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					   SW388R7
Data Analysis &
 Computers II     Analyzing Missing Data
    Slide 1




                        Introduction

                         Problems

                        Using Scripts
   SW388R7
Data Analysis &
 Computers II                Missing data and data analysis
    Slide 2



                     Missing data is a problem in multivariate data
                      because a case will be excluded from the analysis if
                      it is missing data for any variable included in the
                      analysis.

                     If our sample is large, we may be able to allow cases
                      to be excluded.

                     If our sample is small, we will try to use a
                      substitution method so that we can retain enough
                      cases to have sufficient power to detect effects.

                     In either case, we need to make certain that we
                      understand the potential impact that missing data
                      may have on our analysis.
   SW388R7
Data Analysis &
 Computers II              Tools for evaluating missing data
    Slide 3




                     SPSS has a specific package for evaluating missing
                      data, but it is included under the UT license.

                     In place of this package, we will first examine
                      missing data using SPSS statistics and procedures.

                     After studying the standard SPSS procedures that we
                      can use to examine missing data, we will use an SPSS
                      script that will produce the output needed for
                      missing data analysis without requiring us to issue all
                      of the SPSS commands individually.
   SW388R7
Data Analysis &
 Computers II              Key issues in missing data analysis
    Slide 4




                     We will focus on three key issues for evaluating
                      missing data:
                       The number of cases missing per variable

                       The number of variables missing per case

                       The pattern of correlations among variables
                        created to represent missing and valid data.


                     Further analysis may be required depending on the
                      problems identified in these analyses.
   SW388R7
Data Analysis &
 Computers II     Problem 1
    Slide 5
   SW388R7
Data Analysis &
 Computers II     Identifying the number of cases in the data set
    Slide 6




                                    This problem wants to know if a variable is
                                    missing data for half or more of the cases.

                                    Our first task is to identify the number of
                                    cases that meets that criterion.

                                    If we scroll to the bottom of the data set,
                                    we see than there are 270 cases in the data
                                    set.

                                                   270 ÷ 2 = 135.

                                    If any variable included in the analysis has
                                    135 or more missing cases, the answer to
                                    the problem will be true.
   SW388R7
Data Analysis &
 Computers II                    Request frequency distributions
    Slide 7




              We will use the output for
              frequency distributions to
              find the number of missing
              cases for each variable.


                                                      Select the Frequencies… |
                                                      Descriptive Statistics
                                                      command from the Analyze
                                                      menu.
   SW388R7
Data Analysis &
 Computers II     Completing the specification for frequencies
    Slide 8




                       First, move the five
                       variables included in the
                       problem statement to
                       the list box for variables.




                                                     Second, click on the OK
                                                     button to complete the
                                                     request for statistical
                                                     output.
   SW388R7
Data Analysis &
 Computers II     Number of missing cases for each variable
    Slide 9




                                           In the table of statistics at
                                           the top of the Frequencies
                                           output, there is a table
                                           detailing the number of
                                           missing cases for each
                                           variable in the analysis.
   SW388R7
Data Analysis &
 Computers II                      Answering the problem
   Slide 10




                  With 270 subjects in the data set, variables
                  missing data for 135 or more cases would
                  correctly be characterized as missing data for half
                  or more of the cases in the data set.

                  One variable was incorrectly characterized as
                  missing half or more of the 270 cases: "self-
                  employment" [wrkslf] was missing data for 20 of
                  the 270 cases (7.4%).

                  None of the variables in this analysis was missing
                  cases for half or more of the 270 cases in the data
                  set.




                                                                        False is the
                                                                        correct answer.
   SW388R7
Data Analysis &
 Computers II     Problem 2
   Slide 11
   SW388R7
Data Analysis &
 Computers II       Create a variable that counts missing data
   Slide 12




         We want to know how
         many of the five variables
         in the analysis had
         missing data for each
         case in the data set.               To compute a new
                                             variable, select the
         We will create a variable           Compute…
         containing this                     command from the
         information that uses an            Transform menu.
         SPSS function to count
         the number of variables
         with missing data.
   SW388R7
Data Analysis &
 Computers II       Enter specifications for new variable
   Slide 13




                      First, type in the name for
                      the new variable nmiss in
                      the Target variable text box.




