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TexaSoft's
USING KWIKSTAT 4.1
Reference Guide, Condensed Disk Version
(C)Copyright 1995 Alan C. Elliott
(C)Copyright 1991, 92, 93, 94, 95 Alan C. Elliott For additional
information on this product, contact TexaSoft, P.O. Box 1169, Cedar
Hill, Texas 75106-1169 (214) 291-2115, Fax: (214) 291-3400,
Compuserve:70721,3145, Internet: 70721.3145@compuserve.com. Production
team: Alan Elliott, Marcia Stoesz, Paul Witt, Nancy Witt, Carol
Bigler, Doug Pollock, Melanie Walker. Program Testing Team: Leo Bolta,
Shopsy's Foods, Canada Randy Hamlin, Senior Scientist, R&D Dept.,
Hunt-Wesson, Inc. Dick Hawkins, Hunt-Wesson, Inc. Jack Holloway III,
University of Phoenix Robert Jirsa, Southern CT State University Chip
Kloos, Lab Manager, R&D Dept., Hunt-Wesson, Inc. Victor L. Landry,
Ph.D., The Mercy Hospital of Pittsburgh, PA Gerard Leboucher,Labo
Ethologie Et Psychoph, France Allen Lein, Professor Emeritus, UCSD
Randolph Maheux, Tampa, FL Sukanya Misra, SMU Sanford Moos, Lab
Manager, Enzo Labs Joseph Padgett, Raleigh, NC George Sadler, Ph.D.,
USC Prof. Emeritus, Okla. City, OK Dr. Karl-August Schaeffer, Cologne,
Germany Michael Stratil, Ph. D., Pembroke State University Wayne
Woodward, Ph. D., SMU Carter Yeager, Boston University
All rights reserved. No part of this book may be reproduced without
prior permission. For information, address TexaSoft, P.O. Box 1169,
Cedar Hill, Texas 75106-1169.
No patent liability is assumed with respect to the use of the
information contained herein. While every precaution has been taken in
the preparation of this publication, the publisher assumes no
responsibility for errors or omissions. Neither is any liability
assumed for damages resulting from the use of the information herein.
The KWIKSTAT software and manual ("documentation") are copyrighted by
TexaSoft and are protected by both United States copyright and
International treaty provisions. Before you can use this program on an
on-going basis, you must pay a license fee. An order form is on disk
in the file named KSORDER.TXT
Important Information in the file LATENEWS.DOC: On the KWIKSTAT disk
is a file named LATENEWS.DOC, which contains information about the
program that is not in this documentation.
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KWIKSTAT 4.1 Statistical Data Analysis
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===========================
AN OVERVIEW OF KWIKSTAT 4.1
===========================
KWIKSTAT is a statistical data analysis program. It was designed by
professional statistical consultants and researchers to allow you to
quickly and easily use the most commonly needed statistical data
analysis procedures and graphs.
KWIKSTAT REQUIREMENTS
KWIKSTAT is a DOS program and may be run as either a stand alone
application, or as a DOS window executed from within the "Windows"
operating environment. It requires PC-DOS or MS-DOS version 3.0 or
higher. If you are running Windows, version 3.1 or higher is required.
Your computer should contain at least 512K or more of free RAM.
KWIKSTAT graphics require an EGA or VGA compatible monitor. Many
printers are supported. A mouse is optional.
INSTALLATION
In most cases, for a quick installation to a hard disk, you enter the
command:
INSTALL
Follow the instructions on the screen. This procedure will install the
program to a disk, and will automatically run the KWIKSTAT setup
program. After installing KWIKSTAT, you can begin the program from the
DOS prompt by entering the command KS.
See the document on disk named KSWINDOWS.DOC for information on
installing KWIKSTAT as a Windows icon.
USING THE KWIKSTAT MENUS
KWIKSTAT menus are similar to a windows menu system. The main menu bar
contains five options: File, Edit, Analyze, Helps and About. Using the
right and left arrow keys on the cursor pad, you can move the menu
selection to one of the other menu bar options. Pressing the right
arrow key once moves the menu bar option from File to Edit. The File
pull-down menu vanishes and the Edit pull-down menu appears. Pressing
the left arrow key moves the selection back to the File menu. Or,
point to a menu option with the mouse and click.
To select options from an extended menu (pulled-down), use the up and
down arrow keys to highlight the option you desire, then press the
Enter key. Or, press the first letter of the option name. If you are
using a mouse, point to the selection with the mouse pointer and
click. Here is brief description of each menu:
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USING THE FILE MENU
Before you can create a graph or calculate statistics, you must
create a database and enter data. The options are:
NEW DATABASE - You must create a new database and enter data before
doing any analysis or creating a graph. The program creates and reads
dBase (.DBF) type file format databases.
OPEN A DATABASE - Open an existing database. A database must be
opened so the program will know where the data is located.
SUBSET DATABASE - Creates a new database that is a subset of the
current database.
COPY/BACKUP - Creates a copy of the database.It is useful to create a
duplicate copy in case the original copy is damaged.
LIST (DISPLAY) THE CONTENTS OF THE DATABASE - Displays the information
in the database to the screen.
MODIFY OR DISPLAY DATABASE STRUCTURE - Allows you to view or change
characteristics about the database, including field widths and types.
KILL - Deletes a database file from your disk.
FILE UTILITIES - Imports information, creates reports, or outputs
data.
EXIT - Ends the program.
USING THE EDIT MENU
The EDIT menu contains options that allow you to enter new data
into a database, edit data currently in a database, and other
editing options:
EDIT RECORDS - Change data already in the database.
APPEND RECORDS - Add new records to the database.
MISSING VALUE CODES - Define missing value codes for your database.
Refer to the section titled "Setting Missing Value Codes".
PACK DATABASE - Permanently erase all records marked for delete.
ZAP - Get rid of all records in a database.
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USING THE ANALYZE MENU
The KWIKSTAT ANALYZE menu allows you to choose which analysis module
to run. The menu items on the ANALYZE menu are:
Descriptive Statistics
Graphs - Descriptive & Comparative
XYZ Visualization/Spin Plot
t-tests and Analysis of Variance (ANOVA)
Nonparametric Comparisons
Regression & Correlation
Crosstabulations, Frequencies, Chi Square
Life Tables and Survival Analysis
Data Generation, Concepts and Simulations
2-Way Advanced ANOVA Designs (Professional edition)
Multiple Comparisons (Professional edition)
Advanced Regression (Professional edition)
Time Series Analysis (Professional edition)
Quality control graphs and charts (Professional edition)
Pareto Charts (Professional edition)
USING THE HELP MENU
The KWIKSTAT Help system contains items to help you operate the
program. These include:
PROGRAM HELP - Contains general program help information
TUTOR - Learn how to use the program
DECIDE WHAT ANALYSIS TO USE
CHANGE SETUP OPTIONS - Color, Printer, etc.
AUTOHELP/Hints (On or Off)
GO TO DOS, Return with Exit (Shell)
TUTORIAL:TRY THIS EXAMPLE
This short tutorial will give you a feeling for how to use KWIKSTAT.
It will assume you are using KWIKSTAT on a hard disk. To begin
KWIKSTAT, you must first be in the \KS4 directory on your hard disk.
Use the CD (Change Directory) command from the DOS prompt to change to
the \KS4 directory by using the command:
CD\KS4 (or the directory where you installed KWIKSTAT.)
Once in the \KS4 directory, begin KWIKSTAT with the KS command:
KS
The FILE pull-down menu will appear. (If the ANALYZE pull-down menu
appears, press the left arrow key twice to open the FILE menu.) This
example will use data already stored in a dBase ".DBF" file named
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EXAMPLE. Follow these steps:
Step 1 Select a data file: Open the database named EXAMPLE by
selecting the Open a database option from the FILE menu, then choose
EXAMPLE from the list of files. (If the EXAMPLE database does not
appear on the list of databases, you may not have installed the
program correctly.) Once the database is opened, a notice at the
bottom of the screen tells you that the database named EXAMPLE is
open, and it contains 50 records.
Step 2 View the contents of the database: Choose the List (display)
option from the menu.
Step 3 Choose the ANALYZE pull-down menu: From the ANALYZE pull-down
menu, choose the Graphs option. KWIKSTAT now switches to the Graphs
module (which may take a few seconds). Soon, you will see the Graphs
module menu.
Step 4 Select a plot type: From the Graphs menu, choose the TIME
SERIES PLOT option. The program now displays a screen with the fields
available for use by the graph. The field names appear in a pick box
to the left of the screen, and an empty box appears to the right of
the screen.
Step 5 Select fields to plot: From the left screen (list of fields),
choose which fields to plot in the time series plot. Choose the fields
TIME1 and TIME2.
When you choose a field, it will appear in the "Fields to Graph" box.
After you choose the two fields, choose "Finished Choosing Fields."
After a few seconds, a time series plot will appear containing two
lines.
The menu above the graph may be used to select user definable features
of the graphic display. The options include:
EXIT - exit the graph and return to the module menu.
OPTIONS - choose options for the graph including title, axis names,
footnote, and other options.
PRINT - print the graph to your printer.
CAP/PCX - capture the graph as a PCX file.
GET COLORS - choose colors to be used to display the graph.
+/- Smartpoint(tm) pointer used to select a datapoint on the screen.
Information about the selected point will be displayed. (see step 7.)
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Step 6 Control the plot menu: On all graphic screens in KWIKSTAT, a
similar menu will appear at the top of the screen. If you want the
menu to temporarily vanish, press the spacebar. Press the spacebar
again for the menu to reappear. The menu is active even if it is not
shown.
