Monster Media 1993 #2/Image.iso/math/mvsp21.zip/MVSP.DOC

Text File | 1993-06-08 | 126KB | 2,353 lines

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                                S H A R E W A R E
                                -----------------


                        A MultiVariate Statistics Package
                         for the IBM PC and Compatibles

                    (C) Copyright Warren L. Kovach, 1986-1993

                            Kovach Computing Services
                                 85 Nant-y-Felin
                     Pentraeth, Anglesey LL75 8UY Wales U.K.

                      Internet: [e-mail]
                             CompuServe: 100016,2265

                              Ver. 2.1, June, 1993



        This program is being distributed as shareware.  You may evaluate
        it for up to 30 days.  If after that period you decide to
        continue using the program you must register.  This costs 65 UK
        pounds or the equivalent in US dollars.  See page 4 of this
        manual, the file REGISTER.DOC, or the "Register" option on the
        main menu for more details.
        MVSP Ver. 2.1 -- Users Manual                              Page 2

                                 ACKNOWLEDGEMENTS

        In the years since I first released MVSP, I have received
        countless letters about this program, many with some very useful
        suggestions and comments.  I have considered all of these and
        have incorporated most into this new version.  My thanks go to
        all of those who have sent in comments.  Special thanks go to
        John Birks (Bergen, Norway), Geoffrey King (Pickering, Yorkshire,
        England), Lou Maher (Madison, Wisconsin, USA), John Breen
        (Limerick, Ireland), and Bill Briggs (Boulder, Colorado, USA) for
        numerous comments on both the old and new versions of the
        program.  Very special thanks go to my wife, Catherine Duigan,
        for numerous suggestions for improvements in the program, help in
        designing this manual and the cover, assistance in the
        distribution of MVSP, and for putting up with many hours of
        computer-widowhood.

        Warren L. Kovach
        "Tigh an-Oilean"
        Pentraeth, Anglesey, Wales
        June 1993

























        This manual and the accompanying program are protected by
        international copyright laws; (C) Copyright 1986-1993 Dr. Warren
        L. Kovach.  This manual and the accompanying computer program may
        not be reproduced except as outlined in the section below
        entitled "Limited User Licence".

        MVSP Ver. 2.1 -- Users Manual                              Page 3

                                TABLE OF CONTENTS

        Acknowledgements................................................2
        Introduction....................................................4
        The Shareware Concept...........................................4
        Limited Warranty................................................5
        General Use of Program..........................................6
          Starting the program..........................................6
          Menus.........................................................6
          Entering and Editing Text.....................................7
        Menu Options....................................................7
          A-F: Statistical Procedures...................................7
          M: Manipulate Data............................................7
          I: Import/Export..............................................8
          S: Change Drive or Sub-directory..............................8
          Q: Quit MVSP..................................................8
          X: Execute DOS commands.......................................8
          P: Change Program Defaults....................................8
             Screen Colors..............................................8
             Data File and Work File Path...............................8
             Data File Extension........................................9
             Output Format.............................................10
             Graphics Options..........................................11
             Printer Setup.............................................13
        MVSP Data Editor...............................................14
          Entering Data Labels.........................................15
          Entering Data................................................15
          Editing Labels and Data......................................16
          Saving Data Matrix...........................................16
        Data File Format...............................................16
        Data Manipulation..............................................19
        Import/Export Data.............................................22
        Running Numerical Procedures...................................23
          Principal Components Analysis................................24
          Principal Coordinates Analysis...............................26
          Correspondence Analysis......................................26
          Distances and Similarities...................................29
          Cluster Analysis.............................................32
          Diversity Indices............................................34
        Utilities......................................................35
          Sortdata.....................................................35
        Disclaimer.....................................................36
        80x87 Support..................................................37
        Protected Mode Version.........................................37
        Appendices.....................................................38
        References.....................................................39
        Other Products from Kovach Computing Services..................41
        MVSP Ver. 2.1 -- Users Manual                              Page 4

                                   INTRODUCTION

        MVSP is a package of common multivariate statistical procedures
        widely used in many areas of biology and geology, as well as
        other fields.  These procedures include principal components
        analysis (PCA), principal coordinates analysis (PCO),
        correspondence analysis (CA; also called reciprocal averaging),
        distance or similarity measures, hierarchical cluster analysis,
        and diversity indices.  MVSP provides a great deal of flexibility
        in the analyses, but is simple to use.  Options for different
        forms of these analyses can be chosen from menus and these
        settings can be saved for future use.  Most analyses can be run
        with as few as half a dozen keystrokes.

        One possible drawback to ease of use is that some users may be
        very tempted to take a "black box" approach to using these
        statistics, feeding in numbers and coming up with "The Answer".
        I must strongly warn the users of this program that statistics
        can be DANGEROUS!  All these procedures make assumptions about
        the data and have restrictions on what they can and cannot do. If
        these assumptions and restrictions are violated, the results
        could be meaningless.  I urge you to become familiar with the
        methods before you use this program.  This manual contains a list
        of references that I have found very useful in understanding
        these techniques.  In particular, Sneath & Sokal (1973), Gauch
        (1982), Pielou (1984), Manly (1986), Davis (1986), and Kent and
        Coker (1992) are very well written and give very clear
        discussions of these techniques.

        I am always interested to see how MVSP is being used.  I would
        appreciate receiving reprints of any papers you have published in
        which MVSP was used for data analysis.  Thank you!


                              THE SHAREWARE CONCEPT

        This software package is being distributed under the shareware
        concept.  In case you haven't run across this software
        phenomenon, the following is a brief discussion of it's tenets.
        Shareware software is an experiment in "grass-roots" software
        distribution and development.  Andrew Fluegelman, one of the
        pioneers of this phenomenon in the microcomputer world, expressed
        it this way:

          1) The value and utility of software is best assessed by the
             user on his or her own system, under actual working
             conditions.

          2) The creation of new and useful software should be supported
             by the computing community.

          3) Copying and sharing of software that you have found useful
             should be encouraged, rather than restricted.

        Shareware programs are freely distributed to the computing
        community, through the network of electronic bulletin board
        services, local computer user groups, shareware disk vendors, and
        MVSP Ver. 2.1 -- Users Manual                              Page 5

        networks of friends and colleagues with similar interests.  You
        are allowed to try out the program for a certain period to see if
        it fits your needs.  If it does and you intend to continue using
        it, then you must register the program with the author by paying
        a registration fee.  In return you will generally get a copy of
        the latest version of the program, a printed manual, and perhaps
        other extras the author offers to encourage you to register.

        Shareware means that you don't have to pay outrageous prices for
        a program without getting a chance to test drive it first to see
        if it really meets your needs.  Shareware means that if you
        decide that this program is worth supporting, then you support it
        voluntarily, for a reasonable cost, and without the hassles of
        copy-protection and the high cost of advertising.

        You are encouraged to copy and distribute MVSP Shareware.  If
        after a 30 day evaluation period you find this program to be
        useful and decide to continue using it, then a registration fee
        of 65 UK pounds or the equivalent in US dollars should be sent to
        the author.  See the file REGISTER.DOC, or the "Register" option
        on the main menu for details on how to register.

        In return for the contribution, you will receive:

        o the latest version of the program (without the shareware
          reminder messages)
        o a full printed manual, including the graphics and appendices
          that are not in the shareware version
        o the ability to take advantage of the 80x87 math coprocessor for
          faster and more accurate analyses
        o a protected mode version that will directly use up to 16Mb of
          RAM memory for faster analyses of larger data sets
        o the SORTDATA utility that creates graphic representations of
          your data matrices, sorted in the order of the dendrograms
        o notification of future versions as well as of other programs
          produced by Kovach Computing Services
        o special upgrade prices
        o technical support by phone, fax, e-mail or post

        This program is copyrighted.  MVSP Shareware can be freely copied
        and distributed in accordance with the regulations specified in
        the accompanying file VENDOR.DOC.  MVSP Shareware may not be
        modified or dis-assembled in any way or for any reason.
        Distribution of modified versions are also forbidden.


                                 LIMITED WARRANTY

        Kovach Computing Services warrants any physical diskettes and
        physical documentation provided under this agreement to be free
        of defects in materials and workmanship for a period of sixty
        days from the purchase.

        KOVACH COMPUTING SERVICES SPECIFICALLY DISCLAIMS ALL OTHER
        WARRANTIES OF ANY KIND, EXPRESSED OR IMPLIED, INCLUDING BUT NOT
        LIMITED TO ANY WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
        PARTICULAR PURPOSE.

        MVSP Ver. 2.1 -- Users Manual                              Page 6

        The total liability of Kovach Computing Services for any claim or
        damage arising out of the use of the licensed program or
        otherwise related to this licence shall be limited to direct
        damages which shall not exceed the price paid for the program.

        IN NO EVENT SHALL THE LICENSOR BE LIABLE TO THE LICENSEE FOR
        ADDITIONAL DAMAGES, INCLUDING ANY LOST PROFITS, LOST SAVINGS OR
        OTHER INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE
        OF OR INABILITY TO USE THE LICENSED PROGRAM, EVEN IF LICENSOR HAS
        BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

        This agreement does not affect your statutory rights.  The
        agreement shall be interpreted and enforced in accordance with
        and shall be governed by the laws of England and Wales.


                            GENERAL USE OF THE PROGRAM

        Starting the program:
        This program is simple to use and menu-driven, presenting you
        with the possible options at each step.  It is initiated by first
        logging into the disk and directory containing the program (using
        the DOS commands CD, A:, C:, etc.) and typing the name of the
        program, "MVSPSHAR". For instance, if you have installed MVSP on
        you hard disk in the directory C:\MVSP, type:

        C:
        CD C:\MVSP
        MVSPSHAR

        The program file MVSPSHAR.EXE must be in the default directory
        (the one specified in the CD command above) for the program to
        work properly.  If you wish to use the help facility, the file
        MVSP.HLP must also be in this directory.  If you have changed any
        of the program defaults, the configuration file named MVSP.CNF
        (which is created when you save your changes) must also be on the
        default drive for the new options to be reinstated.

        You may also specify the location of the MVSP files using DOS
        environment variables and the commands "SET" and "PATH".  For
        instance, if the MVSP files are in the directory C:\MVSP, you may
        place the two following commands in your AUTOEXEC.BAT file:

        PATH C:\;C:\MVSP   (this line may also contain other directories)
        SET MVSP=C:\MVSP

        After rebooting, you may start the program by typing MVSP,
        regardless of the current directory.  You may edit your
        AUTOEXEC.BAT file with any word processor or text editor that
        produces plain text (ASCII) files.  Many will have a special non-
        document mode for this.  Refer to your word processor manual for
        details.  Also, DOS' EDIT or EDLIN program may be used.

        Menus:
        When the program is loaded, you will see an introductory screen
        giving the name  of the author, then after pressing any key you
        will be presented with a menu of available procedures.  The first
        MVSP Ver. 2.1 -- Users Manual                              Page 7

        option on the menu will be highlighted by a rectangular cursor.
        This cursor can be moved through the list of options by using the
        up and down arrow keys.  A choice is made by pressing the
        carriage return when the correct one is highlighted, or
        alternatively by typing the letter preceding the desired option.
        Usually, choosing an option will bring up a second menu, from
        which you can often call up a third, and so on.  The number
        preceding the title on each menu indicates the level you are at
        in the hierarchy;  If you get lost, remember that pressing 'Q' or
        ESC will bring you back to the previous menu.