                                                      Third, click on the
                                                      up arrow button to
                                                      move the NMISS
                                                      function into the
                                                      Numeric Expression
                  Second, scroll down the list        text box.
                  of functions and highlight
                  the NMISS function.
   SW388R7
Data Analysis &
 Computers II                 Enter specifications for new variable
   Slide 14



                                                        The NMISS function is
                                                        moved into the Numeric
                                                        Expression text box.




                  To add the list of
                  variables to count
                  missing data for,
                  we first highlight
                  the first variable to
                  include in the                Second, click on the
                  function, wrkstat.            right arrow button to
                                                move the variable
                                                name into the function
                                                arguments.
   SW388R7
Data Analysis &
 Computers II               Enter specifications for new variable
   Slide 15




                                                          First, before we add another
                                                          variable to the function, we
                                                          type a comma to separate the
                                                          names of the variables.




                  Second, to add
                  the next variable
                  we highlight the
                  second variable to          Third, click on the
                  include in the              right arrow button to
                  function, hrs1.             move the variable
                                              name into the function
                                              arguments.
   SW388R7
Data Analysis &
 Computers II     Complete specifications for new variable
   Slide 16




                                                     Continue adding variables to
                                                     function until all of the
                                                     variables specified in the
                                                     problem have been added.

                                                     Be sure to type a comma
                                                     between the variable names.




                    When all of the variables have
                    been added to the function,
                    click on the OK button to
                    complete the specifications.
   SW388R7
Data Analysis &
 Computers II     The nmiss variable in the data editor
   Slide 17




                        If we scroll the worksheet
                        to the right, we see the new
                        variable that SPSS has just
                        computed for us.
   SW388R7
Data Analysis &
 Computers II              A frequency distribution for nmiss
   Slide 18




                  To answer the
                  question of how many
                  cases had each of the
                  possible numbers of
                  missing value, we
                  create a frequency
                  distribution.                    Select the Frequencies… |
                                                   Descriptive Statistics
                                                   command from the Analyze
                                                   menu.
   SW388R7
Data Analysis &
 Computers II     Completing the specification for frequencies
   Slide 19




                          First, move the nmiss
                          variable to the list of
                          variables.




                                                    Second, click on the OK
                                                    button to complete the
                                                    request for statistical
                                                    output.
   SW388R7
Data Analysis &
 Computers II     The frequency distribution
   Slide 20




                                    SPSS produces a frequency
                                    distribution for the nmiss
                                    variable.

                                    170 cases had valid, non-
                                    missing values for all 5
                                    variables. 85 cases had one
                                    missing value; 1 case had 2
                                    missing values; and 14 cases
                                    had missing values for 4
                                    variables.
   SW388R7
Data Analysis &
 Computers II     Answering the problem
   Slide 21




                            The problem asked whether or not 14
                            cases had missing data for more than half
                            the variables. For a set of five variables,
                            cases that had 3, 4, or 5 missing values
                            would meet this requirement.

                            The number of cases with 3 missing
                            variables is 0 (not shown in table), with 4
                            missing variables is 14, and with 5 missing
                            variables is 0, for a total of 14.

                            The answer to the problem is true.
   SW388R7
Data Analysis &
 Computers II     Problem 3
   Slide 22
   SW388R7
Data Analysis &
 Computers II     Compute valid/missing dichotomous variables
   Slide 23




          To evaluate the pattern of
          missing data, we need to
          compute dichotomous
          valid/missing variables for
                                                To create the new
          each of the five variables
                                                variable, select the
          included in the analysis.
                                                Recode | Into
                                                Different Variables…
          We will compute the new
                                                from the Transform
          variable using the Recode
                                                menu.
          command.
   SW388R7
Data Analysis &
 Computers II               Enter specifications for new variable
   Slide 24




                  First, move the first
                  variable in the analysis,
                  wrkstat, into the Numeric
                  Variable -> Output Variable
                  text box.                     Second, type the name for the new
                                                variable into the Name text box. My
                                                convention is to add an underscore
                                                character to the end of the variable name.