Step 7 Using SmartPoint(tm): If you are using a mouse, place the mouse
pointer on a datapoint on the screen and click. Or, if you are not
using a mouse, press the + (plus) key, then use the cursor keys to
position the + over a datapoint on the screen, and press Enter.
Information about the datapoint you selected will be displayed on the
screen. This feature is particularly helpful in identifying points
that are interesting or "outliers." Press Enter to return to the plot.
Step 8 Select color options: Press G or click on the "get color"
option. The color menu will appear. From this menu you can select
color options. Most plots contain the following "get colors" menu:
Menu - returns to the main graph menu
graph - changes graph colors
screen - changes background screen colors
labels - changes label colors
default - returns plot to original default colors
b&w - displays plot in black and white
help - displays help system
Some "get color" menus also contain the option:
tile - paints the plot using tiles rather than solid colors
Step 9 End this example: Choose Menu to return to the Graph menu.
Choose Exit to return to the main graph menu. Choose Exit again to
return to the module menu.
TIP: When you choose to print or capture the screen, the menu will
vanish, so the menu will not appear on the printout or PCX graphic.
NOTE: You can also go through an on-screen tutorial on how to create a
chart by choosing the TUTORIAL option on the HELPS pull-down menu.
EXAMPLE 2: DESCRIPTIVE STATISTICS
This example uses the data stored in the database named EXAMPLE.
Step 1 Open the database: To open the EXAMPLE database, select the
Open a Database option, then choose the EXAMPLE database.
Step 2 Select an analysis module: Open the ANALYZE pull-down menu and
choose the Descriptive Statistics option from that menu.
KWIKSTAT switches to the Descriptive Statistics module.
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Step 3 Choose analysis type: From the Descriptive Statistics menu,
choose "Detailed statistics (single interval variable)." The program
now displays the variables available for analysis from the database.
Step 4 Select a field: Select the AGE variable. KWIKSTAT will perform
calculations on the data in field AGE, and will produce a screen of
descriptive statistics. At the bottom of this
screen are several options.
The Descriptive Statistics report screen menu options are:
Exit - return to the main module menu
graph - displays a graphic representation of the data
view/print - allows you to print the information using the KWIKSTAT
text viewer.
ci - allows you to choose the confidence interval level.
percent - allows you to choose what percentiles will be displayed.
new var - returns you to the variable selection menu.
Step 5 Display the graph: Choose the Graph option. This screen allows
you to examine the distribution of numbers in the variable being
analyzed (AGE in this case.) Several options on this menu that were
not described in the previous example are:
exit - returns to the descriptive statistics summary screen.
mean CI off/on - displays a normal curve on the histogram, and shows
where the mean and confidence interval is located on the box plot.
print - prints the screen to the printer.
+ (plus) and -(minus) - redraws the histogram using more or fewer
classes. dist. off/on -- allows you to display a cumulative
distribution for the data.
cap/PCX - captures the graph in a file using the PCX graph format.
b&w or color - displays the graph using black and white or color.
Step 6 End this tutorial: Choose Exit to return to the previous
screen. Choose Exit again to return to the module menu. End KWIKSTAT
by choosing the Quit option. This ends the tutorial.
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===========================
USING THE KWIKSTAT DATABASE
===========================
The FILE and EDIT pull-down menus are used to manage your data.
Here is a roadmap to help you find the area of this chapter that
will be most helpful to you according to your database needs:
YOUR DATA IS ALREADY IN A DBASE DATABASE: If your data is already in a
database, you may not have to use any of the procedures in this
chapter. Simply copy your database into your KWIKSTAT data
subdirectory, and it will be accessible immediately. If you have
missing values, you should review the section titled "Missing Value
Codes." If you have memo fields in your database, review the section
called "Using dBASE files."
YOU NEED TO ENTER YOUR DATA: If your data is not already in a file,
you will need to create a database and enter your data. In this case,
read the next few sections beginning with "An Overview of Database
Creation and Design" and perform the two examples to learn how to
create a KWIKSTAT database. Your data is in a non-dBASE file: If your
data is already on the computer, but not in a dBASE (.DBF) file, you
can usually import the data into KWIKSTAT. See the section titled
"Using data from other programs" later in this chapter.
DATABASE CREATION AND DESIGN
The process for entering data and performing an analysis can be
summarized in three steps:
Step 1: Create a database.
Step 2: Enter data into the database.
Step 3: Choose an analysis option.
OPTIONS FOR CREATING A NEW DATABASE
Before you can enter data into a database, you must create a new
database. The New Database option on the FILE Menu is used to
create a new database. The structure, or layout, of a database must
be described before you enter your data. KWIKSTAT allows you to
create a new database in two ways:
1. Choose from a predefined structure or
2. Create a customized database structure.
The following sections describe these two options.
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CREATING A DATABASE FROM A PRE-DEFINED STRUCTURE
A pre-defined structure is a "blank" database designed for a
particular analysis type. Using a pre-defined database allows you to
create a database for your analysis without having to worry about what
fields are necessary, what type they should be, their width, and so
on.
The list below contains examples of some of the pre-defined database
descriptions available when you choose to create a New Database.
Choose the option that will create a database structure for the kind
of analysis you will perform. (You may have to scroll to see some of
the options.)
CREATE A CUSTOMIZED DATABASE
SINGLE VARIABLE, DETAILED STAT, HISTOGRAM, STEM & LEAF
GROUPED HISTOGRAM, STATISTICS OR STEM & LEAF
SIMPLE BAR CHART: LABEL AND VALUE
PIE CHART: LABEL AND VALUE
ETC...
CREATING A CUSTOMIZED DATABASE
If none of the pre-defined database structures meet your needs, you
need to create a customized database. The following sections describe
how you create a customized database structure to match your analysis
needs.
SPECIFYING FIELD TYPES REQUIRED BY AN ANALYSIS
When you create a new database, you must specify certain
information about each data field, including the field name, type,
width and number of decimals (if any):
1. The FIELDNAME: A fieldname must be 1 to 10 characters in length and
MUST begin with a character (a to z) and can contain letters, numbers
and the underscore character "_". Upper and lower case DO NOT matter,
since the name is always translated into all upper case.
2. The TYPE:Type may be . . .
CHARACTER - May contain any characters.
NUMERIC - Must contain numbers only. Example legal numbers are:1.00,
-4.32, 6, 10000. Example illegal numbers are: 450-23-1232, $23.95,
40%. (For data like these, use the character type.)
DATE or LOGICAL fields can be created in KWIKSTAT, but KWIKSTAT
analyses will only use numeric and character fields. Thus, date and
logical fields are treated the same as CHARACTER fields, except for
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subsettings and in transformations (Replace).
3. The WIDTH of the field: Choose a width so that the maximum number
of characters needed will fit into the field. For DATE or LOGICAL
types, field widths are automatically set at 8 or 1 respectively.
4. DECIMALS:Decimals are only valid for numeric fields. This specifies
to KWIKSTAT how many decimals to retain in the field. For example, if
you wish to store numbers that are dollar prices, your data may look
like "9999.99". This field would have a width of 7, with 2 decimals.
KWIKSTAT DATABASE LIMITATIONS
Maximum of 250 fields.
Maximum width of a field name is 10 characters.
Maximum width of a cell is 60 characters (15 for numbers).
Dates are always 8 characters and logical fields are 1 character wide.
Memo fields are not supported.
DATABASE EXAMPLES
This section provides you with two examples of creating a KWIKSTAT
database. Go over these examples before creating your own database and
performing your own analysis. Following these examples will answer a
number of questions you may have about how to use KWIKSTAT.
EXAMPLE 1, USING A PRE-DEFINED STRUCTURE
This example shows how you would perform an independent group t-test
in KWIKSTAT using one of the pre-defined database structures. In this
example, 13 plants were randomly allocated to two groups. Group one
received the present fertilizer and group 2 received a newer
fertilizer. After a period of time, you observed the heights of the
plants. The results are:
Data for independent group t-test (fertilizer study)
Present Newer Fertilizer
46.2 cm 51.3 cm
55.6 52.4
53.3 54.6
44.8 52.2
55.4 64.3
56.0 55.0
48.9
In order to enter this into a database, you must assign group numbers
(or letters) to each group. For example, we will call the "Present
Fertilizer" group 1 and the "Newer Fertilizer" group 2.
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The database will include thirteen records (one for each plant) and
two fields (one for the response and one for the group indicator).
When entered into the database, the data will look like this:
Group Height
1 46.2
1 55.6
1 53.3
1 44.8
1 55.4
1 56.0
1 48.9
2 51.3
2 52.4
2 54.6
2 52.2
2 64.3
2 55.0
Step 1 Create the Database: From the FILE Menu on the main KWIKSTAT
menu screen select New database.
Step 2 Name the Database: You will be prompted to enter the name of
the database you are creating. Type a name (e.g., TTEST (maximum of 8
characters)) and press Enter.
Step 3 Select a Structure type. A screen with the instruction "Choose
the database type to create from the menu below" will appear. Since
you are performing an independent group t-test, you can select the
option titled INDEPENDENT GROUP T-TEST OR ANOVA from this list. This
process automatically builds a database structure suitable for
entering data for this kind of analysis. In this case, the database
will contain a grouping field GROUP (where you will enter a 1 or 2,
the fertilizer type) and an observation field OBS (where you will
enter the height.)
Step 4 Enter the Data: A data entry screen will appear where you will
enter the data. In the spreadsheet type of entry, the field names are
listed at the top of the screen, and the record numbers at the left
side. The data you will enter in the first record is 1 (press Enter)
and 46.2 (press Enter). When you type the 46.2 and press Enter, your
cursor will automatically move to record number 2, where you will
enter 1 and 55.6, and so on.