        MVSP has an extensive help facility that provides information
        about every menu option.  To get help, just place the cursor on
        the desired option and press the F1 key.  After reading the text,
        pressing any key will bring you back to the menu.

        Entering and editing text:
        You will often be asked to type in a string of text, such as the
        name of a data file.  In some cases you are provided with a
        default choice, which you can accept or modify.  MVSP has a
        number of editing commands to help in this modification.  You can
        use the cursor keys to move the cursor back and forth, the DEL
        and Backspace keys for deleting text, and the letter keys for
        adding text.  When you first begin editing a text string, the
        program is in insert mode, so that any text you type will be
        inserted and the remaining text will be pushed the right.
        Pressing the INS key toggles insert mode on or off (indicated by
        the thickness of the cursor); with it off old text is overwritten
        by the new.  Pressing ESC will clear the input line to allow you
        to start from scratch.  If you press the Enter key after clearing
        the line you will exit that procedure.

        When you are entering the name of the input data file, pressing
        F3 will recall the last valid filename you entered during that
        session.  You may then use that file again or modify it if you
        want to use a similarly named file.

        MENU OPTIONS
        The main menu lists the six available numerical procedures as
        well as a few other options.  It looks like this:

        <Graphic placed here in printed manual>

        Options A-F:
        These options are the basic numerical procedures; principal
        components analysis, principal coordinates analysis,
        correspondence analysis (reciprocal averaging), similarities and
        distances, cluster analysis, and diversity indices.  These are
        described later in this document.

        Option M:
        The MANIPULATE DATA option provides facilities for data entry,
        editing, and transformation.  A simple spreadsheet-like data
        editor is provided for initial entry and subsequent modification
        of the data.  Procedures are also provided for transposing and
        transforming the data, converting to other scales, and deleting
        rows and columns.  The full use of these facilities is described
        MVSP Ver. 2.1 -- Users Manual                              Page 8

        below.

        Option I:
        The IMPORT/EXPORT option allows you to transfer data between MVSP
        files and other file formats.  Currently Lotus 1-2-3/Symphony and
        Cornell Ecology Program file formats are supported.  The full use
        of this option is described on page 8.

        Option S:
        This option, CHANGE DRIVE OR SUBDIRECTORY, allows you to specify
        the default location of the input and output data files.  If you
        enter a path name without a drive specification, the default
        drive is assumed.  If you enter just a drive specification (e.g.
        "A" or "A:") the default path will be the current directory of
        that drive.  A "?" lists the sub-directories of the current
        directory.  A carriage return with no other input exits this
        option with no changes.

        Option Q:
        QUIT MVSP will exit the MVSP program and return to the DOS
        prompt.

        Option X:
        The EXECUTE DOS COMMANDS option allows you to temporarily drop
        out to (or "shell to") DOS while you are running MVSP.  Rather
        than exiting the program completely, this option allows you to
        keep MVSP loaded in memory, with all you current options intact,
        while you work at the DOS prompt.  When you are ready to return
        to MVSP, simply type the command "exit" at the DOS prompt.

        When you shell to DOS, the running program of MVSP will be saved
        to disk or EMS memory, allowing as much DOS memory to be freed up
        as possible.  On typing "exit" this saved image will be reloaded
        and you will be returned to MVSP in the state it was when you
        left.

        Option P:
        The CHANGE PROGRAM DEFAULTS option allows you to change many of
        the default settings for the program.  These specifications can
        be saved to the file MVSP.CNF, which will be reloaded each time
        the program is run, reinstating these defaults.  When you choose
        this option you will be presented with a menu asking which type
        of default should be changed.

        <Graphic placed here in printed manual>

        C - SCREEN COLOURS allows you to change the colour of the regular
        text and background, the menu text and background, the menu
        frame, and the help screens and error messages.  Choosing one of
        these will cause a menu of available colours to appear.  You can
        experiment with colour combinations easily, quitting the colour
        menu when you are satisfied.  Note that option "F" on the menu
        resets black and white colours.  This option can be useful in
        case you get yourself into a colour combination that is so
        unreadable that you can't see the options available!

        P - DATA FILE AND WORK FILE PATH changes the default path used
        MVSP Ver. 2.1 -- Users Manual                              Page 9

        for data files, just like option S above.  If you are using a two
        floppy disk system, it is often most useful to have the program
        files in drive A: and to have the default data file path set to
        B:, so that data files are on another disk.  If you have a hard
        disk, you could have the program files in a subdirectory named
        C:\MVSP (which would be the default directory when you invoke the
        program) and the data either on a floppy disk in drive A: or B:,
        or in a hard disk directory named C:\MVSP\DATA.  You would then
        specify the default data file path through this option.  You can
        even set up separate directories for different types of data,
        which is where the temporary path change option ("S" on main
        menu) would come in handy.  You can always override the default
        path option by specifying the drive and path when you are asked
        for the name of the data file while running one of the
        statistical procedures.

        After entering the default data file path, you will be asked for
        a disk drive where the temporary work files will be stored.  If
        the data set you are analysing is too large to fit in memory,
        parts of it will be stored on disk until needed.  This will slow
        down the calculations considerably, since data retrieval from a
        disk is much slower than from memory.  Floppy disks are much
        slower than hard disks, so always choose a hard disk for the work
        files if you have one available.  If your computer has extended
        or expanded memory (memory above 640K), then you can set this up
        as a RAMdisk that will emulate a disk drive but operate much
        faster, thus speeding up any analyses that must write data to
        disk.  See Appendix 4 (only included with the registered version)
        for details of how to do this and general information on memory
        management in MVSP.

        E - DATA FILE EXTENSIONS allows you to change the default
        extensions for your input and output files.  The default values
        are *.MVS for input files and *.OUT for output files, but you can
        easily change this and save your changes.  The PCO and cluster
        analysis procedures can have different defaults, which
        facilitates the input of similarity or distance coefficients.
        The coefficients program will output a symmetrical matrix in the
        form required by the PCO or cluster procedures, if so asked, and
        will default to the extension that you specify for PCO and
        cluster analysis input (*.MVD is the initial setting).  The
        output files for these can also have their own default extension
        (*.OT2 initially).  You can also specify default extensions for
        the tree description and tree order files produced by cluster
        analysis.

        R - REREAD CONFIGURATION FILE will reread the MVSP.CNF
        configuration file that contains the user default settings.  This
        will reinstate the default settings that are normally active when
        the program is initiated.  This can be handy if you have made a
        lot of changes to defaults during a session (without saving
        them!) and you wish to return to your old defaults.

        S - SAVE DEFAULTS TO FILE MVSP.CNF will save any changes in the
        defaults to a configuration file, which will be reloaded every
        time the program is run.  If this file is not found in the same
        directory as the other MVSP program files, the internal defaults
        MVSP Ver. 2.1 -- Users Manual                             Page 10

        will be set.

        Q - QUIT CONFIGURE will return to the main menu.

        O - OUTPUT FORMAT allows you to change the format of the
        printouts obtained from MVSP analyses as well as the method used
        for writing to the video screen.

        <Graphic placed here in printed manual>

        P - The PAGE WIDTH option sets the number of characters that can
        be printed per line on your printer.  Normally this is 80
        characters, but if you have a wide carriage printer or a printer
        capable of compressed printing at 15 characters per inch, then
        this can be reset to 130.  The "Printer Setup" option described
        below allows you to set your printer to  print in compressed
        mode.  The "Page Width" option also affects the length of lines
        in data files created by the "Data Manipulation" and "Distances
        and Similarities" procedures.

        C - RESULTS COLUMN WIDTH sets the number of characters used to
        represent each number and column heading on the printout of the
        results.  With numbers, this column width is for the entire
        number, including the decimal point, decimal fraction, and the
        space between numbers.  Thus " 2345.67" requires a column width
        of at least 8 spaces, including a leading space.  Narrower column
        widths allow more columns to be printed across a page, thus
        saving paper, but some numbers may be too large to be represented
        in the smaller space.  If a number is larger, the whole number
        will be printed and the alignment of the columns will be
        disrupted.  Symmetrical matrices created by the "Distances and
        Similarities" procedure also use the values specified here and in
        option D.

        D - RESULTS DECIMAL PLACES sets the number of decimal places to
        be displayed for each number.  Generally this should be at least
        2 or 3.  Whole numbers (those that have a decimal portion that is
        zero to the accuracy of the computer) will be displayed without
        the decimal portion.  Numbers that are smaller than can be
        represented in the allotted decimal places will be printed in
        exponential form.  For instance, if the decimal places option is
        set to 3, and a number 0.00001 must be printed, it will be
        printed as 1.0E-05 (1.0 x 10-5).

        O & E - DATA COLUMN WIDTH and DATA DECIMAL PLACES are similar to
        the above two options, but they apply only to printouts of the
        raw data and to data files created by the "Data Manipulation"
        procedure.  For instance, if your data are always whole numbers
        less than 100, then you could set the data decimal places to 0
        and the data column width to 4.

        M - SCREEN OUTPUT METHOD lets you toggle between two methods of
        screen output, direct screen memory output and BIOS output.  The
        direct memory method writes data directly to the area of memory
        that controls the screen, while the BIOS method uses calls to
        your computer's BIOS (basic input/output system).  The direct
        output method is much faster, but only works on computers that
        MVSP Ver. 2.1 -- Users Manual                             Page 11

        are hardware-compatible with the IBM-PC (almost all IBM
        compatibles sold these days are hardware-compatible).  Direct
        output also will cause problems when  used under some windowing
        environments such as older versions (ver. 2) of Microsoft's
        Windows.  If you are using one of these environments, you must
        either run MVSP as a full-screen application or choose BIOS
        output to allow MVSP to run in a window.  Note that both Windows
        3 and Quarterdeck's Desqview will run MVSP in a window without
        choosing BIOS output, thus allowing faster screen output.

        V - CHECK FOR VIDEO "SNOW".  On some brands of colour graphics
        adapter boards (most notably IBM's original), the fast method of
        writing directly to the screen memory can cause interference, or
        "snow", on the screen.  This occurs when both the program and the
        computer's graphics hardware try to work on the screen memory at
        the same time.  This option forces the program to check the
        screen memory before writing to it to make sure there will be no
        interference.  This eliminates snow, but also slows down the
        output somewhat.  If your graphics adapter is not susceptible to
        snow, then this option should be set to "No" for optimal speed.
        If snow appears, then set the option to "Yes".

        G - GRAPHICS OPTIONS allows you to change a number of defaults
        related to the scattergrams produced by the ordination
        procedures.

        <Graphic placed here in printed manual>

        P - SCATTERPLOT/DENDROGRAM TYPE lets you select either text or
        graphics plots.  Text plots are produced using regular characters
        such as "-" and "|" and "*" that can be printed on any printer or
        video screen.  The placement of the points for scatterplots is
        restricted to a grid of 70x22 or 110x55 characters, therefore the
        accuracy of these graphs is limited.   Text-based dendrograms
        will be scaled to fit the width of the page and will extend as
        long as necessary, even over multiple pages.  Graphics plots are
        produced by switching your video monitor to graphics mode and
        drawing the graphs with lines and dots.  These are more accurate
        and aesthetic (see example below).  However you must have a
        graphics monitor to display these.  MVSP supports CGA, EGA, VGA,
        VESA Super VGA, Hercules, and AT&T or Compaq plasma display 400-
        line graphics monitors.  Except for the case of the 400-line mode
        (see "400 LINE GRAPHICS MODE" below), MVSP will detect which type
        of monitor is present and adjust accordingly.  The appropriate
        device driver file (CGA.BGI, EGAVGA.BGI, VESA.BGI, HERC.BGI, or
        ATT.BGI) must be in the same directory as the program files

        <Graphic placed here in printed manual>

        Graphics scatterplots can be printed on dot matrix printers
        either directly or through the DOS GRAPHICS screen-dump facility.
        If you have a printer that is compatible with those listed under
        "Printer Setup", plots can be output directly by choosing the
        PRINT GRAPHICS AUTOMATICALLY option described below.  For those
        with other types of printers, check your DOS manual to see if
        your printer is supported by the GRAPHICS command.  If so,
        running GRAPHICS before MVSP will allow you to print the graph
        MVSP Ver. 2.1 -- Users Manual                             Page 12

        using the Print Screen key.  Note, though, that printing directly
        from MVSP will give much higher resolution plots.

