||PC-ORD for Windows 98, 00, ME, NT,
XP, Vista, 7, and 8
Multivariate Analysis of Ecological Data
To order: In Canada or USA call 1-800-690-4499 or Order
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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
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.
- 3 times faster than previous version!
- Principal Coordinates Analysis (PCoA) with randomization
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
Dufręne and Legendres (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
- 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
- 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
- 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.
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
- 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.
- 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
- Option to display quantile matrix in two-way dendrograms.
- Shift view in large dendrograms and two-way dendrograms without losing view of labels
and dendrogram scales.
- Manually assign points for successional vector segments, useful with unbalanced sampling
- Successional vectors on top of joint plots.
- Shift view in large dendrograms and two-way dendrograms without losing view of labels
and dendrogram scales.
- Improved options for graphing one-dimensional ordinations.
- Hide symbols for particular groups: Groups | Hide Categories
- Text tool to place new labels anywhere on graphs.
- Print Preview with zoom.
- Save Graph as GIF with optional transparent background.
- Increased symbol sizes from 9 to 18.
- Increased Scatterplot Matrix maximum from 10 to 20 variables.
- Added Gray Scale option for black and
- Added Overlay symbol size control.
- Added Cluster Dendrogram, Two-way Cluster Dendrogram, and Ordered Main Matrix symbol
- Added Boxplot box color control.
- Added Convex Hulls.
- Added Group Centroids.
- Added Plot Multiple Distribution Files.
- Added node sequence information to left click on dendrogram node from cluster analysis.
- Added Cluster and Two-way node swapping.
- Added option for direct input of a distance matrix to nonmetric multidimensional scaling
|Data Management and Sampling
- Import/Export | Excel Simple Spreadsheet.
The header data lines are added for you.
The fastest and most reliable way to get spreadsheet data into PC-ORD is to import it from
a "simple spreadsheet." This is the most common way to organize spreadsheets of
data: sample units are rows, variables are columns, and variable names are column headers.
We call this a "simple spreadsheet" because it lacks the additional header lines
that PC-ORD uses to document the contents of the spreadsheet. The complete spreadsheet
data format also has lines specifying the number and content of the rows and columns,
along with a row specifying variable type.
- Batch Commands -- Automate sets of PC-ORD operations.
You can automate a series of commands to perform repetitive tasks or to apply resampling
techniques in your analyses. For example, you may wish to process a series of data
sets in an identical way, changing only the names of the input files. Or, you might
want to use bootstrap resampling to calculate a confidence interval for a statistic of
particular interest. This requires taking a random sample of a data set, performing
an analysis, then repeating those steps many times.
- Tools | Find Duplicate Names
Search for duplicate names in either or both matrices. Duplicate names can
cause problems with procedures in PC-ORD that use these names as unique identifiers.
For example, if you choose a particular column to delete in your predictor matrix,
and two columns have the same name, PC-ORD doesnt "know" which column to
delete, so it cannot proceed.
- Tools | Go To Cell
Jump to a particular cell in a matrix. This is particularly useful for large
matrices that are difficult to navigate by scrolling. After you specify a cell,
PC-ORD scrolls in the matrix (if necessary) and outlines the selected cell.
- Option to view row numbers and column letters as in
Select this option if you wish to display the column letters and row numbers that identify
the cells in your matrix, as in Excel. These are then displayed in addition to your
row and column names.
- Automatic detection and repair of bad data values in
The Matrix Error dialog appears when you open or import a spreadsheet with obvious errors
in it. Errors can be empty cells (missing values) or disallowed values in the data
part of the matrix. For example, the data in the body of a matrix must all be
numeric. Including non-numeric characters will cause the Matrix Error dialog to
- Added several forms of log transformation to deal with
zeros more conveniently.
- Hellinger transformation
The Hellinger transformation is relativization by row (sample unit) totals, followed by
taking the square root of each element in the matrix. Euclidean distances calculated
by a matrix transformed in this way will be Hellinger distances. Some authors
consider this a desirable transformation in some circumstances (Legendre & Gallagher
- Augment Matrix
Attach another matrix on the right.
- Append Graph File
Combine two graph files end-to-end, each containing ordination scores for the same number
- Option to view row numbers and column letters as in Excel.
- Standard deviations of abundances in species lists and lists broken down by groups