                                                If this would make the variable more than
                                                8 characters long, delete characters from
                                                the end of the original variable name.
   SW388R7
Data Analysis &
 Computers II     Enter specifications for new variable
   Slide 25




                                                         Finally, click on
                                                         the Change button
                      Next, type the label for the
                                                         to add the name of
                      new variable into the Label
                                                         the dichotomous
                      text box. My convention is to
                                                         variable to the
                      add the phrase (Valid/Missing)
                                                         Numeric Variable ->
                      to the end of the variable
                                                         Output Variable text
                      label for the original variable.
                                                         box.
   SW388R7
Data Analysis &
 Computers II     Enter specifications for new variable
   Slide 26




                                          To specify the values for the
                                          new variable, click on the Old
                                          and New Values… button.
   SW388R7
Data Analysis &
 Computers II               Change the value for missing data
   Slide 27




                                   The dichotomous variable should be
                                   coded 1 if the variable has a valid value,
                                   0 if the variable has a missing value.



                                                                                     Second, type 0 in
                  First, mark                                                        the Value text box.
                  the System- or
                  user-missing
                  option button.




                                                                  Third, click on the Add button
                                                                  to include this change in the
                                                                  list of Old->New list box.
   SW388R7
Data Analysis &
 Computers II                     Change the value for valid data
   Slide 28




                                                                      Second, type 1 in
                                                                      the Value text box.

                  First, mark
                  the All other
                  values option
                  button.




                                                     Third, click on the Add button
                                                     to include this change in the
                                                     list of Old->New list box.
   SW388R7
Data Analysis &
 Computers II     Complete the value specifications
   Slide 29




                                         Having entered the values
                                         for recoding the variable
                                         into dichotomous values, we
                                         click on the Continue button
                                         to complete this dialog box.
   SW388R7
Data Analysis &
 Computers II     Complete the recode specifications
   Slide 30




                                  Having entered specifications for the
                                  new variable and the values for
                                  recoding the variable into dichotomous
                                  values, we click on the OK button to
                                  produce the new variable.
   SW388R7
Data Analysis &
 Computers II                    The dichotomous variable
   Slide 31




                  The procedure for creating a dichotomous
                  valid/missing variable is repeated for the
                  four other variables in the analysis: hrs1,
                  wrkslf, wrkgovt, and prestg80.
   SW388R7
Data Analysis &
 Computers II     Filtering cases with excessive missing variables
   Slide 32




        If we include the cases
        that have more than
        half of the variables
        missing, we will inflate
        the correlations. To
        prevent this, we                      To filter cases included in
        exclude this cases                    further analysis, we choose
        before creating the                   the Select Cases…
        correlation matrix.                   command from the Data
                                              menu.
        We do this by selecting
        in, or filtering, cases
        that have fewer than
        half missing variables,
        i.e. less than 3 missing
        variables.
   SW388R7
Data Analysis &
 Computers II     Enter specifications for selecting cases
   Slide 33




                                        First, click on the If
                                        condition is satisfied
                                        option button on the
                                        Select panel.




                                                Second, click on the If…
                                                button to enter the
                                                criteria for including
                                                cases.
   SW388R7
Data Analysis &
 Computers II     Enter specifications for selecting cases
   Slide 34




                                          First, enter the criteria
                                          for including cases:

                                                 nmiss < 3




                                          Second, click
                                          on the Continue
                                          button to
                                          complete the If
                                          specification.
   SW388R7
Data Analysis &
 Computers II     Complete the specifications for selecting cases
   Slide 35




                                       To complete the
                                       specifications, click
                                       on the OK button.
   SW388R7
Data Analysis &
 Computers II     Cases excluded from further analyses
   Slide 36




                           SPSS marks the cases that will not be
                           included in further analyses by drawing
                           a slash mark through the case number.

                           We can verify that the selection is
                           working correctly by noting that the
                           case which is omitted had 4 missing
                           variables.
   SW388R7
Data Analysis &
 Computers II     Correlating the dichotomous variables
   Slide 37




                                          To compute a correlation
                                          matrix for the dichotomous
                                          variables, select the Correlate
                                          | Bivariate command from
                                          the Analyze menu.
   SW388R7
Data Analysis &
 Computers II     Specifications for correlations
   Slide 38




                     First, move the
                     dichotomous variables
                     to the variables list box.