        W - WIDE TEXT PLOTS are plots that are produced with a grid of
        110x55 characters.  If you have a wide carriage printer and paper
        or a dot matrix printer capable of compressed mode printing (see
        "PRINTER SETUP" below), then these graphs can be used, giving
        higher resolution.  Normally, a single wide text plot will fill a
        whole page.  However, I usually use a special print mode that is
        a combination of compressed and superscript characters with a
        line spacing of 12 lines per inch instead of the default 6
        ("tiny" print on the "TEXT STYLE" menu below).  This produces
        tiny but readable characters and allows two plots per page.

        G - PLOTS PER PAGE allow you to specify how many plots to print
        before issuing a new page command to the printer, thus ensuring
        that plots aren't printed over the fold of the paper.  In regular
        text mode two plots fit per page but only one fits in wide text
        mode (but see previous paragraph).   In graphics mode you will be
        able to fit one plot per page.  If you are using the DOS GRAPHICS
        utility to do a screen dump of the plot, then set this option to
        one plot per page as well.

        L - DATUM LABEL TYPES.  By default, MVSP represents each plotted
        point with a letter or other character.  These symbols are also
        listed on the printouts in a column headed "PLOT" so that you can
        tell which case or variable is represented by each point.  This
        is the "Sequential" mode of data labelling.  You may also choose
        "Label" mode in which the first character of each datum label is
        plotted.  This is useful if you can assign the cases or variables
        to distinct groups (such as environment type, sociological group,
        or taxon)  In these cases you use different letters or symbols as
        the first character of each label in order to represent each
        group.  With these plotted, you can tell at a glance how well the
        groups are distinguished by the analysis.

        M - 400 LINE GRAPHICS MODE is a special mode used in AT&T 6300
        and Compaq Portable III and 386 computers, among others.  This is
        similar to CGA high resolution mode but uses a resolution of
        640x400 rather than 640x200.  MVSP can usually tell what type of
        display is being used, but these 400 line mode displays will be
        detected as CGA monitors.  To take advantage of the 400 line
        mode, set this option to "Yes".  The file ATT.BGI must be present
        in the directory containing the MVSP program files.

        A - PLOTS PER ANALYSIS allows you to specify how many axes to
        plot for each analysis.  If you know ahead of time that you want
        to see the first three axes plotted against each other, set this
        value to 3.  You may wish to see the results before deciding how
        many axes to plot.  In this case, enter "-1" for the number of
        plots; you will then be asked how many to plot as the procedure
        is running.

        E - PRINT GRAPHICS AUTOMATICALLY specifies that you wish to have
        the graphics plots automatically printed rather than drawn on the
        screen.  Set this option to "Yes" to do this.  If you instead
        wish to examine the plot on the screen before deciding to print
        MVSP Ver. 2.1 -- Users Manual                             Page 13

        it, set this option to "No".  When the plot is drawn on the
        screen, the program will pause to allow you to look at it.  If
        you decide to print it, simply press the "P" key, otherwise press
        any other key to go on.  Also use the "No" option if you aren't
        going to print the graphics mode plots, or if you are using the
        DOS GRAPHICS screen-dump facility to print them.

        T - PRINTER SETUP option - This option allows you to specify what
        type of printer(s) you are using.  Separate printers can be used
        for the output of text results and graphics plots, so that you
        could, for instance, have the results printed on a dot matrix
        printer and the graphs on a plotter or high resolution laser
        printer.  There are several options on this menu:

        <Graphic placed here in printed manual>

        T - TEXT PRINTER - This option allows you to choose one of
        several printers for the output of text results.  This output
        will include the numeric results as well as graphs if text mode
        plots are chosen under the "Scatterplot/Dendrogram Type" option.
        The "Plain ASCII" option will send text to the printer without
        any control codes.  The "Other" option allows you to specify the
        printer codes in a similar manner as in MVSP version 2.0.  To do
        this you must first consult your printer manual to determine the
        codes needed for the desired text effect.  Then, using this
        option, enter the decimal (not hexadecimal) codes with each
        individual value preceeded by a slash (e.g. "\27\69" for bold
        print on an Epson printer).  You may enter the codes to set a
        certain text effect and to reset the printer to its default
        condition at the end.

        Y - TEXT STYLE - MVSP can automatically set up your printer to
        use different text styles for the printouts.  Normal printing
        gives output in your printer's default text mode.  Compressed
        will give text that can fit up to 130 columns on a single page of
        A4 or 8.5"x11" paper.  Tiny print is also compressed to allow for
        130 columns but the text itself is also half as high as normal,
        allowing for twice as many lines per page as well.  If you choose
        compressed or tiny print, make sure to set the "Page Width"
        option (page 10) to 130 columns.

        Z - PAPER SIZE - This allows you to choose the size of paper used
        in your printer.  You may specify letter, legal, or A4 size.  If
        you are using wide carriage paper, choose the size that matches
        the length of your paper.

        P - GRAPHICS PRINTER - You may choose from several types of
        printers and plotters for your graphics output.  You may also
        save the graphs to a .PCX bitmap file at 640x480 resolution.

        M - GRAPHICS PRINTER MODE - Each printer type has a number of
        modes associated with it.  These modes cover the resolution of
        output and/or the page size.  The available modes vary for each
        printer type.  Note that with some printers, most notably the HP
        Laserjet, the highest resolution printouts can often take a long
        time to complete.

        MVSP Ver. 2.1 -- Users Manual                             Page 14

        D - GRAPHICS OUTPUT DEVICE - You may specify to which parallel or
        serial port your printer is attached.  This allows you to have
        two printers attached to one computer on different ports (the
        text printer is always assumed to be on LPT1).  You can also have
        graphics output directed to a file.  You can then send it to the
        printer later using the DOS "COPY /B filename portname" command,
        where "filename" is the name you specify for the output and
        "portname" is LPT1, LPT2 COM1, or COM2.

        You can also save graphics output to a file if you want to import
        the plot into a graphics program for further editing or inclusion
        in other documents.  Many drawing, painting, and desktop
        publishing/word processing programs allow you to import graphs in
        a number of formats.  The three graphics printer types in MVSP
        that can be used for this purpose are HP Plotter, Postscript, and
        bitmap.  The Postscript files can be treated as Encapsulated
        Postscript files (.EPS or .AI) by many programs.

        W - PLOT WIDTH (CM) - This option allows you to specify the width
        (in centimetres) of the graph on the page.  The graph will be
        centred on the page.  If the value you specify is larger than the
        page size it will be scaled to fill the page.

        H - PLOT HEIGHT (CM) - This option, together with "Plot Width",
        allows you to specify the size of the graph.


                                   DATA EDITOR

        Data files may be constructed using the MVSP data editor.  This
        editor is  similar to a spreadsheet program.  Data are entered
        and presented in a tabular format, with the rows being the
        variables and the columns being the individual cases or objects.

        To use the data editor, first choose the "Manipulate Data" option
        from the main menu and specify a filename.  If that file exists,
        it will be loaded into the editor for modification; if not, you
        will be asked if you want to create a new file.  You will now be
        presented with the Data Manipulation menu.  Choose "Enter/Edit
        Data".  If you are creating a new file, you will have the option
        of reading in data from another file for modification and saving
        under the new name.

        You will next be asked to enter the maximum number of rows and
        columns needed for the data matrix.  MVSP must set aside a
        certain amount of memory for working with the data matrix.  If
        you are editing an existing data matrix and don't plan to add new
        rows or columns, then just accept the default values for rows and
        columns.  If you are adding rows or columns to either a new or
        old matrix, then enter the maximum number needed.  If you aren't
        sure of the exact number, over-estimate.  This will only cause
        MVSP to set aside some extra memory while you are editing; it
        will not have any lasting effect.

        You will also be asked to enter or modify a title for the file.
        This title identifies the data and will be printed out along with
        the results of each analysis.  You may enter up to 79 characters,
        MVSP Ver. 2.1 -- Users Manual                             Page 15

        so be as descriptive as you can.  Note, however, that the
        "Distances and Similarities" procedure uses the last few
        characters of the title to place a label on the output symmetric
        matrix file identifying the coefficient used.  If you use most or
        all of the 79 available characters, make sure no vital
        information is at the end of the title, or it will be overwritten
        by the identifier.

        Entering data labels:
        When creating a new file, you are first presented with a blank
        spreadsheet with the cursor in the upper left corner.  You must
        first enter some labels for the rows and columns.  You will
        notice that the cursor will only move about in rows and columns
        that have labels or in the next blank row or column.  This is to
        avoid having spurious values placed in areas that aren't meant
        for data.  By entering a row or column label, you are telling the
        program that this is another variable or case to include in the
        matrix.  When you enter a new label, that row or column will then
        be filled with zeros to indicate that it is now considered part
        of the data matrix.

        To enter labels, all you need to do is to start typing the label
        while the cursor is in the desired row or column.  When you start
        typing, the bottom line will display the word "INPUT>" and the
        characters you type will appear on this line.  You may edit the
        text using the backspace, cursor, insert, and delete keys, as
        described in the section "Entering and editing text" above.  Once
        you are finished typing the label, you then place the label in
        the matrix by typing one of the cursor keys (but not the Enter
        key).  This tells the editor whether the label is for a row or
        column.  Typing the up or down arrow cursor keys declare that
        label to be for a row, while a left or right arrow key indicates
        a column label.  The cursor will also move in the appropriate
        direction so that you are ready to enter another label.

        The labels themselves can be up to ten characters long and may
        consist of any printable character, except spaces.  The following
        are all valid labels:

          ROW1
          COLUMN_2
          1st-Loc.
          #3-Site

        This label is NOT valid:

          SITE 1

        It will be read as two labels, "SITE" and "1".  If you are using
        labels that begin with a number (such as 1st-Loc.), you must
        precede the label with a single or double quote (' or ") so that
        the program will know that you are not attempting to enter
        numeric data.

        Entering data:
        Once you have a few labels entered, you may start entering the
        data themselves.  This is done in a similar way to the labels;
        MVSP Ver. 2.1 -- Users Manual                             Page 16

        just start typing a number when the cursor is in the appropriate
        place.  Input of each number is finished by pressing one of the
        cursor keys or the "Enter" key.  If you enter any characters that
        cannot be converted to numeric form, an error message will be
        displayed and you may edit the input to correct the mistake.  The
        only valid characters for numeric data are '0'-'9', '-', '+',
        '.', and 'E'.  The 'E' is used for entering numbers in scientific
        notation, so that 0.00001 (1.0 x 10-5) may also be entered as
        "1.0E-05".  Binary (presence/absence) data should be entered as
        "0" and "1", with a "0" indicating absence.

