OrdinationsNon-metric Multidimensional Scaling (NMS)
Non-metric Multidimensional Scaling (NMS, MDS, NMDS, or NMMDS) is an ordination method
that is well suited to data that are nonnormal or are on arbitrary, discontinuous, or
otherwise questionable scales. NMS is generally the best ordination method for
community data. Our auto-pilot feature makes it easy to use. A Monte Carlo
test of significance is included.
NMS Scree Plot
NMS Scores
NMS Scores provides a prediction algorithm for non-metric multidimensional scaling
(NMS). This is not prediction in the sense of forecasting, but rather statistical
prediction in the same way as using multiple regression to estimate a dependent variable.
NMS Scores calculates scores for new items based on prior ordinations.
Bray-Curtis (Polar)
We offer numerous options and improvements beyond Bray and Curtis' original method, such
as perpendicularized axes and variance-regression endpoint selection.
| Correspondence Analysis Family |
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Canonical Correspondence Analysis (CCA) |
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CCA is unique among the ordination methods in PC-ORD in that the ordination of the
main matrix (by reciprocal averaging) is constrained by a multiple regression on variables
included in the second matrix. In community ecology, this means that the ordination
of samples and species is constrained by their relationships to environmental
variables. CCA is most likely to be useful when: (1) species responses are unimodal
(hump-shaped), and (2) the important underlying environmental variables have been
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Detrended Correspondence Analysis (DCA, DECORANA) |
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DCA is an eigenanalysis ordination technique based on reciprocal averaging (RA; Hill
1973). DCA is geared to ecological data sets and the terminology is based on samples and
species. DCA ordinates both species and samples simultaneously. |
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Reciprocal Averaging (Correspondence Analysis) |
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Reciprocal averaging is also known as correspondence analysis (CA). It is
performed in PC-ORD by selecting options in program DCA adapted from the Cornell Ecology
Program series. Reciprocal averaging (RA) yields both normal and transpose
ordinations automatically. Like DCA, RA ordinates both species and samples
simultaneously. |
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TWINSPAN |
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TWINSPAN simultaneously classifies species and samples. At its core, TWINSPAN is
based on dividing a reciprocal averaging ordination space. One of the most useful
features of TWINSPAN is the final ordered two-way table. Species names are arrayed
along the left side of the table, while sample numbers are along the top. The
pattern of zeros and ones on the right and bottom sides define the dendrogram of the
classifications of species and samples, respectively. The interior of the table
contains the abundance class of each species in each sample. Abundance classes are
defined by pseudospecies cut levels. |
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Weighted Averaging |
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The simplest yet often effective method of ordination is weighted averaging.
The essential operation is the same: a set of pre-assigned species weights (or weights for
species groups) are used to calculate scores for sites (sample units). The
calculation is a weighted averaging for species or species groups actually present in a
sample unit. Weighted averaging used in Federal Manual and numerous ecological
indices. |
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Groups
Cluster Analysis
We offer eight fusion strategies and eight distance measures, for hierarchical,
polythetic, agglomerative cluster analysis. Results are given for each step in the
analysis, along with a publication-quality final dendrogram.
Cluster Analysis
Two-way Cluster Analysis
The purpose of our two-way clustering (also known as biclustering) is to graphically
expose the relationship between cluster analyses and your individual data points.
The resulting graph makes it easy to see similarities and differences between rows in the
same group, rows in different groups, columns in the same group, and columns in different
groups. You can see graphically how groups of rows and columns relate to each
other. Two-way clustering refers to doing a cluster analysis on both the rows and
columns of your matrix, followed by graphing the two dendrograms simultaneously, adjacent
to a representation of your main matrix. Rows and columns of your main matrix are
re-ordered to match the order of items in your dendrogram.
