Statistics Tutorials Based on the Use of SPSS-XÔ and Minitab®

© 1998 by Dr. Thomas W. MacFarland -- All Rights Reserved


These statistics tutorials have been developed to serve the
needs of the following two groups of graduate students in
the social sciences:

1.  These tutorials should be useful for graduate students in
    the social sciences who have not yet enrolled in a
    statistics class.  In this regard, these tutorials are
    viewed as a useful advance organizer for an academic area
    that is often viewed with a degree of apprehension by many

2.  These tutorials should also be useful for graduate students
    in the social sciences who have completed their required
    statistics class(es), but who have not yet attempted data
    analysis for the thesis/dissertation.  Indeed, the
    complexity of data analysis and the general area of
    statistics are far too often the reasons why there are too
    many graduate students with incomplete ABD (All-but-
    Dissertation) status.  As designed, these tutorials and
    responses to individual questions should offer the level
    of help many graduate students need so that they can
    complete their research requirement(s) in a timely manner.


These tutorials are based on a set of assumptions that
are common to today's contemporary graduate student in 
the social sciences:

1.  Participants have a degree of experience with computing
    technology and file management, but by no means is
    expertise in these areas needed for success with these

2.  Participants have regular access to the Internet so that
    they can receive and send any electronic mail messages
    that may be related to this training activity.

3.  Participants have access to SPSS (Statistical Package for the
    Social Sciences) and/or MINITAB.  (Because it is so common in
    the social sciences, SPSS will be stressed).  Ideally,
    participants will have access to the online versions of these
    two leading software packages, so that the full suite of
    options and commands are available.  Even so, PC-based
    versions of these two software products should be sufficient
    for most participants.  

    Some participants may have SAS, a widely-used statistical 
    analysis program, available at their campus.  SAS is excellent
    for large-scale programming jobs and complicated data 
    warehousing and data mining activities.  But, this level of 
    complexity is beyond the scope of these introductory 
    tutorials and instead these tutorials will only use SPSS and
    MINITAB for demonstration purposes. 


1.  Due to the complexities of multiple hardware and software
    platforms inherent to any distributed distance education
    activity, we will not have uniform access to the same
    computing machinery and software.  When using these

    -- Some participants may do most of their analyses online,
       using a dedicated terminal on a local area network to
       access a campus-based mainframe computer.

    -- Some participants may do most of their analyses online,
       working from home through modem-based connection to a
       campus-based super-mini computer.

    -- Other participants may prefer to work offline, using
       PC-based software.

    Be sure to know how to contact your local system operator
    or other "help" personnel for purely system-specific

2.  These tutorials are based on standard scenarios that may be
    reasonably found in the social sciences.  For the purpose
    of consistency, all examples use problems that a classroom-
    based computing technology teacher would need to address.

File Organization

Each tutorial is comprised of six separate files that have been
joined into one common file:

1.  topic.doc (doc = documentation/background information file)

2.  topic.dat (dat = data file, with all data in FIXED FORMAT)

3.  topic.r01 (r01 = SPSS "run" file 01)

4.  topic.o01 (o01 = SPSS "output" file 01)

5.  topic.con (con = conclusion and explanation file)

6.  topic.lis (lis = list file for the MINITAB addendum)

File Structure

A few comments about each file type may be useful as you continue
with this set of tutorials:

1.  topic.doc (doc = documentation/background information file)

    Each documentation file describes a real-world problem faced
    by a computing technology teacher.  Typically, I'll be sure
    to include background information about each statistical
    test, often describing examples of its correct selection and
    later interpretation.

    The data associated with the exercise are also found in
    this section.  In most cases, the data table is then later
    used as the actual data file.  Of course, there may be a
    few modifications to data in the table as the data file
    is prepared, depending on the complexity of how data are
    organized into sub-groups.

2.  topic.dat (dat = data file)

    Data Organization

    Each data file is organized so that it is in FIXED column
    format.  You may occasionally work with data that are in
    sequential order, such that value_A comes before value_B,
    but their actual line number and column placement is not
    important.  There may be a few occasions where this lack
    of column placement specificity is useful, but in most
    cases it is essential that you work with data that are
    organized in a precise format.