        Editing labels and data:
        Editing of data and labels can be done in two ways.  In either
        case, the cursor must first be placed in the appropriate row and
        column.  Then you may either type the value anew, as you would
        for entering data, or you may use one of the editing function
        keys.  The function of each of these keys is listed at the bottom
        of the screen.  Pressing F2 will bring the datum to the bottom
        line of the screen, where it can be edited.  F3 will allow you to
        edit the row label and F4 the column label.  These can be edited
        and entered into the matrix as described above.

        Saving data matrix:
        Pressing the F9 key will save the data matrix to a file along
        with all the changes you have made so far.  I would suggest doing
        this frequently to avoid losing any changes you have made due to
        malfunction or mistakes in editing.  The F10 key will save the
        changes and exit back to the main menu.  If you decide to abandon
        the current editing session, press the ESC key.  You will first
        be asked to confirm that you want to exit, then you will be
        returned to the main menu.  All changes made since your last save
        will be lost.


                                DATA FILE FORMAT

        Data files from other sources can be imported to MVSP either
        directly or with minor editing.  If your data are in Lotus 1-2-3
        or Symphony worksheets or in files for the Cornell Ecology
        Programs (Decorana and Twinspan) then they can be imported
        directly (see page 22). Otherwise the data can be transferred as
        text files.

        Most database and spreadsheet programs have an option for
        outputting data to plain text (ASCII) files.  A word processor or
        text editor can then be used to modify the resulting files to the
        appropriate format for MVSP (mainly by adding the file header
        information, discussed below).

        Data files for MVSP must be in ASCII format.  This means that
        they should consist only of letters or numbers, spaces, and most
        other symbols represented on the keyboard.  Many word processers
        insert special formatting characters that will not be able to be
        read by MVSP.  You can check whether your word processor is one
        of these by listing a word processed file to the screen with the
        DOS TYPE command and looking for strange characters.  If your
        word processor uses these extra characters, make sure you modify
        MVSP Ver. 2.1 -- Users Manual                             Page 17

        your data files in a non-document mode that creates normal ASCII
        files.

        DATA FILE HEADER: The first line of the data file should be a
        header line, which will give the program some information about
        the data, such as the number of rows and columns.  It should look
        something like this:

        * 10 15

        This header line should begin with an asterisk ("*") in the first
        column of the first line of the file.  This asterisk tells the
        program that a header is present.  If the asterisk is not found,
        the program assumes that the header information is not present,
        and it will prompt the user for the information.  MAKE SURE that
        if this header information is present, there is an asterisk
        before it; if not, the header information will be read as data!
        The two numbers are the number of rows and columns in the data
        matrix.  The above example has 10 rows and 15 columns.

        You may also include data labels in the data file.  These labels
        will be printed on your output to help make sense of the masses
        of numbers that will be spewed out.  If labels are included, this
        must be specified in the file header.  For example:

        *L 10 15

        specifies a data file that includes data labels and that has 10
        rows and 15 columns (NOT including the labels themselves).  The
        "L" must come immediately after the "*", with no intervening
        spaces, or it will be read as the number of rows, and an error
        will occur.  The numbers of rows and columns must be separated by
        at least one space from each other.

        DATA LABELS: The format of the data labels is explained above
        under "Entering Data Labels".  When data labels are included,
        both row and column labels must be present.  The column labels
        should be in the second row of the data file, after the header
        line, and the labels should be separated by at least one space.
        The labels may be continued on to subsequent lines; the program
        will continue reading column labels until it has read as many as
        the number of columns you have specified in the header line.
        Row labels occur on the same line as the data row to which they
        apply, and should precede the first datum in that row, with a
        space separating the label and datum.

        DATA FILE TITLES: A title may also be added to your data file on
        the header line, so that you know what these data represent.
        Here's an example

        *L 10 15 Test data file for MVSP

        This title will be listed to the screen and placed on the output
        when that file is selected.  It must be separated from the other
        elements of the header by at least one space, and it cannot be
        more than 79 characters long.  The Distances and Similarities
        procedure will also place this title in the header of the matrix
        MVSP Ver. 2.1 -- Users Manual                             Page 18

        output file, along with the specification of which coefficient
        was used, so that the title is carried over to the clustering
        program.

        DATA MATRIX: The data matrix itself should consist of the data
        points separated by at least one space.  The data for one row can
        be continued on the next line.  If the number of rows or columns
        you specify is wrong, the data matrix will be read incorrectly,
        often without warning.  If you have a 10x10 matrix without labels
        and specify 9 columns by mistake, the last datum on the first row
        will be read as the first datum of the second row, and so on.
        This, needless to say, can raise havoc with your results!  All
        procedures can print out the raw data so that you can check to
        make sure it was read correctly.   Here is a complete example
        data file:

        *L 5 10 Test data set for MVSP
        COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10
        ROW1 23  2  4 53  6 45  2  3 67  5
        ROW2 10  2  4 34  1  4  3 10 20  3
        ROW3  2 34  0  1 35 12  1 90 10  9
        ROW4 98 12 10  4 10  9 10  5 20 31
        ROW5  1  7  9 11 75  7  5 21  0 10

        The input data files for the cluster analysis and PCO programs
        use a slightly different header format.  Here is an example:

        *L 15 DIS Test data set for MVSP

        Since the clustering and PCO programs use a symmetrical matrix as
        input, it only needs one number for the size of the data matrix.
        In this case the size of the matrix is 15x15.  The third element
        of the header is a three letter abbreviation specifying whether
        the matrix is a similarity (SIM) or distance (DIS) matrix.  This
        code MUST be separated from the number of objects by only one
        space, or it will not be read correctly.  The "Distance and
        Similarity" procedure of this program automatically sets up its
        output files in this manner for input into these procedures.

        Here is an example of a symmetrical input file, generated from an
        analysis of the above matrix, using the Spearman Rank Order
        Correlation Coefficient:

        *L 10 SIM Test data set for MVSP - SPEARMAN
        COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10
         1.00
        -0.15  1.00
         0.36 -0.05  1.00
         0.20 -0.97  0.05  1.00
        -0.60  0.67  0.15 -0.60  1.00
         0.30  0.21 -0.31 -0.00  0.10  1.00
         0.30 -0.05  0.97  0.00  0.10 -0.50  1.00
        -0.80  0.62 -0.41 -0.70  0.60 -0.30 -0.30  1.00
         0.82 -0.55 -0.03  0.62 -0.82  0.41 -0.10 -0.87  1.00
         0.10  0.67  0.67 -0.60  0.70  0.10  0.60  0.10 -0.41  1.00

        Note that this is a lower half matrix, with diagonals (the
        MVSP Ver. 2.1 -- Users Manual                             Page 19

        1.00's) included.  Other forms of matrices may also be specified
        for input to the clustering program, as discussed below, but this
        is the default output format of the similarities and distances
        procedure.


                                DATA MANIPULATION

        When you choose the "Manipulate Data" option from the main menu,
        you are first asked to provide an input filename.  You may then
        transpose or transform those data, convert them to other scales,
        drop rows or columns that are either selected by yourself or that
        have totals of zero.  Any combination of these options may be
        chosen.  When the Run command is chosen, a new data file will be
        produced with all the changes you have selected.  You will be
        asked to provide a name for the new file; this must be different
        from the input file.

        <Graphic placed here in printed manual>

        Transform data:
        The Transform Data option allows you to choose to have the data
        log or square root transformed before analysis.  Most of these
        procedures assume a normal distribution of the data, but this
        assumption is often not met.  Log transforming the data can
        reduce the skewness of the data (Sokal & Rohlf, 1981), resulting
        in a more interpretable analysis.  In my work with fossil plant
        data, I've found this to be invaluable, as I always have some
        samples with extremely high abundances of certain taxa, and these
        taxa tend to dominate the analysis due to their large numbers.
        Log transforming the data evens this out.  You are given the
        option of what base of logarithm to use.  Square root
        transformation is also often used when the data are in the form
        of counts.  Please note that the log transformations are
        performed on the values x+1, rather than x.  This is done to
        avoid computer errors when the data value is 0, since the log of
        0 is undefined, and to avoid negative results when the value is
        less than 1.

        The logratio transformation (Aitchison, 1986) was designed
        specifically for compositional (percentage or proportional) data.
        These data are affected by closure, in which the increase of one
        variable necessitates the relative decrease of another, even if
        the absolute value of the other doesn't change.  This can cause
        many problems in statistical analyses.  The logratio
        transformation eliminates the closure problem by replacing the
        proportions with the log of the ratio between the proportion and
        the geometric mean of the sample.  In mathematical terms, this
        is:

        x'    = log(x    / g )
          i,j        i,j    i

        where:

         x     = proportion of taxon j in the ith sample
          i,j

        MVSP Ver. 2.1 -- Users Manual                             Page 20

         x'    = transformed value
           i,j

         g     = (x   +...+x   )1/n = geometric mean
          i        i,1      i,n

         n     = number of taxa in the sample

        It should be emphasized that, for the logratio transformation to
        be calculated properly, the samples MUST be the columns of the
        data file.  Otherwise the calculations will be meaningless.

        Problems arise with the logratio transformation when some of the
        proportions are zeros, since taking the log of zero produces an
        error.  This is remedied in MVSP by replacing them with a very
        small value and then readjusting all other proportions so that
        the total is 1.0.  The replacement values are calculated using
        Aitchison's (1986, p.269) zero replacement formula.  This formula
        incorporates a maximum rounding-off value that can affect the
        final results.  You can set this value when choosing the logratio
        transformation.  The new value can be saved to the configuration
        file.  You may want to try several runs with different values to
        assess the effect.

        Transpose data:
        The "Transpose Data" option is another that is common to all
        procedures.  This allows you to transpose a matrix before
        analysis, so that the rows of the matrix are treated as columns.

        Convert data:
        Convert Data allows you to change the scale of the data to
        percentages, proportions, standardized scores, binary, the octave
        class scale, or range-through type stratigraphic data.  In
        percentage and proportional data, the values are adjusted so that
        the columns sum to 100 or 1.0 (respectively).  The standardized
        scores are adjusted by rows to zero mean and unit standard
        deviation.  Binary converts all non-zero values to 1.  It is
        sometimes useful to perform analyses on binary data to remove the
        effects of abundance on the results.

        The octave scale, which is often used in plant community ecology
        (Gauch, 1982), is a ten point abundance class scale, roughly
        based on log2.  Percentage data are converted to the classes
        based on the following scale:

            0            = 0
           >0 - 0.5%     = 1
           >0.5 - 1%     = 2
           >1 - 2%       = 3
           >2 - 4%       = 4
           >4 - 8%       = 5
           >8 - 16%      = 6
           >16 - 32%     = 7
           >32 - 64%     = 8
           >64 - 100%    = 9

        The scale was first developed as a convenience for visual
        MVSP Ver. 2.1 -- Users Manual                             Page 21

        estimation of abundances.  It may also be used to convert fully
        quantitative data to a simpler scale.  Much of the minor
        variation in abundances can be viewed as stochastic noise rather
        than significant trends (Gauch, 1982).  By breaking the data into
        ten classes this minor variation is eliminated and only the major
        'signal' is preserved.  Arguably, the multivariate methods
        provided by MVSP should also separate out these major trends,
        leaving the noise in the background but very noisy data can
        complicate this and, in ordinations, will cause the major trends
        to account for only a small proportion of the total variance.  In
        comparisons of PCAs performed on raw, octave transformed, and
        logratio transformed data, the octave scale performed equally as
        well as the logratio, with very little difference in the results
        on the first three axes (Kovach & Batten, in press).