                                                  Second, click on
                                                  the OK button to
                                                  complete the
                                                  request.
   SW388R7
Data Analysis &
 Computers II                              The correlation matrix
   Slide 39



                                                                    Correlations

                                                                                The correlation matrix is           RS
                                                                                                                 OCCUPA
                                                                      NUMBER
                                                                                symmetric along the diagonal
                                                                                    R SELF-EMP                   TIONAL
                                                           LABOR     OF HOURS(shown by the blue line). The
                                                                                    OR WORKS        GOVT OR PRESTIG
                                                           FRCE       WORKED correlation for any pair of E SCORE
                                                                                       FOR          PRIVATE
                                                          STATUS LAST WEEK      variables is included twice in
                                                                                   SOMEBODY EMPLOYEE              (1980)
                                                                                   (Valid/Missin we only count
                                                                                the table. So
                                                         (Valid/Mis (Valid/Missin                  (Valid/Missi (Valid/Mis
                                                            sing)        g)             g)             ng)
                                                                                the correlations below the sing) a
                   LABOR FRCE STATUS Pearson Correlation          .a            .a              .a            .a         .
                  (Valid/Missing)                                               diagonal (the cells with the
                                     Sig. (2-tailed)              .             .               .             .          .
                                                                                yellow background).
                                           N                          256             256        256      256         256
                   NUMBER OF HOURS         Pearson Correlation           .a             1      -.049         .a     -.042
                  WORKED LAST WEEK         Sig. (2-tailed)                .              .     .437          .       .501
                  (Valid/Missing)
                                           N                          256             256       256       256        256
                   R SELF-EMP OR           Pearson Correlation            .a        -.049          1         .a     -.010
                  WORKS FOR                Sig. (2-tailed)                .          .437           .        .       .877
                  SOMEBODY                 N
                  (Valid/Missing)
                                                                      256             256       256       256        256


                   GOVT OR PRIVATE         Pearson Correlation           .a              .a         .a       .a         .a
                  EMPLOYEE                 Sig. (2-tailed)               .               .          .        .          .
                  (Valid/Missing)          N                          256             256        256      256        256
                   RS OCCUPATIONAL         Pearson Correlation           .a         -.042      -.010         .a        1
                  PRESTIGE SCORE           Sig. (2-tailed)               .           .501       .877         .          .
                  (1980) (Valid/Missing)   N                          256             256        256      256        256
                    a. Cannot be computed because at least one of the variables is constant.
   SW388R7
Data Analysis &
 Computers II                                  The correlation matrix
   Slide 40



                                                                    Correlations

                                                                                                                          RS
                                                                                          The correlations marked with
                                                                                                                       OCCUPA
                                                                              NUMBER      footnote letter a could not be
                                                                                           R SELF-EMP                  TIONAL
                                                                   LABOR                                  GOVT one PRESTIG
                                                                             OF HOURS computed because OR of the
                                                                                           OR WORKS
                                                                   FRCE       WORKED                      a constant, i.e.
                                                                                          variables was PRIVATE E SCORE
                                                                                               FOR
                                                                  STATUS LAST WEEK the dichotomous variable (1980)
                                                                                           SOMEBODY EMPLOYEE            has
                                                                 (Valid/Mis (Valid/Missin the same value for all cases.
                                                                                           (Valid/Missin (Valid/Missi (Valid/Mis
                                                                   sing)           g)                  g)             ng)              sing)
                   LABOR FRCE STATUS Pearson Correlation                   .a                .a                  .a            .a              .a
                  (Valid/Missing)    Sig. (2-tailed)
                                                                                                  This happens when one of the
                                                                         .                  .                 .         .            .
                                     N
                                                                                                  valid/missing variables has no
                                                                      256                256               256       256          256
                                                                                                  missing cases, so thata all of
                   NUMBER OF HOURS   Pearson Correlation                 .a                1             -.049          .       -.042
                  WORKED LAST WEEK   Sig. (2-tailed)
                                                                                                  the cases have a value of 1
                                                                           .                 .
                  (Valid/Missing)
                                                                                                          .437          .
                                                                                                  and none have a value of 0..501
                                     N                                256                256                 256            256           256
                   R SELF-EMP OR           Pearson Correlation                 a                                                   a
                                                                           .            -.049                   1              .         -.010
                  WORKS FOR                Sig. (2-tailed)                 .             .437                    .             .          .877
                  SOMEBODY                 N
                  (Valid/Missing)
                                                                      256                256                 256            256           256