Enter the data for the thirteen records. For each record of a "Present
Fertilizer" observation, enter "1" for the GROUP variable. For the
"Newer Fertilizer" observations enter a "2" for the GROUP variable.
The eighth record is 2 and 51.3. Once all 13 records have been
entered, the program will be waiting for a 14th record to be entered.
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Since there is no 14th record, press the F7 function key (Exit) to end
the data entry process. KWIKSTAT will return to the Data main menu.
Step 5 Performing the Analysis: From the main KWIKSTAT menu, select
ANALYZE. From the ANALYZE pull-down menu, select t-tests and Analysis
of Variance (ANOVA). The menu will appear.
Select Compare independent groups (t-test, ANOVA). A field selection
dialog box titled "Choose a grouping variable" will appear with the
following options:
Exit Choices
GROUP (N)
OBS (N)
Select GROUP as the grouping field. Another dialog box will appear
titled "Choose a data (numeric only) variable" with the same options.
Select OBS, as the data variable (OBS contains the height data). Note:
If you want to cancel the analysis, you would choose the Exit Choices
option.
KWIKSTAT will now perform the calculations and display another dialog
box on the screen with the following options:
A) View or print the calculated results
B) Graphical Comparison
Q) Quit, return to main menu
Choose the "A)View..." option. The results of the analysis will appear
on the screen in the KWIKSTAT viewer. Select Exit (F7) to exit the
viewer and return to option menu. Choose "Q)Quit..." to return to the
module menu. Select "X)Exit..." to return to the main KWIKSTAT menu.
EXAMPLE 2, CREATING A CUSTOMIZED DATABASE STRUCTURE
This example shows you how to enter data and perform some simple
statistics and graphs. It will show you both the spreadsheet and
database entry screens. The data that will be used is listed below.
The GRADE variable is the grade received in the class, AGE is age, SEX
is sex, WT is weight and SCORE is the score on a pre-test (maximum of
25 points). In database language, these variables are called fields.
Step 1 Choose the New database option: From the FILE menu, choose the
New Database option. You will be prompted to enter the name of the
database. Enter the name MYDATA (a DOS compatible filename).
Step 2 Choose Customize option: Once you have entered a filename for
the database, a list of database structures will be displayed similar
to the list on page 2-4. For this example, choose the CREATE A
CUSTOMIZED DATABASE option.
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GRADE AGE SEX WT SCORE
1 A 18 M 165 22.3
2 B 19 M 145 22.8
3 B 17 F 122 22.8
4 C 18 M 196 18.5
5 B 17 M 188 19.5
6 B 18 F 140 23.5
7 C 19 F 121 22.6
8 B 20 F 112 21.0
9 C 19 F 122 20.9
10 A 18 M 176 22.5
11 B 18 M 165 23.3
12 A 19 M 135 21.8
13 A 18 F 121 24.8
14 C 19 M 186 16.5
15 B 17 M 148 18.5
Step 3: Define the Database Structure: For each field (each item of
data) in the database, you must specify the following information:
A name of the field - something to identify it
The type of data - is it numeric or character?
The width of the field - enough to hold the biggest entry
Decimal places - if needed
For the data in this example, you will use the following information:
Field name Type Width Dec
GRADE C 2
AGE N 3
SEX C 2
WT N 4
SCORE N 5 1
The GRADE and SEX variables are of type "C" (Character) and the rest
of the variables are numbers "N". Only the SCORE variable requires a
decimal value. Enter the information about the database structure into
the database definition screen.
Step 4 Enter the data: A data entry screen will appear listing the
names of all of the fields and an area to enter the data. KWIKSTAT
includes two types of data entry screens, database type and
spreadsheet type. In the Setup routine, you chose one of these two
entry options. The following discussion shows you how to enter data in
the spreadsheet screen.
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TIP: You can toggle between spreadsheet entry mode and database entry
mode by pressing the F8 (Switch) key.
Step 4A Using a spreadsheet entry screen: The spreadsheet screen, as
shown in figure 2.7 looks similar to a spreadsheet. If you prefer to
use the database entry mode, skip to the section titled "Using a
database entry screen."
The names of the database fields (Grade, Age, etc.) are listed at the
top of the screen (columns) and the record numbers are listed down the
left side of the screen (rows). Initially, since you do not have any
records entered into the database, the only row displayed is the -ADD-
row, which indicates that you are adding a new record.
To enter data into the database, begin typing the entry for the first
field (GRADE). Type an A (upper case), then press Enter. Your cursor
moves to the next field (AGE). Type 18 and press Enter. Type upper
case M and press Enter. Continue until you have entered 22.3 in the
SCORE field. When you press Enter after entering 22.3, a new row
appears to allow you to enter the second record of information, and
your cursor moves to the first field of this record. Continue entering
information in the spreadsheet until all records are entered. If you
make a mistake on a record, you can use the right or left arrow keys
to move your cursor and correct the mistake. If you discover that you
have made an error in a previous record skip to step 5 now. When you
have finished entering the information in the database, end the entry
procedure, press F7 (Exit.).
Step 5 Correcting errors in the database: Before exiting the data
entry screen, you can correct errors in data entry mode by using the
F2 key to toggle into Edit mode. The edit screen is similar to the
screen used to enter data. Use the cursor keys to move to the field to
edit, and change the value. Exit the edit screen/data editor by
selecting the F7 (Exit) command. You will return to the KWIKSTAT main
menu.
Step 6 Perform a Descriptive Statistics analysis: Once you have
entered your data into the database, you are ready to perform one or
more analyses. From the main KWIKSTAT menu, choose the ANALYZE
pull-down menu. Choose the Descriptive Statistics option on the
ANALYZE menu. After a few seconds, the Descriptive Statistics menu
will appear. This menu lists the options you can choose from the
Descriptive Statistics module.
Step 7 Select Detailed Statistics: To calculate detailed statistics
for a variable in your database, select the option called "Detailed
Statistics (single interval variable)". A screen will appear prompting
you to specify what field to use in the calculations. Select AGE. The
detailed statistics screen for the selected variables will appear on
the screen. Once you have examined these results, select Exit to exit
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the screen. This output is discussed later in "Using Descriptive
Statistics."
USING THE KWIKSTAT FILE MENU
The FILE Menu is the first menu you normally use when you begin
KWIKSTAT. From this menu, you open a database or create a new
database. Either way, you usually must have data in a database before
you can perform an analysis. This section describes the options on the
FILE Menu.
NEW DATABASE
When you choose New Database from the FILE Menu, you will be prompted
to enter the name of the database. Enter a file name such as MYDATA.
(Eight characters maximum.) Once you have entered a filename for the
database, you can choose from a list of pre-defined database
structures, or create your own. See Examples 1 and 2 later in this
chapter for a tutorial on using a pre-defined structure or creating a
customized database structure.
OPEN A DATABASE
The Open a database to use option on the FILE Menu allows you to
access information in a dBASE file that you created in KWIKSTAT, in
dBASE, or in any other program that creates .DBF files.
If the database you want to use is not in the current (default)
directory, you can temporarily change the default directory by
selecting "Choose New Path (F2)". You will be asked to enter a path
name (such as \DB3). Then, the .DBF files in that directory will be
displayed in a list, and you can choose the database to use from that
list. Another way to open a database that is not in the default
directory is to enter it by name. To do this select "Enter Choice by
Name (F3)". You will be prompted to enter the name of the database to
use. For example, if the database you want to use is MYDATA.DBF and it
is in the \DB3 directory, you would enter \DB3\MYDATA. Do not include
the .DBF extension in the name.
Once a database is open, you will see its name at the bottom left of
the screen, along with the number of records in the database. Once a
database is open, you can edit, pack, modify, set missing values,
subset and list the database using the other options on the FILE Menu.
SUBSET A DATABASE
The Subset database option on the FILE Menu allows you to create a new
database from an old one. The new database can be a subset of the old
one, using a conditional criteria for outputting information from the
old database to the new one.
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For example, suppose you have a database with a field GROUP with
values 1, 2, 3, 4 and 5. You want to create a database that does NOT
include Group 5. After choosing Subset database from the FILE Menu,
you are asked for the name of the new database. For example, your new
database might be named NO5.DBF. You are asked for the field name to
be used in the selection criteria. In this case, you would choose the
field named GROUP. Next you must enter the selection relationship. It
will be described as a numerical expression. The conditional operators
you may use are:
= (equal)
> (greater than)
< (less than)
>= (greater than or equal to)
<= (less than or equal to)
<> (not equal to)
For example, you would enter the condition
GROUP <5
You can also use the logical operators .NOT., .AND., and .OR.. It is
important that a dot (.) appear before and after each logical
operator. For example, a conditional expression to include only groups
1 and 5 would be
GROUP = 5 .OR. GROUP = 1
Other examples of conditional expressions are
GROUP > STATUS
GROUP < WEIGHT*HEIGHT
TIME1 = TIME2*1.96
SEX <> 'F'
TIME1 <=20 .AND. SEX = 'M'
When you choose the Subset option from the FILE Menu, a Subset dialog
box appears on the screen. There are two items you must enter in the
Subset dialog box. First is a name for the new database. This must not
be the same name as the current database. Then, you must enter the
subset criteria. Examples of subsetting criteria are:
Once you have entered the filename and condition, press the F7 key to
begin the subset procedure. A database with the name you specified
will be created, containing the records selected by your condition
statement. Note: When creating conditional expressions for subsetting,
use the functions described in the table "Database Calculator
Functions" later.