        The range-through conversion is provided as a convenience to
        geological biostratigraphers.  In analysing the stratigraphic
        distribution of fossil organisms it is often desirable to treat
        taxa as being present in all samples between the first and last
        occurrence in a vertical sequence.  This assumes that the absence
        of a species in the middle of its range is due to ecological
        differences or sampling bias rather than the actual absence of
        the organism from the region at that time.  In performing the
        range-through conversion, it is assumed that the columns are
        samples, that they are arranged in stratigraphic order, and that
        the data values are abundance or presence-absence (with absence
        indicated by a 0).  Each row (taxon) is scanned for the first and
        last occurrence of that taxon, then those and all samples in
        between are converted to 1's, to indicate the presence of that
        species.  All other samples are left at 0.

        Drop rows and columns:
        There will often be times when you wish to analyse a subset of
        your data.  This option allows you to easily create new data
        files that are subsets of another.  When this option is set to
        "Yes" and the procedure run, you will be presented with a list of
        the row labels.  You may move the cursor around the list and mark
        the labels of the rows you wish to delete by pressing the space
        bar.  This will cause that label to be shown in reverse
        highlighting (after you move the cursor), indicating that it will
        be dropped.  You may unmark the label by pressing the space bar
        again.  When all the labels to be dropped are marked, press the
        carriage return.  You will next see a list of the column labels,
        which you can mark in the same way.  Press the carriage return
        again and a new data file will be created without those elements
        that were marked.

        Drop zero elements:
        This option will scan through the data matrix looking for and
        removing any rows or columns that have totals of zero.  Often
        when rows and columns are dropped using the previous option, some
        cases or variables are left with only zero elements.  This can
        cause problems with some procedures; the CA procedure won't work
        at all if there are any columns or rows with zero elements while
        they can distort the results of other analyses.  It is a good
        idea to set this option as well when you are choosing rows and
        columns to be deleted.

        MVSP Ver. 2.1 -- Users Manual                             Page 22

                                IMPORT/EXPORT DATA

        You can transfer data between MVSP and two other file formats.
        This is done through the "Import/Export Data" menu option.  With
        this option, you are first presented with a menu allowing you to
        specify which file format you want to use and whether to import
        or export data.  When you choose "Run", you are then asked for
        the file name, and can request a directory listing of all files
        of that format.

        CEP Files:
        These are files produced for the Cornell Ecology Program series,
        including DECORANA, TWINSPAN, as well as related programs such as
        Cajo T.F. ter Braak's CANOCO program (ter Braak, 1986).  These
        programs use a compressed data file format in which only non-zero
        abundances are included.  The data are presented in couplets,
        with the first number indicating the taxon (variable) and the
        second being the actual abundance.  The couplets for each sample
        are grouped on one or more lines, with the sample number being
        specified at the beginning of each.

        This import option works in a similar way, and replaces, the
        separate utility REFORMAT that was distributed with earlier
        version of MVSP.

        Lotus 1-2-3/Symphony Files:
        The spreadsheet files used in Lotus' programs 1-2-3 and Symphony
        can be read and written by numerous other programs, so that this
        format has become a common means of data exchange among IBM-PC
        compatible software.

        MVSP can read files produced for 1-2-3 versions 1 and 2, as well
        as Symphony version 1 files (those with the extensions .WKS,
        .WK1, and .WK2).  The files it produces are .WKS files, for 1-2-3
        version 1.

        When reading Lotus files, MVSP assumes that the data are in a
        matrix form, similar to the MVSP file format itself.  First, it
        will assume that you have a title for the data file at the top of
        the spreadsheet grid, preferably in row 1.  The next row will
        contain the column labels, with each label occurring in the same
        column as the associated data.  Next the actual data will occur,
        with each row of data (variables) on a single row of the
        spreadsheet grid and each sample in a single column.  The row
        labels occur on the same row as their associated data and occur
        before any of the data (preferably in column A).

        MVSP will scan through the file first before actually importing
        it to determine exactly where the data and labels are located, so
        there is some scope for flexibility in the placement of the data.
        However, if you follow the format specified above there is less
        chance of failure in importing the data.  After the data have
        been imported you will want to check the resulting matrix for
        columns or rows with the labels "ROWn" or "COLn", where n is a
        number.  These indicate that MVSP overestimated the extent of the
        data matrix (usually due to stray cells in the spreadsheet).
        These should be filled with zeros but if they actually contain
        MVSP Ver. 2.1 -- Users Manual                             Page 23

        data, then you will need to check the rest of the data and the
        spreadsheet for inconsistencies.

        Any formulae in the data matrix will be read as numbers, with the
        current result of the formula being placed in the MVSP file.
        Otherwise, the data are assumed to be numbers.  If any non-
        numeric data is found in the area where MVSP expects to find
        numeric data, these will be replaced with a missing value marker
        (-999999999) so that you can easily find them and replace them
        with meaningful data.  You will be warned if this has occurred
        during import.


                           RUNNING NUMERICAL PROCEDURES

        When one of the numerical procedure options (A-F on the main
        menu) are chosen, you will be asked for the name of the input
        data file.  The program will automatically add your default
        extension if none is specified.  So, if your datafile is named
        "STUDY1.MVS" and your default extension is .MVS, you need only
        type "STUDY1".  If you specify another extension, or have a
        filename with no extension, the program will recognize those as
        long as the full name is specified.  Pressing the carriage return
        while the line is blank will return you to the main menu.

        You may obtain a directory of the default data disk and path by
        typing a "?".  You may then specify a certain file mask, such as
        "*.MVS" for all files with a .MVS extension or "*.*" for all
        files.  You will then be presented with a list of all files
        matching that specification.  You can now move the cursor around
        with the cursor keys until you find the one you want, then press
        "Enter" to select that file.  If there are more files than can
        fit on one screen you can use the PageUp and PageDown keys to
        move between screens.  Pressing ESC will take you back to the
        filename prompt.

        After an input file has been selected, you will be presented with
        an "Analytical Defaults" menu.  This allows you to set a number
        of options concerning the analysis about to be performed.  The
        following is the menu for the principal components analysis
        procedure:

        <Graphic placed here in printed manual>

         The "Transform" and "Transpose Data" options work in a similar
        way to those in the Data Manipulation procedure.  All procedures
        also allow you to access the "Change Program Defaults" menu,
        described above, and to save the new defaults.  "Quit" will
        return you to the main menu, and "Run" will initiate the running
        of the procedure.

        The "Printed Output" option allows you to specify what ancillary
        information is to be output as well as the destination of the
        output.  You may select to have the raw or transformed data
        printed or other intermediary results such as the similarity
        matrix in the eigenanalysis procedures.  It is useful in initial
        analyses to see the original data to ensure they have been read
        MVSP Ver. 2.1 -- Users Manual                             Page 24

        correctly, and it can be informative to peruse the intermediate
        results.  In the eigenanalysis procedures, you can also choose to
        have the results graphed or to have the original data matrix
        sorted by first axis scores and printed.  This can be useful for
        seeing patterns in the original data.

        <Graphic placed here in printed manual>

        The "Save to WKS File" option allows you to specify that the
        resulting eigenvalues and scores from the ordination will be
        separately saved to a Lotus-format file.  This allows you to use
        a spreadsheet or graphics program to produce plots of the scores
        or to do further numerical analyses with the scores.

        Note that all the results are stored in the file, with the
        eigenvalues and percentages at the top, followed by the
        components loadings or species scores, and ending with the
        component scores or samples scores.  If you wish to transfer just
        one block of scores to your other programs you may need to edit
        the spreadsheet file and delete the unneeded rows.
        Alternatively, some programs that import Lotus files allow you to
        specify in what row and column the results start.

        The "Output Destination" menu allows you to choose whether to
        send output to the printer or a file and whether to also show the
        results on the screen.  I often find it useful to send the
        results to a file so that they can be input to other programs.
        For instance, if you have a publication quality graphics program
        available, you can edit the output file, deleting the extra text
        so that only the loadings and scores are left, and then import
        these coordinates into the graphics program for plotting, thus
        saving you from having to retype them.  You may first get a hard
        copy of the results by sending the file to the printer with the
        DOS command

            COPY filename PRN
              or
            PRINT filename

        If you have specified that the output should be sent to a file,
        you will be prompted for the name of the output file when you run
        the analysis.  If you enter a blank carriage return, this output
        file will default to the input file name plus the default output
        file extension you have specified.  The output file for an
        analysis of STUDY1.MVS will default to STUDY1.OUT if your default
        output extension is  *.OUT.

        Principal components analysis:
        This procedure performs a R-mode principal components analysis.
        The component loadings are scaled to unity, so that the sum of
        squares of an eigenvector equals 1, and the  component scores are
        scaled so that the sum of squares equals the eigenvalue.  Q-mode
        PCA will generally have the opposite scaling.  Note that many
        packages, such as SPSS and SYSTAT, perform Q-mode PCA, and thus
        their eigenvectors will be scaled to the eigenvalue, rather than
        unity.  For details on the computation and assumptions of the
        technique, see Orloci (1978), Gauch (1982), Pielou (1984), Manley
        MVSP Ver. 2.1 -- Users Manual                             Page 25

        (1986), and Jolliffe (1986).  Orloci and Jolliffe give detailed
        mathematical discussion of PCA, while Gauch, Pielou and Manley
        give very clear and understandable discussions of the basis of
        the technique and its use and assumptions.

        In the R-mode analysis, similarity coefficients are calculated
        for the descriptors (or variables), which are the rows of the
        matrix and component scores are calculated for the objects (or
        cases), which are the columns of the matrix.

        STANDARDIZATION AND CENTRING - The Analytical Defaults menu has
        two options that affect how the PCA is calculated.  You may
        choose to standardize the similarity matrix before eigenanalysis
        (thus creating a correlation rather than a covariance matrix),
        and you may use either a centred or uncentred data matrix.
        Generally a centred covariance matrix is used, but if different
        units of measurement are used in the data matrix, these will need
        to be standardized, and thus a correlation matrix should be used.
        Standardization may also be desired in ecological studies to
        reduce the effects of dominant species, so that rarer species
        play a greater role in the resulting configuration.  An uncentred
        data matrix is called for when there is appreciable between-axes
        heterogeneity.  This means that different clusters of points are
        associated with different axes, and have little projection on
        other axes.  This often occurs when different groups of samples
        have completely different sets of common species, with little
        overlap.  See Noy-Meir (1973) and Pielou (1984) for more on this
        phenomenon.

        MINIMUM EIGENVALUE - You may also specify the minimum eigenvalue
        for which components are printed out.  The possible options are
        to have all components printed, only those above a certain
        eigenvalue that you supply, or to base the minimum eigenvalue on
        one of two rules.  Kaiser's rule states that the minimum
        eigenvalue should be the average of all eigenvalues (or 1 if the
        correlation matrix is used).  This is often considered a good
        rule of thumb for determining whether a component is
        interpretable (Legendre & Legendre, 1983).  Jolliffe (1986)
        proposed a modification of this rule in which the minimum
        eigenvalue is 0.7 times the average eigenvalue.  This will
        usually give one or more extra components over Kaiser's rule.

        ACCURACY - The accuracy and speed of the eigenanalysis can be
        controlled by using the "Accuracy of Solution" option.
        Eigenanalysis in MVSP is performed using the cyclic Jacobi
        method, which is an iterative procedure that makes repeated
        passes through the matrix improving the accuracy of the solution.
        The iterations stop when a certain level of accuracy, which is
        supplied by the user, is reached.  Greater accuracy in the
        solution means that more passes must be made through the matrix,
        therefore the program takes longer to run.  The accuracy level
        that you supply to MVSP usually turns out to be roughly equal to
        the number of correct significant digits in the loadings and
        scores of the most important components (those greater than 10%
        of the total variance), so that a level of 1.0 x 10-6 means that
        these should have roughly six significant digits.  You can
        experiment with different levels to determine the trade-offs
        MVSP Ver. 2.1 -- Users Manual                             Page 26

        between speed and accuracy.