Two-way Cluster Analysis
| Group Linkage Methods |
- Nearest Neighbor
- Farthest Neighbor
- Median
- Group Average
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- Centroid
- Ward's Method
- Flexible Beta
- McQuitty's Method
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| Ward's is also know as Orloci's and Minimum Variance Method |
Multi-Response Permutation Procedures
(MRPP)
MRPP is a non-parametric procedure for testing the hypothesis of no difference between two
or more groups of entities. The groups must be a priori. For example, one
could compare species composition between burned and unburned plots to test the hypothesis
of no treatment effect. Discriminant analysis is a parametric procedure that can be
used on the same general class of questions. However, MRPP has the advantage of not
requiring assumptions (such as multivariate normality and homogeneity of variances) that
are seldom met with ecological community data. Eight distance measures options are
available.
Blocked Multi-Response Permutation
Procedures (MRBP)
Randomized block experiments or paired-sample data can be analyzed with a variant of MRPP
called MRBP or blocked MRPP. PC-ORD allows up to 1000 blocks and 100 groups.
Indicator Species Analysis
Dufrêne and Legendre’s (1997) method provides a simple, intuitive solution to the
problem of evaluating species associated with groups of sample units. It combines
information on the concentration of species abundance in a particular group and the
faithfulness of occurrence of a species in a particular group. It produces indicator
values for each species in each group. These are tested for statistical significance
using a Monte Carlo technique.
Mantel Test
The Mantel test evaluates the null hypothesis of no relationship between two dissimilarity
(distance) or similarity matrices. The Mantel test is an alternative to regressing
distance matrices that circumvents the problem of partial dependence in these
matrices. Example applications are: evaluating the correspondence between two groups
of organisms from the same set of sample units or comparing community structure before and
after a disturbance. Two methods are available in PC-ORD: Mantel’s asymptotic
approximation and a randomization (Monte Carlo) method.
PerMANOVA
PerMANOVA performs distance-based multivariate analysis of variance, also known as
nonparametric MANOVA or npMANOVA. Hypothesis are evaluated with permutation tests,
rather than by reference to an assumed distribution. Options include one-way,
factorial, nested, and blocked designs
| Import/Export File Formats |
- Excel (*.xls) and Excel 2007 (*.xlsx)
- spreadsheet (*.wk1)
- compact
- database
- Cornell condensed
- comma-separated values (*.csv)
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Data Modifications |
| Transformations |
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Relativizations |
- power transformation
- logarithmic
- arcsine
- arcsine squareroot
- Beals smoothing
- presence - absence
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- by totals
- by proportion of maximum
- rank
- deviation from mean
- binary with respect to median
- ubiquity
- deviation from mean
- binary with respect to mean
- ubiquity
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Summaries
Descriptive Statistics and Diversity
Indices
Summarize attributes of your rows or columns (mean, standard deviation, sum, minimum,
maximum, skewness, kurtosis), and measures of diversity: richness, equitability, Simpson
index, and Shannon index).
Outlier Analysis
Detect multivariate outliers. These are frequent in ecological data and they often
exert undue influence over the results of multivariate analyses.
Species-area Curves
Species-area curves are constructed by randomly subsampling a data set.
Species-area curves are frequently used during study design to help determine sample
sizes.
Species-area Curves
Principal Components Analysis (PCA)
Principal components analysis is the basic eigenanalysis technique. It maximizes the
variance explained by each successive axis. Although it has severe faults with many
community data sets, it is probably the best technique to use when a data set approximates
multivariate normality. PCA is usually a poor method for community data, but it is
the best method for many other kinds of multivariate data. Broken-stick eigenvalues
are provided to help you evaluate statistical significance.
Species Lists
Easily produce species lists from your spreadsheets, based on a species file.
This file associates your species acronyms with full species names, as they will
appear in your lists. Request a species list for each sample unit, or for your
combined sample units. You can include key summary statistics, such as frequency and
abundance of each species.
Write Distance Matrix
Although many analyses in PC-ORD calculate a distance matrix and offer to write
the distance matrix to the result file, these have limited formats and options.
Consider Write Distance Matrix if you wish to use your distance matrix in other software,
save it for further analysis, or simply calculate a distance matrix with no other
analysis.
Shuffle
Randomly reassign values in columns to new positions in the same column. The
resulting data set has the same column totals, matrix total, and number of elements
containing zeros, but it effectively randomizes the data set. Why shuffle your data?
Explore how multivariate methods can appear to detect pattern from nonsense.
Generate null models for comparison with your unshuffled data.
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