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COPY/BACKUP DATABASE FILE
The Copy/Backup Database File option on the FILE menu allows you to
quickly create a backup copy of your database information. This is
recommended, particularly for large database because sometimes
databases become corrupt or are made unusable for some other reason.
LIST RECORDS
The List (display) the contents of a database option on the FILE Menu
allows you to look at the information in your database.
MODIFY OR DISPLAY STRUCTURE
The Modify or Display database structure option on the FILE Menu
allows you to display the structure of your database, and allows you
to change characteristics about the database structure. When you
choose to display the structure, a list of all field names, their
types, widths and decimals (if any) are listed. When you choose to
modify a database, you are given a chance to modify the
characteristics of each field. Your options are:
Delete the Field
Change Name of Field
Change Type of Field
Change Width of Field
Change Number of Decimal Places
If you change the type of field, say from character to numeric, the
program will attempt to convert the contents of the field to its new
type. When you modify a database, you will be asked to enter the name
of a new database. This means that the modified database will be in a
new file, and your old original database will remain intact. If you no
longer want the old database, you must delete it by choosing the Kill
database file option from the FILE Menu.
KILL (DELETE) A DATABASE
The Kill - Delete database file option allows you to delete a database
and its related missing values files (if any.)
FILE UTILITIES - EXPORT, IMPORT, REPORT
This menu provides several data utilities. When you choose this
option, the KWIKSTAT utilities menu appears. It allows you to choose
from these options:
Export data to an SDF file -- This option allows you to write out the
data in a database to an ASCII file. This option is useful when you
are wanting to transfer data from your KWIKSTAT database to another
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program that does not read .DBF files. See "Exporting Data" later in
this chapter.
Import data from a Comma Delimited file or from a 1-2-3 file -- See
the section below titled "Entering or Importing Data" for information
on how to import data into a KWIKSTAT database.
Report - Allows you to produce a report using the data in your
database. See the section titled "Printing a Report" later in this
chapter
Sort - (Professional Edition Only) Allows you to sort your database in
ascending or descending order using any field in the database.
EXIT KWIKSTAT
Use this option to end the KWIKSTAT program.
USING THE KWIKSTAT EDIT MENU
The EDIT menu allows you to modify and manage data in a KWIKSTAT
database. Often, after you have created a database, you need to add
new data or modify the current data. You can also add new fields,
calculate new variables and delete fields or records. This section
describes the options you can access from the EDIT menu.
EDIT RECORDS, ADD, DELETE OR REPLACE FIELDS
When you choose the Edit records option, the KWIKSTAT data editor will
appear. The data editor is described in detail in the section titled
"Using the KWIKSTAT Data Entry Screens" later in this chapter.
APPEND RECORDS, FROM KEYBOARD OR FILE...
The Append records option allows you to add new records to an existing
database. You have three data entry options:
Enter data from keyboard - Allows you to enter data by typing it on
the keyboard.
Enter data from a text file - Allows you to import data from an ASCII
file. See the Section titled "Entering and Importing Data" later in
this chapter.
Append data from a dBASE file - Allows you to append data from another
in this chapter.
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MISSING VALUES CODES
Sometimes in the collection of data there are values that are lost or
cannot be gathered. These are called "missing values". When such
values occur, it is important for the program to know that the values
are missing so that statistical calculations may take this into
account. Missing values are usually designated as an impossible value.
For example, the missing values designated for the variable AGE may be
-9, since it is impossible for the variable AGE to have the value -9.
When the program is asked to calculate the mean of age, for example,
it will ignore those records where AGE is -9 in that calculation if -9
has been specified as the missing value code. In most KWIKSTAT
procedures, there is a casewise deletion of the record from
calculation whenever a missing value is encountered.
Once you designate a missing value code for a variable, it is up to
you to make sure that this code gets placed into your database in the
proper records and fields. For example, if you have designated -9 as
the missing value code for AGE, you must make sure that in your
database a -9 appears in the field AGE if that data is missing or
unknown.
The Indicate missing value codes option on the FILE Menu is used to
set up these values. When this option is selected, the program will
display an entry screen that is similar to a data entry screen. You
may enter one missing value for each field name. The missing value
must obey the definition of the field in terms of length and type.
Once missing values are entered, they are stored on disk in a file
named filename. MV, where "filename" is the name of the designated
database. If a new variable is created using the transformation
procedure, its missing value is appended to the missing value file.
You may change or correct the missing values for a database at any
time by calling up this option. If missing values are already
designated for the database, they will be displayed on the entry
screen, and you may edit them or accept them as they are.
Note: If missing values are NOT used, and there is a blank numeric
variable in a calculation, it may be treated like the value 0 (zero),
so it is important to use missing values if your data contains such
entries. Otherwise, the statistical calculations may be in error!!
PACK DATABASE
The records marked for delete are not actually erased from the file at
this point. However, they will be ignored in most analyses, and will
continue to be displayed when you edit the database. See "Edit Mode
Options" later.
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If you want to permanently get rid of the records you have marked for
delete, choose the Pack procedure from the FILE Menu. This procedure
erases all "deleted" records from the database.
ZAP - GET RID OF ALL RECORDS
The Zap option in the EDIT menu allows you to quickly erase all
records from a database. To use this option, open a database, then
choose Zap.
USING THE KWIKSTAT DATA ENTRY SCREENS
If there is a need to change data already in a database, you may
choose the Edit records option from the EDIT menu. Editing is similar
to entering data. Use the up and down arrow keys to move from field to
field within a record and type in any change you want to make in the
field. The section below describes the menu bar options available to
you in the data entry screen.
USING APPEND & ENTRY SCREEN MENU BAR OPTIONS
When you are appending information to the database, there are several
function key options that you can choose. These options are listed at
the bottom of the entry screen.
APPEND MODE OPTIONS
To choose an option, press the function key related to the option, or
point to the option with the mouse and click. The options available
are:
F1 Help - Displays the KWIKSTAT Help menu.
F2 Edit - Toggles between edit mode (correct current entries) and
append mode (add new entries).
F7 Exit- Exits entry mode and returns you to the main KWIKSTAT menu.
F8 Switch - Switches between spreadsheet type entry and database entry
mode.
F10 Print - Print the current record to the printer or to a file.
EDIT MODE OPTIONS
When you are in edit mode, a slightly different menu bar appears
containing the following items:
F1 Help - Displays the KWIKSTAT Help menu.
F2 Append - Toggles between edit mode and append mode.
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F3 Delete - Marks one or more records for deletion. When you choose
this option you will be able to choose from the following options:
A) Mark this record for delete
B) UNMark all records where fieldname = value
C) Mark all records for delete where fieldname = value
D) UNMark a range of records
E) Mark a range of records
Q) Quit this option
You can mark as many records as you choose. Once you have marked the
records for delete, you can pack the database using the Pack option in
the Edit pull-down menu.
ANALYSIS TIP: Marking records for delete is a quick and simple way to
do an analysis on a portion of your database. Mark the records you
want to eliminate from an analysis, then perform the analysis.
KWIKSTAT will ignore the deleted records. Later, you can undelete the
records.
Note: A ^U (Ctrl-U) also deletes and single undeletes records. Place
your cursor on the record to delete or undelete, and press ^U.
F4- Erase/Insert - the current record permanently from the database.
(Only in spreadsheet entry mode.) When you choose this option the
following menu items will appear:
A) Erase records beginning with record #
B) Insert blank records before record #
Q) Quit this option
To erase one or more records, display the record in Edit mode.
Highlight the record to erase, and press the function key F4. You can
then choose to erase the single record or a range of records.
F5 Goto - Go to a record number.
F6 Undo - Returns last record changed to its previous values.
F7 Exit - Exits entry mode and returns you to the main KWIKSTAT menu.
F8 Switch - Switches between spreadsheet type entry and database entry
mode.
F9 Field - Insert or Delete a field in the database or Replace the
contents of a field. See "Creating New Fields and Replacing the
Contents of a Field" below.
F10 Print - Prints the contents of the current record to a printer or
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file.
CREATING NEW FIELDS AND REPLACING THE CONTENTS OF A FIELD
Using the F9 Field option in the Spreadsheet data entry screen, you
can create new blank fields of any field type, and place information
in those fields that is either a numeric or character expression. The
option menu displayed when you choose F9 Field is:
A) Insert a new field after the field: fieldname
B) Delete the field named: fieldname
C) Replace contents of field: fieldname
D) Set missing values for fields
Q) Quit this option
The following sections "Creating a New Field" and "Replacing the
Contents of a Field" describe these procedures.
CREATING A NEW FIELD
You may create a new field in a database within an edit screen by
choosing the F9 (FIELD Insert) option. After creating a new field, you
can then use the F9 (FIELD Replace) option to place a value in the new
field.
When you choose the Field/Insert option in the edit screen (F9), you
will be prompted to enter information about the new field.
Define a name for the new field
Define the field type
Define a width for the new field
For numeric variables,
Define the number of decimals, if any
Define a missing value code. If none is selected, it is assumed to
be 0 (zero).
After entering a new name for the field, you will be prompted to enter
the field type, width and decimals (if numeric). For example, if your
new field is numeric with a width of 8, and 2 decimal places, you will
enter
N,8,2
If the field is Character with a width of 3, you would enter
C,3
After you enter the type and width information, you will be asked if
you want to enter missing value codes.
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Note: All of the normal restrictions of defining a field remain.
TIP: To create a new field containing a new value that is a numeric
transformation of other fields, first insert the new field using the
F9 Field/Insert option, then use the F9 Field /Replace option to place
the value in the new field.
REPLACING THE CONTENTS OF A FIELD (TRANSFORMATIONS)
You can use the F9-Field Replace option in the Edit screen to replace
the existing contents of a field, or place new information in a newly
created blank field. KWIKSTAT provides a number of numeric and
character functions to enable you to do this.