        RUNNING THE ANALYSIS - Choosing "Run" will initiate the analysis.
        Status messages will be listed to the screen during the analysis
        to let you know how things are proceeding.  When it is done, the
        eigenvalues and their percentage of the total variation will be
        printed along with the component coefficients (or eigenvectors),
        then the component scores for each principal component will be
        calculated and printed.

        If you have chosen to have the results graphed and have provided
        a set number of axes to plot through the Graphics Options menu,
        then these plots will be produced automatically.  If the "Plots
        Per Analysis" option on the Graphics Options menu has been set to
        "Ask", you will first be prompted to enter the number.  Entering
        a zero will bypass the plotting procedure.  See the Graphics
        Option section above for more details about plotting in MVSP.

        Principal coordinates analysis:
        Principal coordinates analysis (PCO) is a generalized form of
        PCA.  Whereas PCA implicitly uses either a covariance or
        correlation matrix, PCO allows you to input any matrix of metric
        values.  PCO may be used with any of the distances calculated by
        MVSP except for the squared Euclidean distance.  Of the
        similarity measures only Gower's is metric.  PCO is calculated as
        a Q-mode eigenanalysis, therefore it only gives the eigenvectors,
        not scores.  Note that a PCO of Euclidean distances will give the
        same results as a Q-mode PCA.

        Many of the options available for PCA are not applicable to PCO.
        There is one new option:

        MATRIX INPUT - A matrix of distance measures must first be
        calculated using the "Distances and Similarities" procedure (see
        below).  This matrix is then read by the PCO procedure and the
        eigenvalues and eigenvectors are calculated.  A number of
        different input formats are available, including various forms of
        half matrices and full matrices.  This defaults to the same form
        specified in the "Matrix Output" option of the "Distances and
        Similarities" procedure.

        Correspondence analysis:
        The correspondence analysis (or reciprocal averaging) procedure
        performs several varieties of correspondence analysis (Pielou,
        1984; see also Hill, 1973, Gauch, 1982, Greenacre, 1984),
        including detrended correspondence analysis (DCA; Hill & Gauch,
        1980).  Correspondence analysis in general is well suited for
        working with count or presence/absence data, whereas PCA is
        geared more towards measurement data on a continuous scale
        (although PCA can also be performed on count and binary data;
        Jolliffe, 1986).

        DCA was developed by Hill and Gauch (1980) in order to correct
        two flaws in most ordination techniques.  The "arch effect" or
        "horseshoe effect" is a common feature of most ordinations.  This
        is manifested by the points on the ordination plot being arranged
        along an arch on the first two axes, rather than a straight line
        MVSP Ver. 2.1 -- Users Manual                             Page 27

        as expected if the first axis represents a gradient.  This is a
        artifact of the data reduction process that occurs in ordination
        and represents a mathematical relationship between the first two
        axes, which are supposed to be independent.  As a result of this
        arch, the second flaw occurs in which the points at either end of
        the first axis are closer together than those in the middle.
        These flaws also occur in subsequent axes.

        DCA was designed to remove this arch from the ordination diagram.
        It does this by dividing the first axis into a number of
        segments, then adjusting the scores of the points on the second
        axis so that the mean score within each segment is the same.
        Thus it is like cutting the plot into a number of vertical strips
        and moving each up and down until the points are in a straight
        line.  The scores are also adjusted along the first axis so that
        they are more evenly spread.

        This method can often give more interpretable results, but it can
        also introduce distortion of its own.  It is always a good idea
        to try both regular and detrended correspondence analysis on a
        data set and compare the results.

        Detrended correspondence analysis assumes that the actual data
        being analysed are abundances of a set of variables (taxa in an
        ecological study) in a set of samples.  Presence/absence data may
        also be used (entered as 0 and 1), but the none of the data may
        be negative.  It is also assumed that the samples come from a
        gradient in which different variables (taxa) characterize
        different parts of the gradient.  Although it is most commonly
        used in ecology, this method may also be used in other fields
        where these assumptions hold, such as archaeology or market
        research.

        Many of the options in CA/DCA are similar to those in the PCA
        procedure.  There are several new ones:

        ALGORITHM - MVSP normally uses the cyclic Jacobi method of
        calculating ordinations.  This method calculates the scores for
        all axes simultaneously. However, the detrending process cannot
        be performed with this algorithm, since each axis must be
        detrended against the final scores of the previous axis.  Thus an
        alternative algorithm can be used in which the solution for each
        axis is calculated separately.  This is done using the reciprocal
        averaging method described by Hill (1973).  The two algorithms
        are referred to as "Cyclic Jacobi" and "Reciprocal Averaging"
        respectively.

        Reciprocal averaging must be used if detrending is desired.  You
        may also want to use the algorithm for non-detrended analyses as
        well.  The algorithm only extracts the first four axes and is
        usually much faster than the eigenanalysis by the cyclic Jacobi
        algorithm, which must extract all axes.  This is most pronounced
        with large data sets.  However, you often need to see more than
        the first four axes, particularly if the first four do not
        account for much of the total variability in the data set.  Also,
        in cases where two or more of the axes have similar eigenvalues
        the reciprocal averaging method may not give accurate results.
        MVSP Ver. 2.1 -- Users Manual                             Page 28

        If this happens a warning message will be displayed.

        The actual scores produced using the two algorithms will differ,
        because the scaling is different, but the actual configuration on
        a plot will be the same.  The scores produced by the reciprocal
        averaging method will be scaled to the standard deviation of the
        species abundance along the gradient represented by the axis.  If
        we assume species abundance along a gradient is normally
        distributed, then a species will appear, rise to its highest
        abundance, and disappear in about 4 standard deviation units
        (sd).  Thus if the ordination axis is relatively short (less than
        3-4 sd units) then the species turnover along the gradient will
        be low, whereas long axes (say 12 sd units) will probably have
        completely different sets of species at either end.  Following
        Hills' original DECORANA program, the sd units are multiplied by
        100, so a distance of 400 along the axis represents 4 sd units.
        The scaling of the axes produced by the eigenanalysis algorithm
        will be related to the original species abundances, unless the
        option is chosen to scale them to percentages.

        DETRENDING - This option invokes the detrending procedure.  It
        can only be used with the reciprocal averaging algorithm and the
        setting of the algorithm option will be changed when this option
        is chosen.

        WEIGHTING - When using the Jacobi algorithm, the analysis can be
        run with a weighting of either the rare or the common species.
        See Orloci (1978, pp. 152-168) for details of these methods of
        weighting.  Also, the scores can be adjusted to percentages.  The
        data file should have species as the rows and samples as the
        columns, as in the PCA procedure.

        DOWNWEIGHT RARE SPECIES - MVSP follows Hill's DECORANA program in
        allowing the rare species to be downweighted before the analysis.
        This is only available when the reciprocal averaging algorithm is
        used.  It can be useful if you want most weight to be given to
        the common species, but you still want to see how the rarer taxa
        are affected.  Those taxa that occur in fewer than 1/5 the number
        of samples that the most common taxon occurs in will be
        downweighted.  The amount that the species is downweighted is
        related to its frequency of occurrence.

        SEGMENTS FOR DETRENDING - This option sets the number of segments
        the axis should be divided into for the detrending process.  The
        default value, 26, should be adequate for most analyses, but if
        the detrending does not seem to be as effective as it could be a
        larger number can be tried.

        RESCALING CYCLES - When detrending is in force, the axes can also
        be rescaled so that the points at the end are not closer together
        than those in the middle. This rescaling is done several times
        and this option allows you to vary the number of times.  It is
        generally not advisable to change this from the default of 4,
        however, as further rescaling may reduce the effectiveness of the
        ordination.  Rescaling may be bypassed by entering 0 for this
        option.

        MVSP Ver. 2.1 -- Users Manual                             Page 29

        Distances and similarities:
        This procedure calculates a variety of distance and similarity
        measures.  The distances are calculated between the columns of
        the data matrix.  An option to transpose the data matrix is
        included, to allow analysis of the rows without requiring re-
        entry of the data.  There are numerous publications that discuss
        different type of measures.  I have relied on the following in
        implementing the formulae used in this procedure:  Prentice
        (1980), Sneath & Sokal (1973), Pielou (1984), Greig-Smith (1983),
        Gordon (1981), and Everitt (1980).  You may refer to these for
        details about the measures provided in MVSP.

        MATRIX OUTPUT -  This procedure is set up to allow easy input of
        the resulting symmetric matrices into the cluster analysis and
        PCO procedures.  If you choose to input the distance matrix into
        these, a copy of it, along with the appropriate header
        information, will be put into a file.  This matrix file can then
        be used as input to the other analyses.  When the procedure is
        run, another filename must be specified for this matrix file.
        This filename defaults to the symmetric matrix default extension.
        You may use the matrix output option to specify the type of
        matrix (e.g. upper or lower half matrix, diagonal present or
        absent).

        COEFFICIENT - There are presently eighteen measures available.
        These, and their formulae, are listed below.  In these formulae,
        i and j represent two columns of the data matrix, k represents
        the rows, and therefore X   would be the datum in the kth row of
                                 ik
        column i.  Following the name of each measure is the marker
        placed in the output file created by the "Distances and
        Similarities" procedure (see section on "Data file format").
        This marker identifies the coefficient that was used to calculate
        the matrix.  It is checked by the cluster analysis procedure when
        the minimum variance strategy is used.  Minimum variance
        clustering can only be performed on squared Euclidean distances,
        so this marker allows the program to ensure that the correct
        distance is being used.

