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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