For example, if you wanted to replace the contents of the field NEW
with the values TIME1/AGE:
Step 1 Highlight the field to replace: In the edit mode, highlight the
field whose contents you want to replace. Press the F9 (Field) option,
and choose "Replace the Contents of a Field" option from the Field
menu. A dialog box will appear.
Step 2 Specify which records to replace: The default is ALL, which
means all records in the database. Or, enter a range such as 1-20,
which would mean only perform the replacement in records numbered 1
through 20. Then, press Enter.
Step 3 Specify what to place in the field: For example, enter the
formula TIME1/AGE in the Replace With entry field, where TIME1 and AGE
are two other fields in the same database.
Step 4 Specify a condition for replacing (if any): The default is
NONE. For example, if you only want the replacement to be for records
whose value of AGE is greater than 20, you would enter the expression
AGE>20 in the condition entry field.
Step 5 Begin the replacement: Press F7 when you have finished entering
the Replace information, and the replace will begin. When it is
finished, you will return to the edit screen.
USING DATABASE AND MATHEMATICAL EXPRESSIONS
The kinds of expressions you can use in Subset and Replace options are
described below. KWIKSTAT supports two kinds of expressions.
1. Database expressions (most normally used.)
2. Mathematical expressions (signaled with an = preceding the
expression.)
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USING DATABASE EXPRESSIONS
Database expressions allow the use of common character, numeric, date
and logical fields in the expression. Use the mathematical expression
only when you must use mathematical functions not in the normal
database expression list. Here are the usage criteria:
In a REPLACE WITH field: Use either a database expression or a math
expression.
In a CONDITION field: Use only a database expression.
Most expressions can be handled with the database expressions. If you
find that you cannot create an expression using the database
functions, go to the section titled "Using Mathematical Expressions"
later in this chapter. The following information on how to use
expressions is useful for both the database and mathematical
expression types:
Arithmetic operators:
Add +
Subtract -
Divide /
Multiply *
Exponentiation ^ (Mathematical expressions only)
For Character fields, the database calculator supports the
operation:
Add + (appends one string to another)
Following are a few examples of correct expressions:
AGE/HEIGHT
LTRIM(FIRST)+' '+LAST
(AGE*TIME1)+3.2
Note: Literal strings included in expressions must be surrounded by
single quotes. For example, 'Hello' is a literal string. Character
field names are used without quotes. For example, NAME is a field
name. A correct string expression using these two strings would be:
'Hello '+NAME
DATABASE CALCULATOR FUNCTIONS SUPPORTED
The following functions may be used in expressions both in the
"Replace With" and "Condition" fields. In this table the arguments
have the following meanings
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NUM - Numeric argument
STG - String (Character) argument
DATEFMT - Date argument, MM/DD/YY
LOGICAL - T or F
LEXP - Logical Expression
AEXP - Any Expression
| means OR, choose one or the other option.
[ ] means optional argument
Database Calculator Functions
Name Meaning Example of use Type
------- ------------------------------------------------
ABS Absolute value ABS(NUM) N
ASC Ascii value ASC(STG) N
AT AT Find AT(STG1,STG2) N
CALENDAR Number to Date CALENDAR(NUM) D
CAPS First Letter Cap CAPS(STG) C
CHR Number to String CHR(NUM) C
DATE System Date DATE() D
DELETED Is record Deleted DELETED() L
IIF Logical If IIF(LEXP,AEXP1,AEXP2) CNL
INT Integer Round INT(NUM) N
JULIAN Date to Number JULIAN(DATE) N
LEFT Left string LEFT(STG,NUM) C
LEN String Length LEN(STG) N
LOWER Lower Case LOWER(STG) C
LTRIM Trim Left LTRIM(STG) C
MAX Max of 2 Nums MAX(NUM1,NUM2) N
MIN Mini of 2 Numbers MIN(NUM1,NUM2) N
REPLICATE Repeat String REPLICATE(STG,NUM) C
RIGHT Right String RIGHT(STG,NUM) C
RTRIM Trim Right RTRIM(STG) C
SPACE Space SPACE(NUM) C
STR Number to String STR(NUM) C
STRING Create String STRING(NUM,NUM|STR) C
RIGHT Right String RIGHT(STG,NUM) C
STUFF Stuff String STUFF(STG,NUM,NUM,STG2)C
SUBSTR Extract String SUBSTR(STG,NUM,[NUM]) C
TIME System Time TIME() C
TRIM Trim blanks TRIM(STG) C
UPPER Upper Case UPPER(STG) C
VAL String to Number VAL(STG) N
The following functions are supported only in the "Replace With" entry
field, and only for numeric field types. You MUST precede expressions
using these functions with an = sign.
An example of the RECODE function, which appears on the following
table is:
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=RECODE(SCORE,1,AGE,10,15)
The five arguments in the RECODE function are:
No. Example Meaning
1 SCORE Field to use in compare
2 1 Value to assign if comparison is true
3 AGE Value to assign if comparison is false
4 10 Low range of field to compare
5 15 High range of field to compare
Thus, this example means that the value of the RECODE is 1 if SCORE is
between 10 and 15, else the value is the current value of the AGE
field for that record.
USING MATHEMATICAL EXPRESSIONS
In the REPLACE WITH field, the default expression type is the database
type. In order for an expression to be evaluated as a strictly math
expression, you must place an equal sign "=" at the beginning of the
expression.
The major difference between the database and mathematical expression
types are their capabilities. The database expression can handle most
common calculations, including simple math, string evaluation, and
date evaluation. The math expression can be used only for strictly
numeric calculations using one or more of the functions listed in the
table below, or that uses the exponentiation operator.
For example, if you want to perform the calculation WEIGHT/HEIGHT, you
can enter the expression as-is in the REPLACE WITH field. However, if
you want to calculate the log of WEIGHT/HEIGHT, you must enter the
expression as
=LOG(WEIGHT/HEIGHT)
since the LOG function is not supported as a database expression
function. The equal sign signals to the program to use the math
calculator. For example, if you want to create a field that contains
the record number, you would use the expression
=RECNO
To create a field containing a random number from 0 to 100, you would
use the expression
=RAND*100
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Math Calculator Functions
Name Meaning Example of use
-------- ----------------------------------
ABS Absolute value ABS(SCORE)
AVE Average (Mean) AVE(LIST))
ACOS Arc Cosine ACOS(SCORE)
ASIN Arc Sine ASIN(SCORE)
ATAN Arc Tangent ATAN(SCORE)
ATAN2 Arc Tangent y/x ATAN2(y,x)
CSC Cosecant CSC(SCORE)
COS Cosine COS(SCORE)
COT Cotangent COT(SCORE)
EXP Exponentiation EXP(SCORE)
INT Integer INT(SCORE)
LN Natural Log LN(SCORE)
LOG Log base 10 LOG(SCORE)
MAX Maximum of list MAX(1,T2,3)
MIN Minimum of list MIN(1,T2,T3)
MOD MOD of number MOD(9,2) is 9 mod 2
PI PI PI = 3.14159265358979
RAND Random number number between 0 and 1
RECNO Record number database record number
RECODE Recode number RECODE(SCORE,1,0,1.1,2,2)
ROUND Rounds a number ROUND(1.236,2)=1.24
SD Standard Deviation SD(LIST)
SEC Secant SEC(SCORE)
SIN Sine SIN(SCORE)
SQRT Square root SQRT(SCORE)
SUM Sum of list SUM(1,2,3) = 6
TAN Tangent TAN(SCORE)
ENTERING & IMPORTING DATA INTO KWIKSTAT
When you choose the Append records... option from the FILE Menu, you
will be asked to specify entry from the keyboard or from a file (ASCII
file). For most small data sets, you will probably enter data from the
keyboard. If your data is already in another program that supports
ASCII, dBASE and 1-2-3 type files, you may be able to import the data
from that program into KWIKSTAT. The following information describes
how to enter data from the keyboard, from an ASCII file or from other
programs.
Once you have opened or created a database, you can enter data from
the keyboard by choosing the Append Records/from keyboard option from
the EDIT pull-down menu. When you choose this option, a sub-menu will
appear allowing you to choose to enter data from the keyboard, from an
ASCII file or from a DBF file.
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APPENDING DATA FROM ANOTHER DBASE FILE
If you have a dBASE file containing data that you want to append to a
current dBASE file, use the following procedure.
Note: For this procedure to work, the names of the fields in the two
databases must be the same. Only fields with the same name will be
imported.
Step 1 Open a database: Open a dBASE file by choosing the Open a
Database option on the FILE Menu.
Step 2 Choose Data Entry: From the EDIT menu, choose the Append Data,
from dBASE option.
Step 3 Specify the name of the dBASE file to read from: Enter the name
of the dBASE file containing the records you want to append. KWIKSTAT
will read the data, and will append data from the new database based
on the fieldnames in the currently opened database.
Step 4 Verify the import: After appending, you should perform a list
to verify that the database contains the information you want.
USING LOTUS 1-2-3 TYPE FILES
If you have a Lotus 1-2-3 WKS or WK1 file and cannot use the Lotus
program to translate it, you can use the KWIKSTAT import feature from
the File Utilities/Import option from the FILE Menu.
Note: Import will allow you to import a maximum of 128 fields.
USING COMMA DELIMITED ASCII FILES
If your program outputs comma delimited ASCII files, that is, there is
a comma between each field, KWIKSTAT can import this data using the
"Comma Delimited" option in the File Utilities FILE Menu option.
The data to be imported can contain numbers and character fields.