        Euclidean distance (EUCLID):

                             2 ½
        Ed   = (S (X   - X  ) )
          ij     k  ik    jk

        Squared Euclidean distance (SEUCLID):

                               2
          SEd   = S (X   - X  )
             ij    k  ik    jk

        Standardized Euclidean distance (STEUCLID):

                                      2 ½
           StEd   = (S (X   - X  /sd ) )
               ij     k  ik    jk   k

        MVSP Ver. 2.1 -- Users Manual                             Page 30

                where:  sd  = standard deviation of all the elements of k
                          k

        Cosine theta (or normalized Euclidean) distance (COSINE):

                                             2 ½
           CTd   = (Sk((X  /ss ) - (X  /ss )) )
              ij     k   ik   i      jk   j

                                     2 ½
                where: ss  = (S (X  ) )
                         x     x  xk

        Manhattan metric distance (MANHAT):

           MMd   = S  |X   - X  |
              ij    k   ik    jk

        Canberra metric distance (CANBER):

           CMd   = S  (|X   - X  | / (X   + X  ))
              ij    k    ik    jk      ik    jk

        Chord distance (CHORD):

                         ½      ½ 2 ½
           Cd   = (S (X    - X   ) )
             ij     k  ik     jk

        Chi-square distance (formula X2 of Prentice, 1980) (CHISQR):

                                  2        ½
           CSd   = (S ((X   - X  ) /S X  ))
              ij     k   ik    jk    l lk

        Average distance (AVERAGE):

                                  2   ½
           Ad   = ((S (X   - X  )) /n)
             ij      k  ik    jk

                where: n = number of elements in each variable (i or j)

        Mean character difference distance (MEANCHAR):

                                       ½
           MCDd   = ((S |X   - X  |)/n)
               ij      k  ik    jk

                where: n = number of elements in each variable (i or j)

        MVSP Ver. 2.1 -- Users Manual                             Page 31

        Pearson product moment correlation coefficient (PEARS):

                                      _           _
                             S (X   - X  ) (X   - X )
                              k  ik    i     jk    j
           PCC   =  ----------------------------------------
              ij                  _  2 ½           _  2 ½
                        (S (X   - X ) )  (S (X   - X ) )
                          k  ik    i       k  jk    j

        Spearman rank order correlation coefficient (SPEAR):

                                           2
                            6 S (R   - R  )
                               k  ik    jk
           SCC   = 1 -    -----------------------
              ij                    3
                                   n  - n

                where: R = rank order of element in variable

        Percent similarity coefficient (PERCENT):

                            S  min(X  , X  )
                             k      ik   jk
            PSc   =  200   --------------------
               ij              S (X   + X  )
                                k  ik    jk

                where: min = minimum of two values

        Gower general similarity coefficient (GOWER):

                        S (w    s   )
                         k  ijk  ijk
           GGSc   =   ------------------
               ij           Skw
                               ijk

                                   |x   - x  |
                                     ik    jk
               where: si   = 1 -  -------------  for quantitative data,
                        jk          range(k)

                           = 1 for matches of binary or multistate data,
                           = 0 for all mismatches
                   w       = 0 for negative matches of binary data,
                    ijk    = 1 in all other situations

        For this coefficient, the data type for each variable (row) must
        be declared.  This is done through the first two characters of
        the data labels:  those beginning with "B_" are taken to be
        binary, those with "M_" multistate, anything else is considered
        quantitative.  For instance a variable indicating the presence or
        absence of sepals in a flower would have the label B_SEPAL, that
        indicating the colour of the petals (one of four possible) would
        be named M_COLOUR, and petal length would be recorded in the row
        MVSP Ver. 2.1 -- Users Manual                             Page 32

        with the label LENGTH.

        The following binary (presence/absence) coefficients are based on
        a table of frequency of matches and mis-matches of the presence
        or absence of a single variable.  The binary data should be
        entered into the data matrix as 0 (zero) and 1 (one).  Any number
        that is not zero is also treated as a one, indicating presence.

                                                Sample j

                                        Presence        Absence
                                       ┌───────────────────────┐
        Sample i        Presence       │   a                b  │
                                       │                       │
                        Absence        │   c                d  │
                                       └───────────────────────┘

        Sorensen's coefficient (SOREN):

           Sc   = 2a / (2a + b + c)
             ij

        Jaccard's coefficient (JACCA):

           Jc   = a / (a + b + c)
             ij

        Simple matching coefficient (MATCH):

           SMc   = (a + d) / (a + b + c + d)
              ij

        Yule coefficient (YULE):

           Yc   = (ad - bc) / (ad + bc)
             ij

        Cluster analysis:
        This procedure performs hierarchical agglomerative cluster
        analysis of an input matrix of distance or similarity measures.
        Seven forms of clustering are presently available: the four
        average linkage procedures (unweighted pair group, unweighted
        centroid, weighted pair group, and weighted centroid [or
        median]); nearest and farthest linkage, and minimum variance.
        The actual algorithm is based on Lance & William's (1966)
        generalized clustering procedure.  For clear and concise
        explanations of the theory and practice behind cluster analysis,
        see Sneath and Sokal (1973), Everritt (1980), Grieg-Smith (1983),
        and Pielou (1984).

        MATRIX INPUT - A number of different input formats are available,
        including various forms of half matrices and full matrices.  This
        defaults to the same form specified in the Matrix Output option
        of the Distances and Similarities procedure.

        TREE DESCRIPTION FILE - When the clustering is finished, you can
        have a description of the resulting dendrogram output to a file.
        MVSP Ver. 2.1 -- Users Manual                             Page 33

        This description is in the form of labels enclosed in parentheses
        and commas, which delimit the clusters.  Also after each label
        and closing bracket is the distance between that object or group
        and the next in the hierarchy.  An example of this description
        is:

        ((LENGTH:125.71,WIDTH:125.71):170.50,HEIGHT:296.21);

        This would correspond to a dendrogram of the form:

        <Graphic placed here in printed manual>

        Christopher Meacham has written a program called PLOTGRAM which
        can be used to plot dendrograms and cladograms described in the
        above format.  For PLOTGRAM to properly read the description
        produced by MVSP, the following two options must be set:

           DIAGRAMTYPE Y
           TIPS Y

        Plotgram is no longer included with MVSP, since MVSP can now
        automatically plot dendrograms (see below).  If you wish to get a
        copy of Plotgram that will work with MVSP-generated files, one
        may be obtained, along with the Pascal source code, at cost from
        Kovach Computing Services.  We cannot, however, provide support
        for the program or endeavour to add new types of printers.

        TREE ORDER FILE - MVSP can also produce a file in which the data
        labels are listed in the order they occupy in the dendrogram.
        This type of file can be read by the program SORTDATA, which
        accompanies the registered version of MVSP.  This program is
        useful for producing combination dendrograms in which two
        dendrograms, one for the columns of the data matrix and another
        for the rows, are plotted together with the original data matrix
        in between in graphic form (see example below; also Kovach,
        1988a,b; 1989 and Duigan & Kovach, 1991).  This allows you to see
        how the data are affecting the clustering.  See the Utilities
        section below for details about SORTDATA.

        <Graphic placed here in printed manual>

        RANDOMIZE INPUT ORDER - There have recently been some suggestions
        (Bayer, 1985; Lespérance, 1990) that input order of the data
        matrix can affect the results of clustering with certain types of
        data sets.  Changing the input order can not only change the
        order of objects in the dendrogram but more importantly can also
        cause some objects to be joined to different clusters.  This is
        particularly possible when two or more pairs of objects have
        identical similarities either at the beginning or after
        recalculation during the clustering procedure.

        Normally the clustering procedure scans through the similarity
        matrix sequentially looking for the next pair of objects to fuse.
        Choosing the "Randomize" option causes the matrix to be scanned
        in a random order which changes each time the procedure is run.
        In order to check for chaotic behaviour in clustering, try
        running two or three clusterings of the same data matrix with
        MVSP Ver. 2.1 -- Users Manual                             Page 34

        this option set, then compare the dendrograms.  Note that changes
        in the actual order of objects in the dendrogram are to be
        expected; a cluster diagram can be viewed as a 'mobile' hanging
        from a ceiling in which the different clusters can rotate around.
        It is the branching order in the dendrogram that is important and
        this is what should be compared when testing for chaotic
        behaviour.

        CONSTRAINED CLUSTERING - As stated above, normally the actual
        order of objects in the dendrogram is not important.  However, if
        you are working with sequential data (such as in stratigraphic
        geological studies), a special constrained form of cluster
        analysis can be used (Birks & Gordon, 1985; Kovach, in press).
        When this option is chosen, clustering proceeds as usual except
        that the objects to be fused are constrained to be adjacent in
        the data matrix.  Therefore, the dendrogram that is produced will
        have the objects in the same order as the input matrix.

        This type of constraint can often cause distortion in the
        dendrogram.  In particular, reversals often occur where the
        distance (and therefore the branching level) between two objects
        is greater than that between the cluster of those two and the
        next object in the hierarchy.  In sequences where there is a lot
        of variability, this can cause the dendrogram to be almost
        uninterpretable.

        OUTPUT - The output of the procedure consists of a report of the
        status of the clustering procedure as each new object is added to
        the cluster.  The average similarity or distance of the two
        groups that have just been joined is printed out, along with a
        listing of the two groups and the number of objects in the newly
        fused group.  If a single object is added to another cluster, the
        label for that object (or a numerical label corresponding to its
        position in the data matrix) is printed out.  If a whole group is
        added, the node at which that group was last added to is printed
        out.  For instance, a report such as:

                                                   NUMBER OF OBJECTS
        NODE   GROUP 1   GROUP 2    DISSIMILARITY   IN FUSED GROUP
          1     LENGTH      WIDTH         125.706        2
          2     NODE 1     HEIGHT         296.206        3

        would correspond to the dendrogram shown previously.

        The results of the cluster analyses are also automatically
        displayed as dendrograms.  These may either be text-based or
        drawn in graphics mode, depending on the setting of the
        "Scatterplot/Dendrogram Type" option of the "Graphics Output"
        menu (under the "Program Defaults" menu).  The text-based
        dendrograms will automatically be directed to the same file or
        printer that the results are going to.  Graphics dendrograms may
        be printed by pressing "P" when the dendrogram is on the screen.
        See the "Printer Setup" options on page 13 for more information.

        Diversity indices:
        This procedure computes three diversity indices commonly used in
        ecology, Simpson's, Shannon's, and Brillouin's.  See Pielou
        MVSP Ver. 2.1 -- Users Manual                             Page 35

        (1969) for a discussion of the use and derivation of these
        indices.

        The input data file should be set up with species as rows and
        samples as columns.  The diversity, then, is calculated for each
        column.  Be forewarned that the Brillouin index calculates
        factorials of the species abundances, and if any of your
        abundances are high, this could take a very long time!  For
        abundances greater than 1000 the factorial is estimated using
        Stirling's formula, which is much faster and, at these
        abundances, provides a close approximation.

        The LOG BASE option allows you to specify whether to use
        logarithms to the base 10, 2, or e.  The output consists not only
        of the diversity index, but also the number of species and the
        evenness, which is defined as the diversity divided by the log of
        the number of species.


                                    UTILITIES

        Sortdata:
        In many of my analyses I perform clusterings of both the samples
        and species.  I've found it very valuable to present the
        resulting two diagrams with the original data matrix in between,
        sorted in the order of the dendrograms.  The data can be split
        into abundance classes, which are represented by different
        characters, so that the differing abundances can be seen at a
        glance.  In this way the structure revealed by the cluster
        analyses can be seen directly in the data matrix (see Kovach,
        1988a,b; 1989 for some examples).  SORTDATA is a utility I've
        written to help produce these diagrams.  It is only included with
        the registered version of MVSP.

        To produce one of these combination diagrams, you must first run
        two cluster analyses of the same data matrix, one with the matrix
        transposed, the other not.  Make sure that the "Tree Order"
        option is turned on.  This will produce two files with the order
        of the objects in the dendrogram for SORTDATA.  Next run SORTDATA
        with the following parameters:

         SORTDATA datafile.MVS order1.ORD order2.ORD [output.SRT]

        where "datafile.MVS" is your original data file used for input to
        the distance and similarity procedure, "order1.ORD" and
        "order2.ORD" are the tree order files for analyses of the
        transposed and non-transposed matrices, and "output.SRT" is the
        file that will contain the sorted data matrix.  If "output.SRT"
        is missing the output will be put into a file named "datafile"
        with a .SRT extension.

        When the program is run, it will first read the original data
        matrix, determine the lowest and highest data values, and then
        ask you to define the ranges of four data classes.  First you
        must enter the value below which no symbol is plotted; if your
        data are counts, this value will be 1.  Then enter the cutoff
        points between the four classes.  When you are done the program
        MVSP Ver. 2.1 -- Users Manual                             Page 36

        will sort the data and translate them to the abundance classes,
        placing the results in a file.

