resemblance matrix, whose sample names correpond to the original resemblance matrices’ names. An MDS of the resulting matrix is a ‘second-stage’ MDS. Another option is to calculate resemblances between subsets of a chosen resemblance matrix, by nominating an ‘Outer’ and an ‘Inner’ factor. The levels of the ‘Outer’ factor split the whole resemblance matrix into the smaller ones which are to be compared. Its levels will be used to label the entries in the output resemblance matrix. The levels of the ‘Inner’ factor identifies corresponding samples in the sub-matrices.

Test the null hypothesis that a species list from one locality (or time) has the same taxonomic distinctness (AvTD, delta+) and/or variation in taxonomic distinctness (VarTD, lambda+) structure as a ‘master’ list (e.g., of all species in that biogeographic region) from which it is drawn. Achieved by random draws of species from the master list for a given number of species (S). Choose to plot a histogram (one value of S), funnel (one or more samples and a user-specified range of S values, but for just AvTD or VarTD only) or ellipse plot (AvTD and VarTD plotted together bivariately for a user-specified range of S values) to show the distribution of values obtained under random draws, and showing sample values within this context. Choose to weight the random selection of species by their abundances (frequencies) in a master frequency worksheet. Choose the significance level for contours in funnels and ellipses.

Ordination of bootstrap averages and confidence regions for groups of samples from a resemblance matrix. First, a metric MDS of sufficient dimension (m) to represent the resemblance matrix is produced first. Second, a set of n_boot random bootstrap re-samples within each of several (g) groups (specified by a factor) are calculated in that metric MDS space. Third, averages are calculated from the bootstrap samples in each group, yielding g x n_boot bootstrap averages. Ordination of all g x n_boot bootstrap averages can be done using metric, threshold-metric or non-metric MDS. Options include: choice to specify m directly or automate the choice using matrix correlation (i.e., choose m yielding rho greater than a user-specified value); output m-dimensional data to a worksheet (replicates, bootstrap averages and/or group averages); display bootstrap averages, group averages and/or bootstrap confidence regions at 50%, 80% or 95% significance levels.

Create a Box-and-whisker plot of a univariate variable to compare the distirbutions of observations across different groups (identified by a Factor). Optionally change the opacity, colours, and degree of saturation of the colours.

Visualise the empirical distribution of a univariate set of data. Choose a factor to compare distributions of samples for different groups. Plot a dot for every data point at its appropriate location on the number line (y axis). Observations that have the same value are ‘stacked’ alongside one another at that same position and a horizontal line for the median is also shown. Optionally change the opacity of the dot symbol, the colour, and/or the saturation of the colour.

Plot the cumulative empirical distribution (expressed as percentages or proportions) as a line for either Variables or Samples, with the option to split these into multiple distributions (lines on the plot) by specifying a Factor or Indicator, respecitvely.

Plot the values of variables as lines (across all samples), or values for samples as lines (across all variables). Optionally draw separate plots for groups specified by an Indicator (for variable lines) or a Factor (for sample lines).

Create a Violin plot to show an empirical probability density function of a univariate variable for each of several groups (identified by a Factor), obtained by a non-parametric kernel density estimate (kde), which is mirrored horizontally. Also shows the median and inter-quartile range. Optionally change the bandwidth (Silverman’s rule of thumb or customised values, separately for each group), change the method of rescaling (none, area, width or count), set upper/lower cut-off bounds for truncated variables types (e.g. a lower cut-off of zero for biomass data), or customise the opacity, colour and/or saturation of the colours used in the plot.

Individual or stacked bar plots showing the values of variables across samples in 2D or 3D.

Ranked Species abundance (or biomass) plot. For each sample, species are ranked in decreasing order of abundance. Their relative abundance (i.e. percentage of the total abundance in the sample) is plotted against the increasing rank (x axis), the latter on a log scale. Choose to plot relative abundance, cumulative relative abundance (a k-dominance plot) or partial dominance.

Put dominance curves for abundance and biomass, separately calculated, onto the same plot. Calculate the W statistic (difference in the two curves) as a measure of perturbation.