Character fields must be enclosed in quotes "". An example file on
disk is EXCOMMA.DAT. The first few lines of this file are:
"A",12,22.3,25.3,28.2,30.6,5,"Text"
"A",11,22.8,27.5,33.3,35.8,5,"Text"
"B",12,22.8,30.0,32.8,31.0,4,"Text"
"A",12,18.5,26.0,29.0,27.9,5,"Text"
The import procedure looks at the first line of the file to determine
how many fields to create. This file has 8 fields. The first and last
are character. The fields will be named VAR1, VAR2, etc. You can
change these names in the "modify database" option, main menu. The
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import will attempt to create widths that will allow full storage of
numbers and text. Everything after that is automated. Look at the
file with the List option to verify that the imported data is correct.
EXPORTING DATA
You may output the data from your KWIKSTAT (DBF) file into a standard
ASCII TEXT file. (Often called an SDF file - Standard Data Format
file.) Outputting the data is useful for transferring your data to
other programs. Along with the output of data, you may also output a
"format" file, which describes the contents of the text file. This
file can be output in "dBASE" style or "SAS" (Statistical Analysis
System) style. The SAS format could be used in a SAS INPUT statement
to read the ASCII data file into the SAS program.
To export data, choose the File Utilities option from the DATA
pull-down menu to display the KWIKSTAT. From the Utilities menu,
choose the "Output data to an ASCII file (SDF Standard Data Format)"
option.
PRINTING A REPORT
You may output a listing of the data in the dataset (or a selected
subset of the database) by using the report facility. To use this
procedure, choose the "Report: Output data in a report format" option
after choosing the File Utilities option on the FILE Menu. In this
procedure you may specify the following report features:
Which Data Fields To Output
Output Record Number As A Column
Title
Number Of Lines Per Page
Width Of Page (default is 80)
Output To A File Or Printer
Output A Subset Of The Data (search)
NOTE:You may want to place a coded variable in your data set which
will allow you to easily select a subset of data to output. Subset
searches can be:
1) Exact: case is ignored.
2) First one or more letters in a field: (AL* matches ALLEN, ALBERT,
etc)
3) Keyword: match a letter pattern within a field (i.e., [AL] matches
ALLEN, BALES, etc).
The REPORT procedure is menu driven. Simply answer the questions as
you are prompted. If the report is too wide to fit on a single width
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of the specified paper width, the report will be printed in parts.
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BASIC STATISTICAL ANALYSIS PROCEDURES
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This section of the KWIKSTAT manual describes the statistical analysis
procedures available in the BASIC KWIKSTAT edition. The data
generation and simulations module contains several examples of
statistical concepts such as a coin flip, sampling from a
distribution, and confidence intervals.
USING DESCRIPTIVE STATISTICS
The Descriptive Statistics module allows you to examine summary
statistics of the data in a database.
DETAILED STATISTICS FROM AN EXISTING DATABASE
This option calculates the mean, standard deviation, median, standard
error of the mean, minimum, maximum, sum, variance and other
descriptive statistics for a single variable (field) from a set of
data.
If your data is already in a database, perform the analysis using the
following steps. For example, suppose you want to calculate statistics
for the TIME1 field in the EXAMPLE database.
Step 1 Open the database: Choose Open Database from the FILE pull-down
menu. Select the EXAMPLE database.
Step 2 Choose Analysis option: Choose the Descriptive Statistics
option from the ANALYZE menu.
Step 3 Choose the analysis type: Choose the "Detailed Statistics"
option from the Descriptive Statistics menu.
Step 4 Choose the field to analyze: Choose the TIME1 field.
A screen will appear displaying statistics on that variable.
DEFINITIONS
C. I. - Confidence interval - This is a range that describes (with
some confidence -- usually 95% confidence) where the actual mean of
the data probably lies. That is, the true mean of the data shown
above is somewhere between 20.79 and 21.23, with 95% confidence.
MAXIMUM - The largest number.
MEAN - A measure of central tendency. The arithmetic average. For
example if you average the three grades 82, 100 and 88 (82+100+88)/3 =
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90 -- the average (or mean) is 90.
MEDIAN - A measure of central tendency. The mean is a statistic such
that 50% of all numbers in the sample are above the mean and 50% are
below the mean. For example, in the list 1, 2, 3, 4, 5 the median
would be 3.
MINIMUM - The smallest number.
MISSING - Reports how many numbers had a missing value code.
N - How many numbers were used to calculate the statistics.
PERCENTILES - Tells you what percent of numbers are lower than the
percentile. For example, the 50th percentile is the median.
S.E.M. - The Standard Error of the Mean measures the spread of the
data around the mean value.
ST. DEV. - Standard Deviation - measure of the spread of the data. It
is calculated two ways, using n-1 as a divisor and using n as a
divisor. Usually, most people use the n-1 version.
SUM - The total of all the numbers added together
TEST FOR NORMALITY - (Professional edition) - This is a test that the
data is normally distributed. The test statistic is D. If the p-value
is < 0.05, there is evidence to assume that the data are NOT normal.
TUKEY 5 NUMBER SUMMARY - Essentially, the 0th, 25th, 50th 70th and
100th percentile. See the Hoaglin, et al. reference.
VARIANCE - A measure of the spread of the data.
SUMMARY STATISTICS ON A NUMBER OF VARIABLES
This option allows you to calculate statistics on several variables
(sample size, mean, standard deviation, minimum, maximum, and standard
error of the mean). If you have a grouping variable in your database,
you may request output of summary statistics by group.
Suppose you want to know the means of all the quantitative variables
(AGE, TIME1, TIME2, TIME3, TIME4, STATUS) within each of the three
groups (A, B, C) in the EXAMPLE database. Follow these steps:
Step 1 Open the database: Choose Open Database from the FILE pull-down
menu. Select the EXAMPLE database.
Step 2 Choose Analysis option: Choose the Descriptive Statistics
option from the ANALYZE menu.
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Step 3 Choose the analysis type: Choose the "Summary Statistics"
option from the Descriptive Statistics menu.
Step 4 Choose the fields to analysis: Select the fields AGE, TIME1,
TIME2, TIME3, TIME4, then select the "Finish choosing fields" option.
Step 5 Choose the grouping field: Select STATUS as the grouping field.
The KWIKSTAT viewer will appear displaying statistics on that
variable.
Step 6 Exit the viewer: Then exit the module or perform another
analysis.
DETAILED STATISTICS FROM DATA ENTERED BY COUNTS
If you have a small amount of data or if your data is grouped so that
you know how many of each number you have (i.e., you have 12 people
13 years old, 5 people 14 yrs old, 6 people 15 yrs old, etc.) you can
enter the data at the keyboard. When you choose this option a screen
will appear allowing you to enter your data. Either enter a single
value or a value followed by a comma and the number of times that
number should be used. For example, entering 34,5 would mean that you
are entering 5 values of 34. When you enter nothing on a line, this
signals that you are finished entering the data. A detailed statistics
screen will appear similar to the one described above.
APPROXIMATE P-VALUE DETERMINATION
This option calculates p-values for four test statistics: normal (z),
student's t, F, chi-square. Enter the statistic, degrees of freedom
and the calculated value of the statistic, and the program will tell
you the p-value associated with that statistic.
To calculate a p-value, follow these steps:
Step 1 Begin the Descriptive Statistics module: From the main menu
bar, open the ANALYZE pull-down menu, then choose the Descriptive
Statistics option.
Step 2 Choose the p-value option: Select Approximate p-value
determination.
Step 3 Enter the p-value information: You will be prompted to enter an
equation. On the left hand side, designate the test statistic being
used, i.e., z= , t(df)= , F(dfn,dfd)= , or X(df)=. In parentheses, as
shown by (df), enter the appropriate degrees of freedom. On the right
hand side of this equation, enter the calculated value of the
statistic you wish to know the p-value. For example:
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t(20)=2
means you want the two-sided p-value for a calculated t-statistic of
2.00 with 20 degrees of freedom. In this case, the result is p=0.059.
Step 4 Exit p-values: To exit the p-value determination procedure,
enter End.
STEM AND LEAF DISPLAY
The Stem and Lead Display is a graph created from a series of numbers.
The Stem part of the display is the leading digit for the data (such
as 5 in 54) and the leaf is the trailing digit (such as the 4 in 54).
When larger numbers are used, the rightmost digits are often ignored.
For example, if the numbers range from 241 to 845, the stem might be
the 2 to 8, representing 200 to 800, and the leaf would be 0 to 9,
representing the 10's. The 1's place would be ignored. KWIKSTAT gives
you options for choosing the magnitude of the stem and leaf values.
DESCRIPTIVE AND COMPARATIVE GRAPHS
The Graphs - Descriptive and Comparative module allows you to create a
number of different charts and graphs.
CREATING A BAR, LINE OR AREA CHART
The Bar/Line Area chart option allows you to create a graph using any
combination of these kinds of charts. You can also choose other
options for this graph as discussed later in this section. The
following two examples show you how to display a bar chart by creating
a new database using a current database.
BAR CHART EXAMPLE 1
Step 1 Create the database: Create the database and enter the data.
Your database should contain a Label field and a Value field (the
value field contains the numbers to use for the plot.) You can use the
"SIMPLE BAR CHART" pre-defined structure when creating a new database
for this graph. For this example MAGNET is the LABEL field and NAILS
is the VALUE field.
----These are the fields.-----
RECORD LABEL VALUE
------ ------
1 SMALL 31 -+
2 MEDIUM 38 |--- This is the data to plot.
3 LARGE 51 -+
|
+----------------- These are the plot labels.
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Step 2 Enter the Data: Enter the 3 records shown above.