    Consider the following data file (cent_tnd.dat) that
    identifies final examination scores for a class of
    23 students:

                   01                 089
                   02                 092
                   03                 073
                   04                 083
                   05                 056
                   06                 082
                   07                 077
                   08                 092
                   09                 100
                   10                 067
                   11                 071
                   12                 076
                   13                 083
                   14                 086
                   15                 077
                   16                 049
                   17                 071
                   18                 084
                   19                 091
                   20                 088
                   21                 082
                   22                 077
                   23                 097

       -- If you have 99 or fewer students, then be sure to
          allocate TWO columns for each student identification
          code:  01 to 99, found here in columns 20-21. 
       -- If each test score has 100 has a maximum score, then
          be sure to allocate THREE columns for each student
          test score:  000 to 100, found here in columns 39-41.

    The following ten lines represent a data file prepared
    in response to a five-question survey (responses to each
    question range from 1 = Very Low Opinion to 5 = Very High
    Opinion), by ten survey participants:

01 3 4 2 5 5
02 4 5 2 5 5
03 4 4 4 5 5
04 5 5 5 3 5
05 4 4 5 3 5
06 4 5 3 4 1
07 5 5 5 5 2
08 2 4 3 2 2
09 5 4 3 4 5
10 4 4 4 5 3

    As you examine this FIXED column format data file, be
    sure to notice how:

    -- Participant code number, ranging from 01 to 10, is
       placed (i.e., FIXED) in column 1 and column 2.

       Equally, notice how I used leading zeros for participants
       01 to 09, keying in "01" instead of "1" for the first
       participant.  I recommend that you develop the practice
       of keying in leading zeros also, to be sure that data are
       consistently placed in the correct column.

    -- Otherwise, notice how I keyed in the 1-5 response to
       question 1 in column 4 and then allowed a blank space
       before keying in the 1-5 response to question 2 in column
       6, until finally the 1-5 response to question 5 is placed
       in column 12.

       White space (i.e., blank space) is ignored by most
       statistical analysis programs, provided data are
       declared in the proper column in the run file.
       The blank spaces in this example are purely for
       eye appeal and convenience in case you need to look
       closely at the file at a later time. 

    Data File Construction

    Of course, there are many ways that you can use computing
    machinery and software to create a data file:

    -- When working offline, I usually use the old-fashioned
       DOS "edit" editor, since it conveniently displays the
       line number and column number in the lower right corner
       of the user interface.

       Another advantage of the DOS edit program is that it
       can only present and save data in a FIXED column format
       Courier font.  This font is not only easy to see on
       the screen, but it fully supports the concept of FIXED
       column format.

    -- Other times, I may use WordPerfect, Word, or any of the
       other leading word processing packages as data-entry

       When using a fully-embellished word processing package
       for data entry, just be sure to immediately change the
       font to Courier, a fixed width font.  Equally, be sure
       to save the file in plain-text ASCII format.

    -- Of course, when working online at the UNIX shell (if
       you use this system configuration), the vi, pico, and
       emacs editors are useful data entry tools.

    -- In some cases, I'll also use a spreadsheet such as
       Lotus, Excel, or Quatro to enter data.  However, I tend
       to avoid this type of data entry tool since leading
       zeros are usually deleted when spreadsheets are used.
       Again, this issue is critical when considering the issue
       of FIXED column format data files).

    Data File Hints

    When constructing a data file, your emphasis should be on
    accuracy.  Here are a few hints that you may find useful:

    -- Consider the coding scheme that you plan to use for
       distinct groups, such as "Female" and "Male."  It is
       nearly always easier to work with numbers instead of
       letters in a run (i.e., operation) file.  For this
       scheme, it is often best to declare female as code =
       1 and male as code = 2.

       By using this type of code, you avoid the problem of
       consistently remembering to use caps/no_caps for F/f
       and M/m.  Some statistical analysis programs are case
       sensitive and inconsistency in capitalization could be
       a problem.