        To assemble the resulting diagram, you must first print out the
        sorted data matrix.  You can use your word processor to print it,
        perhaps adjusting the character font (pica, elite, or condensed)
        and the line spacing to fit the diagram on one page.  Then
        measure the width and length of the matrix and use MVSP to
        produce the dendrograms, setting the "Plot Height" and "Plot
        Width" parameters on the "Printer Setup" menu to the appropriate
        length (in cm) so that the dendrogram will be the same size as
        the sorted data matrix.  Alternatively you can reduce or enlarge
        dendrograms you've already plotted with a photocopier or
        photographically.  The whole diagram may then be assembled on a
        large (A3 or 11"x17") piece of paper.

        To obtain the registered version of MVSP, with the SORTDATA
        utility, see page 4, the REGISTER.DOC file, or the "Register"
        option on the main menu.


                                    DISCLAIMER

        The accuracy of this program has of course been extensively
        tested against the results of other programs.  However,
        unforeseen errors in computation can and have crept up even in
        the most sophisticated and widely used statistical packages.  You
        may wish to initially run comparisons with the results of other
        programs, using your own data set, to ensure that it is working
        properly with your type of data.

        Note when running comparisons that there are often many methods
        of computing the same routine, and results may vary, especially
        in the more complex eigenanalysis procedures.  In principal
        components analysis, for instance, there are numerous ways of
        transforming the data before eigenanalysis (see Greig-Smith,
        1983, pp. 247ff), and the component loadings can be scaled either
        to unity (as they are here) or to the variance of that principal
        component, or in other manners.  Also, the eigenanalysis can
        rotate the cloud of points in different directions, so that signs
        of the scores are reversed and the actual values different.  The
        configuration of the points will be the same, however.

        If you do run into any problems with this program, whether they
        be in the results or abnormalities in the running of the program,
        please contact me by post or through electronic mail at the
        addresses given on the cover page.  Please give full details of
        the problem and, if possible, the data set which you were running
        when the bug cropped up.

        Please note that no warranty is given for this program.  The
        author (Warren L. Kovach) shall not be legally liable for any
        damages or lost profits arising from use or misuse of this
        program.   Refer to the "Limited Warranty" section on page 5 for
        full details.


        MVSP Ver. 2.1 -- Users Manual                             Page 37

                                  80x87 SUPPORT

        If you aren't satisfied with the speed of this program, a faster
        version that uses the 80x87 math coprocessor is distributed with
        MVSP Plus, the registered version of MVSP.  This coprocessor
        (which is an optional chip that can be plugged into your
        computer) greatly speeds up the processing of real number,
        floating point arithmetic.  Often this increase in speed can
        amount to 10 times!  This is particularly noticeable for
        calculation that use logarithms and trigonometric calculations.
        The calculation of the Brillouin diversity index, which uses log
        factorials, for an 84x84 matrix took 9 minutes 14 seconds without
        a math chip but 2 minutes 41 seconds with one.  A PCA, which uses
        mostly arithmetic operations, of a 45x45 data matrix took one
        hour with the standard version of the program, but only twenty
        minutes with the 80x87 version (tests run on a 12 MHz 80286 based
        Compaq Portable III).

        Borland Pascal, the compiler used in developing MVSP, has an
        option for creating programs that take advantage of this
        processor.  The programs compiled using this option will only
        work on machines that have the 80x87 installed.  The installation
        program will detect whether your computer has a math chip and
        will install the appropriate version.

        To obtain the registered version of MVSP, with 80x87 support, see
        page 4, the REGISTER.DOC file, or the "Register" option on the
        main menu.


                              PROTECTED MODE VERSION

        New with MVSP ver. 2.1 is a special protected mode version.  It
        is only provided with MVSP Plus, the registered version of MVSP.
        This is compiled to run in what is called "protected mode" on the
        Intel 80286, 80386, 80486, and Pentium microprocessors.  The
        primary advantage in using protected mode, as opposed to the
        "real mode" which is compatible with the older 8088 and 8086
        chips, is that all of the RAM memory in the machine can be
        directly accessed, whereas real mode programs are limited to
        640Kb of RAM memory.  So, if you have 16 Mb of RAM in your
        computer MVSP in protected mode can directly use all of it for
        storing data while calculating.  Under real mode, MVSP would have
        to dump parts of large arrays onto disk while calculating, which
        slows down the process tremendously.  For example, a cluster
        analysis of a 400x400 matrix, which needs to store 937kb of data
        on disk under real mode, took 191 minutes whereas the same
        analysis under protected mode took only 41 minutes. (test run on
        a 16MHz 386SX based machine with 5Mb RAM).

        MVSP Protected Mode requires a computer with a 80286 or higher
        microprocessor and at least 2 Mb of RAM.  If your computer has
        these capabilities, then the MVSP installation program will give
        you the option of installing the protected mode version as well.

        The protected mode version of MVSP was produced using Borland
        International's Borland Pascal 7.0 compiler.  The program runs
        MVSP Ver. 2.1 -- Users Manual                             Page 38

        under the DPMI (DOS Protected Mode Interface) standard.  This
        requires that a DPMI compatible server is installed. Some 386
        memory managers (such as QEMM 386) provide optional DPMI support,
        as does Microsoft Windows 3.x in enhanced mode.  If you do not
        have a DPMI server installed, then Borland's server will
        automatically be loaded and used.  You need do nothing except
        type the command MVSPPROT at the DOS prompt.

        For MVSP Protected Mode to work properly, two files must be
        present in the same directory as the MVSPPROT.EXE program.  These
        are DPMI16BI.OVL and RTM.EXE.  These are files produced by
        Borland International.  They will be automatically installed
        along with MVSP Protected Mode.  Accompanying them is a
        documentation file called DPMIUSER.DOC that explains more about
        running protected mode programs, as well as discussing some other
        utility programs that are included with MVSP Protected Mode.  If
        you have any problems running the protected mode version refer to
        this documentation file first.

        To obtain the registered version of MVSP, with the protected mode
        version, see page 4, the REGISTER.DOC file, or the "Register"
        option on the main menu.


                                    APPENDICES

        The printed manual with the registered version of MVSP has
        several large appendices at this point, describing the example
        data files, listing error messages and their meanings, explaining
        the format of the configuration file, and giving information on
        efficient memory management.  These have been omitted from the
        shareware version for brevity.

        MVSP Ver. 2.1 -- Users Manual                             Page 39

                                    REFERENCES

        Aitchison, J., 1986.  The Statistical Analysis of Compositional
        Data.  Chapman and Hall, London.

        Bayer, U., 1985.  Lecture notes in earth sciences. 2 Pattern
        recognition problems in geology and palaeontology.  Springer-
        Verlag.

        Birks, H.J.B. & Gordon, A.D., 1985.  Numerical Methods in
        Quaternary Pollen Analysis.  Academic Press, London.

        Cooke, D., Craven, A.H., & Clarke, G.M., 1982.  Basic Statistical
        Computing.  Edward Arnold (Publishers) Ltd., London.

        Davis, J.C., 1986.  Statistics and Data Analysis in Geology, 2nd
        Edition.  John Wiley & Sons, New York.

        Duigan, C. A. & Kovach, W.L., 1991.  A study of the distribution
        and ecology of littoral freshwater chydorid (Crustacea,
        Cladocera) communities in Ireland using multivariate analyses.
        Journal of Biogeography, 18:267-280.

        Everitt, B., 1980.  Cluster Analysis.  2nd Edition.  Gower
        Publishing Co., Hampshire, 136 pp.

        Gauch, H.G. Jr., 1982.  Multivariate Analysis in Community
        Ecology.  Cambridge University Press, New York.

        Gordon, A.D., 1981.  Classification.  Chapman and Hall, London.

        Greenacre, M.J., 1984.  Theory and applications of correspondence
        analysis.  Academic Press, London.

        Greig-Smith, P., 1983.  Quantitative Plant Ecology.  University
        of California Press, Berkeley.

        Hill, M.O., 1973.  Reciprocal averaging: An eigenvector method of
        ordination.  Journal of Ecology, 61:237-249.

        Hill, M.O., & Gauch, H.G. Jr., 1980.  Detrended correspondence
        analysis: An improved ordination technique.  Vegetatio, 42:47-58.

        Jolicoeur, P., & Mosimann, J.E., 1960.  Size and shape variation
        in the Painted Turtle.  A principal component analysis.  Growth,
        24:339-354.

        Jolliffe, I.T., 1986.  Principal Components Analysis.  Springer-
        Verlag, New York.

        Kent, M., & Coker, P., 1992.  Vegetation description and
        analysis. A practical approach.  Belhaven Press, London.

        Kovach, W. L., 1988a.  Multivariate methods of analyzing
        paleoecological data.  In: W. A. DiMichele & S. L. Wing (eds.),
        Methods and applications of plant paleoecology.  The
        Paleontological Society Special Publication, 3:72-104.

        MVSP Ver. 2.1 -- Users Manual                             Page 40

        Kovach, W.L., 1988b.  Quantitative palaeoecology of megaspores
        and other dispersed plant remains from the Cenomanian of Kansas,
        USA.  Cretaceous Research, 9:265-283.

        Kovach, W.L., 1989. Comparisons of multivariate analytical
        techniques for use in pre-Quaternary plant paleoecology.  Review
        of Palaeobotany and Palynology, 60:255-282.

        Kovach, W.L., in press.  Multivariate techniques for
        biostratigraphical correlation.  Journal of the Geological
        Society, London.

        Kovach, W.L. & Batten, D.J., in press.  Association of
        palynomorphs and palynodebris with depositional environments:
        quantitative approaches.  In: Traverse, A. (ed.), Sedimentation
        of Organic Particles.  Cambridge University Press.

        Lance, G.N. & Williams, W.T., 1966.  A generalized sorting
        strategy for computer classifications.  Nature, 212:218.

        Legendre, L., & Legendre, P., 1983. Numerical Ecology.  Elsevier
        Scientific Publishing Company, New York.

        Lespérance, P.J., 1990.  Cluster analysis of previously described
        communities from the Ludlow of the Welsh Borderland.
        Palaeontology, 33:209-224.

        Manly, B.F.J., 1986.  Multivariate statistical methods.  A
        primer.  Chapman & Hall, London.

        Noy-Meir, I., 1973.  Data transformations in ecological
        ordination. I. Some advantages of non-centering.  Journal of
        Ecology, 61:329-341.

        Orloci, L., 1978.  Multivariate Analysis in Vegetation Research,
        2nd edition.  W. Junk, Boston.

        Pielou, E.C., 1969.  An Introduction to Mathematical Ecology.
        Wiley-Interscience, New York.

        Pielou, E.C., 1984.  The Interpretation of Ecological Data.
        Wiley-Interscience, New York.

        Prentice, I.C., 1980.  Multidimensional scaling as a research
        tool in Quaternary palynology: A review of theory and methods.
        Review of Palaeobotany & Palynology, 31:71-104.

        Sneath, D.H., & Sokal, R.R., 1973.  Numerical Taxonomy.  W.H.
        Freeman & Co., San Francisco.

        Sokal, R.R. & Rohlf, F.J., 1981.  Biometry.  2nd Edition.  W.H.
        Freeman & Co., San Fransisco.

        ter Braak, C.J.F., 1986.  Canonical correspondence analysis: A
        new eigenvector technique for multivariate direct gradient
        analysis.  Ecology, 67:1167-1179.

        MVSP Ver. 2.1 -- Users Manual                             Page 41

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        Coming soon: Oriana - Orientation analysis for the IBM-PC and
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        This program calculates circular statistics on orientation data
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        Coming soon: Rarefact - Rarefaction analysis for the IBM-PC and
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        This program estimates ecological diversity while taking into
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