Step 3 Choose Analysis option: Choose the Graphs option from the
ANALYZE menu.
Step 4 Choose the analysis type: Choose the "Bar/Line/Area" option
from the Graphs menu.
Step 5 Choose the field to graph: Since there is only one numeric
field, KWIKSTAT automatically select the Data field.
The resulting chart contains 3 bars labeled SMALL, MEDIUM & LARGE.
(You could also use this same data to create a pie chart.
BAR CHART EXAMPLE 2
This example will use data already in the database named BARCHART.
When creating a bar/line/area chart, you can choose more than one
value field and create a side-by-side bar chart, a stacked bar chart,
a line chart, an area chart, a point chart, or a chart containing a
mixture of these types. The data in this example will be used to
create a chart that includes 2 bars and a line graph.
Step 1 Open the database: Open the database named BARCHART.
Step 2 Choose fields: Choose the fields VAR1, VAR2 and VAR 3 as the
data fields, then choose "Finished Choosing Fields." Select LABEL as
the label field. A chart will appear containing three side-by-side
bars.
Step 3 Choose <options> from the graph menu: An option screen will
appear that allows you to enter a title, footnote and other options.
At the bottom of the screen choose <PgDn-Next>. This will display the
second option screen. See "Options While Displaying a Bar Chart"
below.
Step 4 Choose types: For Var3 choose the W (Wide Line) type by
entering a W in the Type column or by clicking on the option until a W
appears.
Step 5 Display plot: Choose (F7-Continue) to display the plot. You can
use the <get color> option to select whether the bars will use colors
or tile patterns.
Your chart can contain any combination of bars, lines, area and point
charts.
While displaying a bar chart, you can choose from a number of
options. Some of these options are:
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<options> from the menu at the top of the screen, and a two-screen
option form will appear. On the first screen of the form, you can
specify the axes labels, footnotes, and whether the bars should be
stacked.
Select the <Next> option to display the second screen option form.
On this form you can specify :
Legend - For each bar/line etc.
Type - choose from Bar, Line, Wide Line, Area or Point
Cumulative - Yes or No
Color or Patterns - Choose from 14 colors or 10 patterns. Patterns are
displayed if the Tile option has been chosen from the main graph menu.
Display Counts - Yes or No
By clicking on the the Type, Cumulative or Display counts option, the
options will cycle through the list of options. For Legend, Colors or
Patterns, enter the desired or color or pattern number. After making
changes in the options, display the chart by selecting <<F7 -
Continue>> option.
CREATING A PIE CHART: A pie chart is created from a list of counts.
(See Help)
CREATING A TIME SERIES/LINE PLOT: A time series plot is useful in
examining data that are time related, such as profit by month, etc.
(See Help)
CREATING AN XY PLOT (SCATTERPLOT): An XY plot (scatterplot) displays
the relationship between two variables. (See Help)
PRODUCING A HISTOGRAM: A histogram can be helpful in determining if
the distribution of a continuous variable is approximated by a normal
distribution. (See Help)
DISPLAYING BY-GROUP PLOTS: By Group plots allow you to display graphs
that show comparisons across groups. (See Help) Types of plots you
can display in by-group plots include:
A) Box Plot Comparison
B) Dot Plot Comparison
C) Mean and Error Bar Comparison
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3-D SCATTERPLOT/ SPIN PLOT
The KWIKSTAT "SPIN" module allows you to interactively view three
dimensional (XYZ) scatterplots and allows you to rotate the plot
along the x, y, or z axes, spin the data, and choose other display
options.
CREATING A SPIN PLOT
The Spin Plot procedure expects your database to contain at least
three numeric fields and (optionally) a group field. From these
fields, it can display a three dimensional XYZ plot. For example,
using the CAR database, follow these steps to create a graph:
Step 1 Open the database: From the main KWIKSTAT FILE menu, open the
database named CAR. Or, if you are already in the SPIN module, open
the database by selecting the "ChooSe a database to open" option.
Step 2 Begin the Spin module: If you have not already done so, begin
the Spin plot module by choosing the Spin Plot option from the ANALYZE
pull-down menu. The Spin Plot module menu will be displayed.
Step 3 Select the plot type: From the Spin Plot menu, choose choose
the "3D XYZ Data visualization plot."
Step 4 Select the fields to plot: A pick list of fields will appear
allowing you to choose three data fields, and optionally, choose a
grouping field. For the CAR database, choose the following fields (in
this order) MPG, WEIGHT and HP. For the grouping field, choose
CYLINDERS.
Note: When a grouping variable is used, the points on the plot will be
displayed where points for each different group (up to 10 groups) will
appear in different colors or points for different groups will be
displayed using a different shaped point (such as a circle, square,
diamond, etc.) Once you have chosen the fields, an initial plot
appears.
Step 5 Spin the Plot: To examine the relationships between the
variables, spin the plot on one or more axes to view the relationships
from different angles by pressing an arrow key or PgUp or Pg Dn or
click on the Spin menu options.
SPIN PLOT MANIPULATION OPTIONS
Manually rotate the plot (up-, down-, left- and right-arrow, PgUp and
PgDn keys) by choosing Roll, Pitch or Yaw. Either point to one of
these options with the mouse and click, or press the designated
keyboard button to choose one of these options. Click and hold on a
spin option and the plot will continue spinning until you let up on
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the mouse button.
Automatically spin the plot by pressing CTRL, plus a Roll, Pitch or
Yaw button (i.e., CTRL-rightarrow). Stop the spinning plot by pressing
a Roll, Pitch or Yaw button (without CTRL).
Grow or Shrink: + or -
Increase or decrease the degree of move: > or <
USING T-TESTS AND ANOVA PROCEDURES
T-tests and Analysis of Variance (ANOVA) procedures are used to test
hypotheses about population means using data obtained through random
sampling of those populations.
EXAMPLE: TWO SAMPLE T-TEST (INDEPENDENT GROUPS)
The data used here are heights of 13 plants grown using two different
fertilizers. Suppose you want to know if there is a difference in the
average heights of plants in the two treatment groups.
Data for independent group t-test (fertilizer study)
Present Newer Fertilizer
46.2 cm 51.3 cm
55.6 52.4
53.3 54.6
44.8 52.2
55.4 64.3
56.0 55.0
48.9
Step 1 Create a database: See the tutorial example earlier for
information on how to enter this data into a database.
Step 2 Enter the data into the database.
Step 3 Select the analysis to perform: Choose the t-tests and Analysis
of Variance (ANOVA) option from the ANALYZE pull-down menu, then
choose the "Compare independent groups (t-test, ANOVA)."
Step 4 Select the fields to use: Select GROUP as the grouping variable
and OBS (Height) as the data (response) variable. The results appear
on the screen.
Step 5 Analyze the results: A menu will appear allowing you to view
the results or display a graphical comparison. Choose to view the
results. Exit the viewer by choosing F7-Exit.
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Step 6 View the graphical comparison: Select "Graphical Comparison"
from the options menu to display a comparison of the results. This is
the same graph described earlier in the section "Displaying By Group
Plots." Initially, this plot shows an error bars comparison. Exit the
viewer by choosing the <Exit> option.
EXAMPLE: SINGLE FACTOR ANOVA
When more than two independent groups are compared with respect to one
variable, one-way or single factor analysis of variance techniques are
appropriate. This example uses data for hogs which have been randomly
assigned to four groups, with each group being given a different feed.
The response is weight gain.
Data for Independent Group ANOVA
Gp 1 Gp 2 Gp 3 Gp 4
60.8 78.7 92.6 86.9
67.0 77.7 84.1 82.2
54.6 76.3 90.5 83.7
61.7 79.8 90.3
The database to analyze this data is similar to the one used for the
t-test example above, differing only with respect to the number of
groups. In fact, this one-way ANOVA is an extension of the t-test when
there are three or more groups. To perform this analysis, use these
steps:
Step 1 Create or Open a database: Create a database using the "FOR
INDEPENDENT GROUP T-TEST OR ANOVA" pre-defined structure. GROUP will
be the grouping field. The groups will be numbered 1,2,3,4 according
to the type of feed used. The response field will be OBS. Or, open the
database named HOG, and skip to step 3.
Step 2 Enter the data: The data, as entered into the database will
look like this:
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RECNO GROUP OBS (WEIGHT)
1 1 60.8
2 1 67.0
3 1 54.6
4 1 61.7
5 2 78.7
6 2 77.7
7 2 76.3
8 2 79.8
9 3 92.6
10 3 84.1
11 3 90.5
12 4 86.9
13 4 82.2
14 4 83.7
15 4 90.3
Step 3 Select the analysis to perform: Choose the t-tests and Analysis
of Variance (ANOVA) option from the ANALYZE pull-down menu, then
choose the "Compare independent groups (t-test, ANOVA)."
Step 4 Select the fields to use: Select GROUP as the grouping field
and OBS (Weight) as the response variable. The results appear on the
screen.
Step 5 Analyze the results: The results of this test are summarized in
the p-value. In this case, the small p-value (p<<0.001) means that
there is a significant difference between groups. This is taken as
evidence of a "real" difference between feeds, a difference not due to
chance.
The ANOVA tells you only that there is a difference among the feeds.
In order to find out which groups are significantly different from
which others, examine the multiple comparison results. The
Newman-Keuls multiple comparison test (or whichever you specified at
setup) will describe which of the means are significantly different
from which others (at the 0.05 significance level). One part of the
output is the multiple comparison test. The test performed depends on
what option you chose during setup. This example will describe the
results of the Newman-Keuls test. The results of this test are as
follows:
Gp Gp Gp Gp
1 2 4 3
-------
----
----
The group numbers are given in increasing order of the value of their
group means. That is, Group 1 has the smallest mean, Group 3 the
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largest. At the 0.05 significance level, the means of any two groups
underscored by the same line are not significantly different. This
display tells you that (at the 0.05 significance level):
1) The mean for group 1 (feed 1) is statistically significantly less
than the means for all other groups.