Plot bivariate scatter plots for p variables in a p x (p-1)/2 array. Examine distributional patterns and patterns of correlation structure across the variables and calculate correlations for every pair of variables.

Plot the number of species (y axis) that fall into a set of geometric (x 2) abundance classes (x axis). Each line on the plot gives the number (or %) of species represented in the sample by a single individual (class 1), 2-3 individuals (class 2), 4-7 individuals (class 3), 8-15 individuals etc. Also called Species Abundance Distribution (SAD) curves.

Plot Histograms for each variable in a Data sheet. Optionally change the colours of the bins or boundaries, or change the bin size.

Plot means and 95% confidence intervals of a univariate variable for different levels of a Factor (groups). Optionally join those means with a line and/or use a common variance estimator to produce the confidence intervals.

Plot a 2D bivariate scatter plot of two chosen variables, or a 3D tr-variate scatter plot of three chosen variables, with the option to preserve the aspect ratio.

Create a shade plot (heatmap) of the data matrix (Variables are rows and Samples are columns, or vice versa), with a grey-scale (from white-to-black) showing increasing values of abundance/biomass in a mosaic. Change from grey-scale to a single colour, two colours, or a spectrum. Specify the maximum, the number of levels to appear in the key and optionally reverse the palette. Show in 2D or as bars in 3D. Alter the relative size of dendrgrams (if included), draw sample and/or variable constraint group boundaries.

Change the ordering of samples and/or variables in a shade plot. You can keep the original/worksheet order, order by a numeric factor/indicator, order by some other chosen variable, order to maximise the degree of seriation (where you also choose the number of restarts for optimising the seriation), order according to nearest neighbour, or by reference to a resmblance matrix. Add additional constraints to the re-ordering, such as to maintain groups or the structure of a dendrogram from a cluster analysis of the samples/variables. Note that separate re-ordering options and/or constraints are chosen and applied for samples and variables.

Plots the cumulative species count against sample number and (optionally) outputs several different estimators of total richness based on the plot (S, Chao 1, Chao 2, Jacknife 1, Jacknife 2, Bootstrap, Michaelis-Menton, Ugland-Gray-Ellingsen). Choose to keep samples in their original order, or specify an order via selecting samples. A permutation option is also offered, where different (permuted) sample orders are taken and the resultant curves are averaged.

A 3D plot of samples by variables with the height and colour gradient corresponding to data values. Optionally change the opacity of the surface.

Run a suite of basic multivariate analysis methods with user-specified settings on a set of data: (1) Pre-treatment (standardisation/transformation); (2) Resemblance; (3) one-way ANOSIM (user-specified factor); (3) CLUSTER analysis (optionally with SIMPROF); (4) Non-metric MDS; and (5) SIMPER.

Create a shade plot (heatmap) of the data, enabling a direct visualisation of the data values, where ordering of samples and variables are each separately re-arranged to maximise a pattern of seriation along each axis of the plot, but constrained by a cluster analysis of the samples (based on Bray-CUrtis) and a (separate) cluster analysis of the variables (based on the Index of Association). Samples may also be retained in groups based on the levels of a chosen factor. Optionally do an overall transformation and/or reduce the species set to retain only a chosen number of ‘important’ variables (based on % contribution to any one sample).

Display plots of variables which are functionally similar via the following automated steps: (1) CLUSTER analysis on the variables; (2) SIMPROF tests (at a chosen alpha-level and number of permutations) to identify maximal groups of variables with no structure (i.e., ‘coherent variables’); (3) line plots of the coherent variable sets. For biotic data (type = abundance or biomass), there are options to standardise the variables, choose the resemblance measure (e.g., Index of Association) and reduce the species set to ‘important’ species (based on % contribution to any one sample). For environmental/other data, there are options to scale variables via normalisation or ranking, choose the resemblance measure (e.g., Pearson).

Choose to plot additional Information and History as an extra text pane. Choose the line width, line pattern, and overall font scale for History panes and text.