What's New

Multivariate Analysis for Community Ecologists: Step-by-Step using PC-ORD
	Custom-made for the beginning data analyst, this book also includes techniques and tips useful to advanced users.  A 10-step analysis process using tools available in version 6 guides both users who can, and cannot, participate in PC-ORD training.
Decision Tree for Community Analysis Poster The purpose of the PC-ORD Advisor Wizard is to help you to decide how to analyze your data, based on a decision tree. You can also use it as a self teaching tool.  The logic of the decision tree is now available as a poster.
New Analyses
3 times faster than previous version! Principal Coordinates Analysis (PCoA) with randomization test Principal Coordinates Analysis is an eigenanalysis technique similar to PCA, except that one extracts eigenvectors from a distance matrix among sample units (rows), rather than from a correlation or covariance matrix.  In PCoA one can use any square symmetrical distance matrix, including semi-metrics such as Sorensen distance, as well as metric distance measures such as Euclidean distance. Redundancy Analysis (RDA) Redundancy Analysis models a set of response variables as a function of a set of predictor variables, based on a linear model.  RDA thus applies to the same conceptual problem as canonical correspondence analysis (CCA).  RDA is, however, based on a linear model among response variables and between response variables and predictors.  CCA, on the other hand, implies a unimodal response to the predictors. Blocked Indicator Species Analysis Dufrêne and Legendre’s (1997) method for Indicator Species Analysis can be adapted to a randomized block experiment or a paired-sample design.  The data are pre-relativized by species within blocks (or pairs), such that the sum across groups equals one for each block.  If a species is absent from a block, the abundances are maintained at zero.  The relativization alters the relative abundance portion of the Indicator Value (IV) index to focus on within block differences.  Then the ISA is run as usual.  The randomization test differs from regular ISA in that instead of an unconstrained permutation of group identifiers, groups are randomly permuted within blocks. Phi Coefficient for Indicator Species Tichý and Chytrý's (2006) phi coefficient is a method for evaluating the indicator value (or diagnostic value) of a species with respect to a one-way grouping of sample units.   It applies only to presence-absence data.  If have quantitative data you choose this option in the Indicator Species Analysis Setup, then the data are automatically converted to presence-absence.  Any value greater than zero is transformed to 1, while values less than or equal to zero are transformed to zero.   Tichý and Chytrý's method corrects for unequal sample sizes among groups.   The adjusted phi coefficient also allows comparisons across studies with different sample sizes. Chao estimators for species richness Under the Species-Area choice PC-ORD also provides two jackknife estimators and a Chao estimator of species richness (Chao 1987; Colwell & Coddington 1994).  Palmer (1990, 1991) compared several ways of estimating species richness of an area when it is subsampled with smaller sample units.  Included in these comparisons were two jackknife estimators, nonparametric resampling procedures.  The number of observed species in a sample will typically be smaller than the true number of species.  These jackknife estimators produce more accurate and less biased estimates, at least when subsampling a restricted area. Compare ordinations: calculate redundancy between two ordinations of any kind Compare Ordinations provides a statistical evaluation of the similarity of two ordinations, independent of any rotation, reflection, units for axis, and number of dimensions. Randomization test for DCA and CA (RA) Partial Mantel Test The partial Mantel test requires three matrices, the main matrix, a second matrix, and a control matrix.  The null hypothesis is of no relationship between the main and second matrices, after controlling for the relationship with the third (control) matrix.   If we call the main matrix Y, the second matrix X, and the control matrix C, then we seek the partial correlation between X and Y while controlling for C. SumF A simple but surprisingly effective method of comparing two or more groups of sample units is to calculate a univariate F statistic for each variable, sum those F statistics, then compare the resulting sum to the distribution of F statistics based on randomizing the data under the null hypothesis.  This is the core of the SumF method, as suggested by Edginton (1995).  Good performance of this method, as compared to distance-based methods, was found by Warton and Hudson (2004).  An advantage to this method is that by aggregating a simple, well-known test statistic, the F ratio, into a summary statistic across multiple variables, we simultaneously obtain information about differences between groups both across all variables and for individual variables.  Thus for the generic question, "Do communities differ between groups?", the SumF method allows us to report an answer for communities as a whole as well as for individual species. Compare Scores (Compare Ordinations) Evaluate the similarity of two ordinations, independent of any rotation, reflection, units for axis, and number of dimensions.  This is accomplished by evaluating the correlation between the interpoint distances of two ordinations. Squaring this correlation expresses the redundancy between two ordinations.  A formal test of the hypothesis of no relationship between the two ordinations is provided by a Mantel test. Batch Processing Batch processing automates repetitive tasks and allows bootstrap resampling for CA, CCA, DCA, ISA, Mantel Test, MRPP, NMS, PCA, PCoA, perMANOVA.  Generate empirical distributions and confidence intervals for eigenvalues, stress, gradient lengths, p values from randomization tests, F ratio, A from MRPP, etc.
Additions to Existing Analyses
Options for tie handling in nonmetric multidimensional scaling. Select Kruskal's primary approach or secondary approach. Option for rotation to principal axes nonmetric multidimensional scaling, in addition to the existing option for varimax rotation. The underlying logic of Advisor | Show Current Profile is improved, making it both smarter and more accommodating to user's wishes. Average p values and indicator values provided for Indicator Species Analysis. Added an overall test of differences among groups across all species for Indicator Species Analysis.  This is based on a test statistic that is the sum of IVmax across all species.