       Another advantage of this type of coding scheme is that
       it promotes accurate and rapid data entry.  Look at the
       keyboard and notice how the F key and the M key are not
       immediately adjacent to each other.  Then, notice how
       the 1 key and the 2 key are adjacent.  The first time
       you have to key in responses to 1,234 56-question
       surveys, these time-saving coding schemes may become
    -- With the possible exception of your advisor and anyone
       who may help you with data entry, no one is going to see
       your data file.  The data file is merely a resource that
       supports your research.  Keep the file in FIXED column
       format and use a font with fixed width, such as Courier,
       saving more attractive fonts for your actual thesis/

       To be brief, use an editor that best meets your needs
       for data entry, instead of the use of an editor that
       supports any desired style and presentation.  I suggest
       that you practice with the DOS "edit" editor as a
       possible tool for data entry.  As an example, you may
       want to practice with edit to create topic.dat as a
       sample data file.  If so, key the following at the DOS
       C prompt:

       C:\> edit topic.dat

       You will then go into an interface that has on the top 
       toolbar a set of options that you have surely seen when
       using other software programs:

       File  Edit  Search  View  Options  Help

       The user interface of edit has the look and feel of other
       leading word processing programs and with a few practice
       trials you may find it very useful for data entry.

    -- To further promote accuracy, I suggest that you develop
       a template for each line of data, with an x placed in
       each column that will have a datum entered.  Then, place
       your editor in insert mode and merely "overwrite" the x
       with the correct datum.

       For example, using the prior data file for responses to
       the five-question survey, I first prepared the following
       one line template of x characters:

xx x x x x x

       Then, I used edit's Edit/Copy option and later used the
       Edit/Paste option nine times to create a ten line data
       file that now consists of a template with x characters
       in the column positions where data will be entered.

xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x
xx x x x x x

       Once the data file template was completed, I then
       put the editor into insert mode and typed over each
       x with the correct datum.  Using this method, it
       is easy to visually scan your data file so that you
       maintain correct column placement when entering data.

3.  topic.r01 (r01 = SPSS run file 01)

    Construction of a SPSS Run File

    The way you prepare a run file is dependent upon the
    specific software program you use for statistical analysis.
    In these tutorials, I will prepare a complete run file
    using the online version of SPSS.  I will then also
    include, as an addendum, an example of an interactive
    session of data analysis with MINITAB.

    The following 17 lines from cent_tnd.r01 represent a SPSS-
    based run file:

SET WIDTH      = 80
TITLE          = Descriptive Statistics and Central Tendency
COMMENT        = This file examines scores on a computing
                 technology final examination
DATA LIST FILE = 'cent_tnd.dat' FIXED
     / Stu_Code   20-21
       Score      39-41

Variable Labels
       Stu_Code   "Student Code"
     / Score      "Exam Score  "

     / STATISTICS     = All

    To show that this run file is perhaps not as cryptic as it
    possibly first appears, let me dissect each of these 17

    -- SET WIDTH = 80 is used in this case to set the width
       of the output file (cent_tnd.o01) to 80 columns wide.
       This option is used merely to support printing to 8-1/2
       inch by 11 inch paper, as well as most computer screens.

    -- SET LENGTH = NONE is used to turn off page ejects,
       which promotes printing of the output file as one
       continuous page, reducing wasted paper.

    -- SET CASE = UPLOW is used to display labels in the
       output file to either upper case or lower case, as
       opposed to the default of upper case only.

    -- SET HEADER = NO is used to turn off the printing of
       a header on each page of the output file, which again
       reduces wasted paper/printing.

    -- TITLE = is used to provide a unique title at the
       beginning of the output file.

    -- COMMENT = is used to provide a descriptive comment any
       place within a run file.  As with any programming
       activity, use comments liberally to help refresh your
       memory when you come back to the run file weeks or
       months later.

    -- DATA LIST FILE = 'cent_tnd.dat' FIXED
            / Stu_Code   20-21
              Score      39-41

       This portion of the run file can be broken down into
       its component parts:

       -- DATA LIST FILE = translates into "get the following

       -- 'cent_tnd.dat' is the file that the DATA LIST FILE
          is used to get.  Be sure to notice how single
          quotation marks are placed before and after the file

       -- FIXED is used to declare that the data file
          'cent_tnd.dat' is in fixed format.  Be sure to
          review the need for FIXED column placement, as
          shown in previous examples.

       -- / Stu_Code 20-21 is used to declare that data for 
          the variable Stu_Code (Student Code) are placed in
          column 20 and column 21. In turn, data for the 
          variable Score (Final Examination Score) are found
          in columns 39 to 41.  All other columns represent
          blank space and they are ignored since they were
          not declared in the run file.
          It is useful to know that the / character before
          Stu_Code CANNOT be placed in column 1.