                   GOVT OR PRIVATE         Pearson Correlation           .a                  .a                  .a            .a            .a
                  EMPLOYEE                 Sig. (2-tailed)               .                   .                   .             .             .
                  (Valid/Missing)          N                          256                 256                 256           256           256
                   RS OCCUPATIONAL         Pearson Correlation           .a             -.042               -.010              .a           1
                  PRESTIGE SCORE           Sig. (2-tailed)               .               .501                .877              .             .
                  (1980) (Valid/Missing)   N                          256                 256                 256           256           256
                    a. Cannot be computed because at least one of the variables is constant.
   SW388R7
Data Analysis &
 Computers II                                     The correlation matrix
   Slide 41



                                                                    Correlations

                                                                                                                                       RS
                                                                                                                                    OCCUPA
                                                                               NUMBER          R SELF-EMP                           TIONAL
                                                                   LABOR      OF HOURS         OR WORKS          GOVT OR           PRESTIG
                                                                   FRCE       WORKED               FOR           PRIVATE           E SCORE
                                                                  STATUS LAST WEEK             SOMEBODY EMPLOYEE                     (1980)
                                                                 (Valid/Mis (Valid/Missin      (Valid/Missin    (Valid/Missi       (Valid/Mis
                                                                    sing)         g)                g)              ng)               sing)
                   LABOR FRCE STATUS Pearson Correlation                  . a            .a                 . a            .a                .a
                  (Valid/Missing)    Sig. (2-tailed)                      .              .                  .              .                 .
                                     N                                 256           256                 256            256               256
                   NUMBER OF HOURS   Pearson Correlation                  .a            1              -.049               .a           -.042
                  WORKED LAST WEEK   Sig. (2-tailed)                      .              .              .437               .            .501
                  (Valid/Missing)
                                     N                                256             256               256             256              256
                   R SELF-EMP OR           Pearson Correlation                a                                                a
                                                                          .         -.049                  1               .            -.010
                  WORKS FOR                Sig. (2-tailed)                .          .437                   .              .             .877
                  SOMEBODY                 N In the cells for which the correlation could be computed, the
                  (Valid/Missing)             probabilities indicating significance are 0.437, 0.501, and
                                                                   256          256         256        256                               256
                                              0.877.

                   GOVT OR PRIVATE            The Correlation
                                           Pearson correlation of -.042 between .the missing/valid pair for
                                                                        .a            a
                                                                                                .a        .a                                .a
                  EMPLOYEE                    "number
                                           Sig. (2-tailed) of hours worked in the past week" [hrs1] and .
                                                                        .           .           .                                           .
                  (Valid/Missing)          N "occupational prestige score" [prestg80] was not statistically
                                                                     256         256         256       256                               256
                   RS OCCUPATIONAL            significant (p=0.501) .and should not be interpreted as .a
                                           Pearson Correlation            a
                                                                               -.042       -.010                                           1
                  PRESTIGE SCORE              indicating
                                           Sig. (2-tailed) a non-random pattern of missing data.
                                                                        .       .501        .877          .                                 .
                  (1980) (Valid/Missing)   N                         256         256         256       256                               256
                    a. Cannot be computed because at least one of the variables is constant.
   SW388R7
Data Analysis &
 Computers II                                    Answering the problem
   Slide 42



                                                                    Correlations

                                                                                                                                       RS
                                                                                                                                    OCCUPA
                                                                               NUMBER          R SELF-EMP                           TIONAL
                                                                   LABOR      OF HOURS         OR WORKS          GOVT OR           PRESTIG
                                                                   FRCE       WORKED               FOR           PRIVATE           E SCORE
                                                                  STATUS LAST WEEK             SOMEBODY EMPLOYEE                     (1980)
                                                                 (Valid/Mis (Valid/Missin      (Valid/Missin    (Valid/Missi       (Valid/Mis
                                                                    sing)         g)                g)              ng)               sing)
                   LABOR FRCE STATUS Pearson Correlation                  . a            .a                 . a            .a                .a
                  (Valid/Missing)    Sig. (2-tailed)                      .              .                  .              .                 .
                                     N                                 256           256                 256            256               256
                   NUMBER OF HOURS   Pearson Correlation                  .a            1              -.049               .a           -.042
                  WORKED LAST WEEK   Sig. (2-tailed)                      .              .              .437               .            .501
                  (Valid/Missing)
                                     N                                256             256               256             256              256
                   R SELF-EMP OR           Pearson Correlation                a                                                a
                                                                          .         -.049                  1               .            -.010
                  WORKS FOR                Sig. (2-tailed)                .          .437                   .              .             .877
                  SOMEBODY                 N False is the correct       answer.
                  (Valid/Missing)
                                             None of the correlations among the missing/valid variables
                                                                  256         256           256       256                                256
                                             were statistically significant. The correlation matrix does not
                   GOVT OR PRIVATE
                                             indicate a non-random pattern of.a
                                           Pearson Correlation       .a
                                                                                  missing data..a        .a                                 .a
                  EMPLOYEE                 Sig. (2-tailed)          .           .           .        .                                      .
                  (Valid/Missing)          N Fourteen cases were excluded from the calculations for the
                                                                 256         256         256      256                                    256
                   RS OCCUPATIONAL            correlation matrix because they were missing more than .a
                                           Pearson Correlation      .a     -.042       -.010           half                                1
                  PRESTIGE SCORE              of the variables.
                                           Sig. (2-tailed)          .       .501        .877         .                                      .
                  (1980) (Valid/Missing)   N                     256         256         256      256                                    256
                    a. Cannot be computed because at least one of the variables is constant.
   SW388R7
Data Analysis &
 Computers II                           Using scripts
   Slide 43