          It is also useful to know that the variable name
          can be no longer than eight characters.

          Finally, it is best to avoid special characters in
          the eight-character variable names that you declare.
          I tend to start each variable name with a capital
          letter, but that practice is a preference and not a
          requirement.  Otherwise, the only non-alphabetical
          or number character that I use in variable names is
          _, the underscore character, to "join" compound
          words into one name, such as Stu_Code for "Student
    -- Variable Labels
              Stu_Code   "Student Code"
            / Score      "Exam Score  "

       This portion of the run file can be broken down into
       its component parts:

       -- Variable Labels is used to give more descriptive
          labels to the previously declared eight-character
          variable codes.

       -- Stu_Code "Student Code" is used to provide a more
          descriptive label in the output file to the
          variable Stu_Code. The same logic applies to the
          other label.

          Again, it is useful to know that the / character
          before Score CANNOT be placed in column 1.

          It is also best to keep variable labels at 40
          characters or less, avoiding special characters
          within the label.
          Be sure to notice how double quotation marks are
          placed before and after the variable label.
            / STATISTICS     = All

       This final portion of the run file can also be broken
       down into its component parts:

       -- The code FREQUENCIES VARIABLES = Score is the
          command to conduct a frequency analysis of the
          variable called "Score."  By using this command,
          you will get a printout of how often each datum
          has been found.

       -- The code / STATISTICS = All is the command to
          conduct all available descriptive statistics on
          the variable named "Score."  The leading
          descriptive statistics included in the output
          file are:

          -- N or the number of valid scores read into the

          -- Mode or the most frequently occurring score.

          -- Median or the mid-point of all scores placed
             in an array.

          -- Mean or the arithematic average of all scores.

          -- Std dev or the standard deviation of all scores.

          -- Range or the dispersion from the lowest score
             to the highest score.

    Batch Processing with SPSS vs.
    Interactive Processing

    I prefer to work with SPSS in batch mode, where all files
    have been prepared in advance.  This practice is the
    alternative to the interactive use of SPSS, where all
    analyses are keyed in real time.  My preferences for batch
    processing are:

    -- As you progress through this series of tutorials, you
       will learn how to use and reuse complete SPSS run files
       and/or sections of SPSS run files.

       This concept is similar to modular programming, where
       you recycle modules or sections of a program in other
       programs. This practice reduces errors, while
       increasing efficiency.

    -- Interactive processing does not support the reuse of 
       run files and/or sections of run files.  Instead,
       everything is typically keyed over and over again,
       which wastes time while increasing the possibility
       of errors.

    Communicating Between a SPSS Run 
    File and a Data File

    I suggest that you always keep the data file separate
    from the run file, although there are options with SPSS
    for you to place the two files into one common file.

    The advantages of keeping the two files separate, with
    each file having a unique ending to the filename (.dat
    and .r01) are:

    -- As you obtain and then enter data, it is easier to
       have data and only data in the data file.

    -- Run files can be reused, with only slight modifications,
       for new analyses.  It is messy if data that have
       nothing to do with the new analyses are found in the
       run file, requiring you to delete old data.
    The method you use to direct the run file to act upon the
    data file (Go back to the DATA LIST FILE = 'cent_tnd.dat'
    FIXED section of code to review this process.) depends on
    the unique way your operating system is organized.  Again,
    I suggest that you check with your system operator to
    determine how your local environment is organized for the
    use of SPSS and/or MINITAB in batch mode.

    In this series of tutorials, I will present the online
    use of SPSS at a host computer using the UNIX operating
    system, working in batch mode:

    -- Nearly all colleges and universities that have
       a computing center will also likely have this common
       software program online and available to students.  Of
       course, you may need to make a series of phone calls to
       finally get an online account at your institution.  You
       may also need to obtain an information packet to learn
       if the software is available through menu selections
       or some other organized format.

    -- You may also choose to use a PC-based version of SPSS
       or MINITAB.  Obviously, file setup will be totally
       dependent on how you organize directories and files.

    At the online system where these tutorials were developed,
    the % character is the UNIX operating system prompt.  This
    set of tutorials was designed to have the run file
    communicate with the data file by using the following
    typical command when working at the % UNIX prompt:

    % spss -m < cent_tnd.r01 > cent_tnd.o01

    Let's translate this command into Standard English:

    -- spss -m tells the system to prepare to use the SPSS
       data analysis and statistics software program in
       batch mode.