                     The process of evaluating missing data requires
                      numerous SPSS procedures and outputs that are time
                      consuming to produce.

                     These procedures can be automated by creating an
                      SPSS script. A script is a program that executes a
                      sequence of SPSS commands.

                     Thought writing scripts is not part of this course, we
                      can take advantage of a script that I use to reduce
                      the burdensome tasks of evaluating missing data.
   SW388R7
Data Analysis &
 Computers II            Using a script for missing data
   Slide 44




             The script:
              “EvaluatingAssumptions_MissingData_Outliers_2004.SBS”
              will produce all of the output we have used for evaluating
              missing data, as well as other outputs described in the
              textbook.

             Navigate to the link “SPSS Scripts and Syntax” on the
              course web page.

             Download the script file:
              “EvaluatingAssumptions_MissingData_Outliers_2004.exe”
              to your computer and install it, following the directions
              on the web page.
   SW388R7
Data Analysis &
 Computers II     Open the data set in SPSS
   Slide 45




                                 Before using a script, a data
                                 set should be open in the
                                 SPSS data editor.
   SW388R7
Data Analysis &
 Computers II     Invoke the script
   Slide 46




                                To invoke the script, select
                                the Run Script… command
                                in the Utilities menu.
   SW388R7
Data Analysis &
 Computers II     Select the missing data script
   Slide 47




                              First, navigate to the folder where you put the script.
                              If you followed the directions, you will have a file with
                              an ".SBS" extension in the C:\StudentData\SW388R7
                              folder.

                              If you only see a file with an “.EXE” extension in the
                              folder, you should double click on that file to extract
                              the script file to the C:\StudentData\SW388R7 folder.




                  Second, click on the
                  script name to highlight it.




                                                                             Third, click on
                                                                             Run button to
                                                                             start the script.
   SW388R7
Data Analysis &
 Computers II     The script dialog
   Slide 48




                                The script dialog box acts
                                similarly to SPSS dialog
                                boxes. You select the
                                variables to include in the
                                analysis and choose options
                                for the output.
   SW388R7
Data Analysis &
 Computers II           Complete the specifications
   Slide 49




                  We accept the
                  default option to
                  Check missing data.


                                        Select the variables for the analysis. This
                                        analysis uses the variables for the last
                                        problem we worked. For the missing data
                                        check, it does not matter what role we
                                        assign to the variables.



                                                       Click on the OK
                                                       button to produce
                                                       the output.
   SW388R7
Data Analysis &
 Computers II     The script finishes
   Slide 50




                                   Since it may take a while to
                                   produce the output, and
                                   since there are times when it
                                   appears that nothing is
                                   happening, there is an alert
                                   to tell you when the script is
                                   finished.

                                   When you see this alert, click
                                   on the OK button and view
                                   your output.

                                   Note: the script dialog box
                                   does not close by itself. This
                                   is purposeful so that you can
                                   test assumptions or detect
                                   outliers without having to
                                   redo variable selection.
   SW388R7
Data Analysis &
 Computers II     Output from the script
   Slide 51




                                  The script will produce lots of
                                  output. Additional descriptive
                                  material in the titles should
                                  help link specific outputs to
                                  specific tasks.