    -- < cent_tnd.r01 means that the program should "read in"
       the run file named cent_tnd.r01.

    -- > cent_tnd.o01 means that the program should direct the
       output of the SPSS session into the output file named 

    By using this approach to batch data processing with

    -- Output files are separate from the run files and the
       data file.

    -- If you plan to conduct multiple analyses of the
       cent_tnd.dat data file, then you only need to modify
       the run file(s) and use the numbering sequence of 01
       to 99 (cent_tnd.r01, cent_tnd.r02, cent_tnd.r03, 
       etc.) to conveniently rename them.

4.  topic.o01 (o01 = SPSS output file 01)

    Interpretation of a SPSS Output File

    A SPSS output file (cent_tnd.o01 in this set of
    examples) begins by repeating the organization of
    the run file.  After this beginning section is
    presented, the output file then displays the analyses
    requested in the series of commands included in the
    run file.

    The following 61-line file is presented as a sample
    SPSS-based output file:

    -- The first 27 lines are a repeat of the run file,
       with additional information about the format of
       each variable.

       Notice how the variable Stu_Code is in FIXED format,
       requiring two columns and Score is also in FIXED
       format, requiring three columns.

   1  SET WIDTH      = 80
   2  SET LENGTH     = NONE
   3  SET CASE       = UPLOW
   4  SET HEADER     = NO
   5  TITLE          = Descriptive Statistics and Central
   6  COMMENT        = This file examines scores on a computing
   7                   technology final examination
   8  DATA LIST FILE = 'cent_tnd.dat' FIXED
   9       / Stu_Code   20-21
  10         Score      39-41

This command will read 1 records from cent_tnd.dat

Variable   Rec   Start     End         Format

STU_CODE     1      20      21         F2.0
SCORE        1      39      41         F3.0
  12  Variable Labels

  13         Stu_Code   "Student Code"
  14       / Score      "Exam Score  "
  18       / STATISTICS     = All

    -- The next set of 27 lines show a frequency
       distribution of the variable Score.

       To interpret this part of the output file, be sure
       to notice how there was one occurrence of the score
       "49" and that this score represented 4.3 percent of all
       scores, there were three occurrences of the score "77"
       and this score represented 13.0 percent of the entire
       data set.  In turn, there were two occurrences of the
       score "82" and two occurrences of the score "83."

Score   Exam Score

                                                  Valid   Cum
Value Label            Value  Frequency  Percent  Percent Percent

                          49         1      4.3      4.3   4.3
                          56         1      4.3      4.3   8.7
                          67         1      4.3      4.3  13.0
                          71         2      8.7      8.7  21.7
                          73         1      4.3      4.3  26.1
                          76         1      4.3      4.3  30.4
                          77         3     13.0     13.0  43.5
                          82         2      8.7      8.7  52.2
                          83         2      8.7      8.7  60.9
                          84         1      4.3      4.3  65.2
                          86         1      4.3      4.3  69.6
                          88         1      4.3      4.3  73.9
                          89         1      4.3      4.3  78.3
                          91         1      4.3      4.3  82.6
                          92         2      8.7      8.7  91.3
                          97         1      4.3      4.3  95.7
                         100         1      4.3      4.3  100.0
                                -------  -------  -------                       
                       Total        23    100.0    100.0

    -- The last seven lines of the output file were generated
       because of the / STATISTICS = ALL command.  In this
       example, you will notice that:  there were 23 valid
       cases to this data set, the Mean was 80.130, the Median
       was 82, the Mode was 77, the Standard Deviation (Std
       dev) was 12.211, and the Range was 51(Minimum = 49 to
       Maximum = 100).

Mean         80.130      Std err       2.546      Median     82.000
Mode         77.000      Std dev      12.211      Variance  149.119
Kurtosis       .914      S E Kurt       .935      Skewness    -.813
S E Skew       .481      Range        51.000      Minimum    49.000
Maximum     100.000      Sum        1843.000

Valid cases      23      Missing cases      0

    Error Messages and Warning Messages in
    a SPSS Output File

    If you have illogical code in the SPSS run file or an
    outright mistake in some way or another, the SPSS output
    file will have an Error message.  In most cases, the
    Error message will give you the line/column number in
    the run file which caused the Error.  Quite frequently,
    the Error message will give you the information needed
    to correct the run file.

    Warning messages are also common, and by no means do they
    mean that you have a problem.  Instead, they merely warn
    you about something in the output file that needs some
    degree of attention.

5.  topic.con (con = conclusion file)

    By choice, I always summarize the analysis in the topic.con
    conclusion file.  When working with inferential tests such
    as Student's t-Test or Oneway ANOVA, I'll be sure to
    summarize outcomes by referring back to the Null Hypothesis

    A sample conclusion from a study on student examination
    scores in a C programming class may be useful at this
    point, with more exposure to this area presented in
    later tutorials:

    -- Ho (Null Hypothesis):

       There is no difference in examination scores in a C 
       programming class between students from the various
       townships representing the general sending district
       of Cape May County (e.g., Upper Township, Middle
       Township, Lower Township, Cape May City) at p <=

    -- Outcome:

       Computed F  = 6.79

       Criterion F = 3.29 (alpha = .05, df = 3,15)

       Computed F (6.79) > Criterion F (3.29)

    -- Conclusion:

       The computed F statistic exceeds the criterion F
       statistic and the null hypothesis is not accepted.
       That is to say, there are differences in examination
       scores in the C programming class between students from
       the various townships representing the general sending
       district of Cape May County (e.g., Upper Township,
       Middle Township, Lower Township, Cape May City) at
       at alpha (or p) = .05.

       Again, the conclusion file is a summary of outcomes
       from the analysis and this summary should be helpful
       when you prepare the results section of your thesis/

6.  topic.lis (lis = list file for the MINITAB analysis)

    By using SPSS in batch mode, I am able to develop run files
    that support a complex array of statistical analyses.
    Further, these SPSS run files can serve as modules for
    later analyses.  Some editing many be required, but it is
    very common to save up to 80 percent of your SPSS
    programming time after you develop a personal collection of
    run files and then use these run files in other analyses.

    However, there are times when you just want to do a quick
    analysis and you do not want to spend too much time
    developing a complex and elaborate run file.  When this is
    the case, I find MINITAB in interactive mode a very useful
    software program.

    As such, I end each tutorial with a MINITAB addendum,
    showing the use of MINITAB in an interactive mode.  If
    you have MINITAB available on your campus computing system,
    you may find it interesting to try a few these sample
    interactive sessions.

    Again, ask your system operator if MINITAB is available on
    your campus computing system.  At the % UNIX prompt, I go
    into MINITAB by keying:

    % minitab

    Then, I save the output by placing it into a topic.lis
    list file, which is identified in each MINITAB addendum.

File Placement at an Online
Host Computing System

As you will notice in the Limitations section of this
introduction, it is only expected that there will be 
considerable variance in computing hardware and software
among the individuals who use this series of tutorials.
You will also notice that my examples are based on the
use of SPSS and MINITAB at an online host computing
system, instead of using the PC versions of these two
software programs.  If you use a PC-based version of SPSS,
nearly all of the examples in these tutorials can be (and
should be) replicated in the dialog box.

Again, you may need to contact your local system administrator
to learn how to access online files.  If you prepare the ASCII-
based run file and data file offline, using edit or any other
word processing program, you will also need to learn how to
upload files from your PC to the online host computer.  Of
course, you will also want to learn how to download the output
files from the online host computer to your PC. 


Best wishes as you continue with these tutorials.  Send e-mail 
to if you have questions about these tutorials 
and how they can help you complete the statistical analyses 
associated with your graduate research project.

Disclaimer:  All care was used to prepare the information in this 
tutorial.  Even so, the author does not and cannot guarantee the 
accuracy of this information.  The author disclaims any and all 
injury that may come about from the use of this tutorial.  As 
always, students and all others should check with their advisor(s) 
and/or other appropriate professionals for any and all assistance 
on research design, analysis, selected levels of significance, and 
interpretation of output file(s).

The author is entitled to exclusive distribution of this tutorial. 
Readers have permission to print this tutorial for individual use, 
provided that the copyright statement appears and that there is no 
redistribution of this tutorial without permission.

Prepared 980316
Revised  980914
end-of-file 'introduc.ssi'

Please send comments or suggestions to Dr. Thomas W. MacFarland

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