2) The mean for group 2 (feed 2) is significantly greater than the
mean for group 1, and significantly less than the means of groups 4
and 3.
3) The means for groups 4 and 3 are not significantly different from
each other, but they are both significantly greater than the means of
groups 1 and 2.
You can conclude that feeds 3 and 4 are better than feeds 1 and 2, but
there is not enough evidence to say that either feed 3 or 4 is the
best overall.
Step 6 View the graphical comparison: Select "Graphical Comparisons"
from the options menu to display a graphical comparison of the
results. This is the same graph described earlier in the section "By
Group Plots." Initially, this plot shows a comparison using error
bars. This figure shows a box plot comparison. From this plot you can
visually see that groups 3 and 4 are similar and that group 1 is much
lower than the rest. Exit the viewer by choosing the <Exit> option.
PARAMETRIC REPEATED MEASURES (PAIRED) ANALYSIS
Repeated measures are observations taken on the same or related
subjects over time or in differing circumstances. Examples would be
weight loss, or reaction to a drug across time.
EXAMPLE PAIRED T-TEST
The data in this example are before and after weights for eight
persons on a diet. Notice that in this case, both data values are
taken from the SAME entity (person). Follow these steps to perform
this analysis:
Step 1 Create or Open the database: Use the pre-defined database
structure named "FOR PAIRED T-TEST OR McNEMAR's TEST." This will
create a database with the fields REP1 and REP2. The REP1 will be used
for Before and REP2 will be used for After. Or, open the database
named DIET, and skip to step 3. Data for paired t-test
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Person Before After
1 162 168
2 170 136
3 184 147
4 164 159
5 172 143
6 176 161
7 159 143
8 170 145
Step 2 Enter the data: Enter the data for the eight records. The
database should look similar to the listing of the data above.
Step 3 Choose the analysis: Choose the t-tests and Analysis of
Variance (ANOVA) option from the ANALYZE pull-down menu. Then choose
the "Compare repeated or paired data (t-test, ANOVA)" option from the
module menu.
Step 4 Select the fields to use: Select REP1 (BEFORE) as the first
field and REP2 as the second field.
Step 5 Analyze the results: Choose to View the results from the
options menu. Select "Graphical Comparisons" from the options menu to
display a graphical comparison of the results.
EXAMPLE ONE-WAY REPEATED MEASURES ANOVA
For more than a pair of repeated measures on the same subject, a
one-way repeated measures analysis of variance is appropriate. The
data in this example are repeated measures of reaction times of five
persons after being treated with four drugs in randomized order.
One-way repeated measures ANOVA data
Person Drug 1 Drug 2 Drug 3 Drug 4
1 31 29 17 35
2 15 17 11 23
3 25 21 19 31
4 35 35 21 45
5 27 27 15 31
The results of this ANOVA are summarized in the p-value. In this case,
the small p-value (The (p=)0.000 on the "Repeated Factor" line in the
ANOVA table.) means that there is a statistically significant
difference in the mean response times for the four drugs.
The Newman-Keuls multiple comparison test (or whichever multiple
comparison test you chose at setup) describes which of the means are
significantly different from which others (at the 0.05 significance
level). See previous ANOVA example.
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SINGLE SAMPLE ANALYSIS
This option allows you to choose a single variable, and test a
hypothesis that the mean differs from an hypothesized mean. You must
enter the hypothesized population mean.
DUNNETT'S TEST
Dunnett's test is a multiple comparison procedure following a one-way
ANOVA that compares a control mean with the other means in the
analysis.
NON-PARAMETRIC PROCEDURES
Non-parametric procedures are appropriate when the assumption of
normality cannot be made for a small data set or when a large data set
is known to be from a non-normal population. Non-parametric procedures
are generally based on ranks rather than actual data values, so these
procedures can be useful also when actual data values are not known,
but the order or ranks of the data values are known.
MANN-WHITNEY PROCEDURE
If two independent groups, such as in this example, are being
compared, the Mann-Whitney U-statistic is calculated.
EXAMPLE: MANN-WHITNEY TEST OF TWO INDEPENDENT GROUPS
The fertilizer data from the t-test example are used in this example.
If you have not already created the database for this data set, do so
now by referring to that example. Follow these steps to do this
example:
Step 1 Open the database: Open the database named FERTILIZ and choose
the Non-Parametric Comparisons option from the ANALYZE menu. Or, if
you are already in the Non-Parametric module, select the "ChooSe a
Database" option and open the FERTILIZ database.
Step 2 Select analysis type: From the Non-Parametrics Comparisons menu
select "Independent groups - Mann-Whitney, Kruskal-Wallis."
Step 3 Select fields to use: Choose GROUP as the grouping variable
and OBS (HEIGHT) as the data (response) variable.
Step 4 View the results: KWIKSTAT will display the results, including
the Mann-Whitney U statistic, the rank sums, sample sizes and mean
ranks of the groups, a z statistic and an approximate p-value. In this
case, U'=24.00, U = 16, z=0.357 and p=0.721.
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The p-value of 0.721 is large so the null hypothesis of no difference
in medians between groups is not rejected. There is not sufficient
evidence based on this procedure to say that there is a difference
between the median heights of plants in the two groups grown using
different fertilizers.
KRUSKAL-WALLIS PROCEDURE
If more than two independent groups are being compared using
non-parametric methods, KWIKSTAT uses the Kruskal-Wallis test. The
database used is of the same form as for the one-way independent
gropu analysis of variance.
KWIKSTAT will display the Kruskal-Wallis H-statistic, the rank sums,
sample sizes and mean ranks of the groups, a chi-square statistic and
an approximate p-value, and a graph of the results similar to the
one described for the one-way ANOVA.
NON-PARAMETRIC REPEATED MEASURES ANALYSIS - FRIEDMAN'S TEST
When repeated observations are taken on the same subject, and there is
interest in comparing the observations for each repeated measure
(e.g., each type of treatment), then a repeated measures analysis may
be appropriate. Data for Friedman's test is the same as described in
the one-way repeated measures ANOVA. The results include a multiple
comparison of groups.
NON-PARAMETRIC DICHOTOMOUS DATA ANALYSIS - COCHRAN'S Q
Cochran's Q procedure is a non-parametric procedure appropriate for
use with dichotomous data when the experiment involves repeated
measures on blocks. The response of the subjects to the treatments is
dichotomous if it is taken as one of only two possible outcomes, often
labeled "success" and "failure", rather than as a measurement.
USING REGRESSION & CORRELATION PROCEDURES
To examine the linear relationship between variables, correlation and
linear regression are used.
SIMPLE LINEAR REGRESSION ANALYSIS
Data for this example of simple linear regression are Homicide Rate
and Handgun Licenses Issued per 100,000 population for the years 1961
to 1973 in Detroit (Fisher, 1976, reprinted from Gunst and Mason,
1980).
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Data for simple linear regression (handgun study)
Year Homicide Handguns
Rate Registered
1961 8.60 178.15
1962 8.90 156.41
1963 8.52 198.02
1964 8.89 222.10
1965 13.07 301.92
1966 14.57 391.22
1967 21.36 665.56
1968 28.03 1131.21
1969 31.49 837.60
1970 37.39 794.90
1971 46.26 817.74
1972 47.24 583.17
1973 52.33 709.59
Since you want to compare the homicide rate with handguns registered,
you need a database with only these two sets of numbers (you can
exclude year.) The data for this example is stored on your disk as
HANDGUNS.DBF with the variables HOMICIDES and HANDGUNS. See chapter 2
if you need information about how to create a database. To perform a
simple linear regression using this data, follow these steps:
Step 1 Open the database: Open the database named HANDGUNS. If you are
at the main menu, select the Open a Database option from the FILE
menu, then choose Regression and Correlation from the ANALYZE menu. If
you are in the Regression module, select "ChooSe a Database."
Step 2 Select analysis type: From the Regression menu, choose the
"Simple Linear Regression" option.
Step 3 Select the fields to use: Select HOM_RATE as the DEPENDENT (Y)
variable first, then select HAND_REG as the INDEPENDENT (X) variable.
Step 4 View the results: KWIKSTAT will perform calculations and
display a menu. Choose "View/Print Results," which will display
information as shown in figure 4.21. Exit the viewer with F7/Exit.
Step 5 View the Plots: View a scatterplot of the original data with
the fitted regression line, and a plot of the residual values by
choosing "Display Plot" items from the options menu.
Step 6 Forecast new values: You may optionally want to predict new
values from the calculated regression line. If so, choose that option,
and enter the number or range of numbers of the Independent variable
you want to use to predict.
Pearson's correlation coefficient (r) is reported (0.7263) as well as
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R2 (R-Square, 0.5275). The linear regression equation given is a
mathematical representation of a straight line that passes through a
plot of the data, and can be used to predict the dependent variable
(HOMICIDES) given a value for the independent variable (HANDGUNS). In
this case the linear regression equation is:
HOMICIDES = 4.910512 + 3.761144E-02 * HANDGUNS
If you want to predict the homicide rate for 300 handguns registered,
you would use the equation:
HOMICIDES = 4.910512 + 3.761144E-02 * 300
A t-test is performed to test the statistical significance of the
linear relationship between the two variables. A low p-value means
that the two variables are significantly related.
Regression Plots: These plots are helpful to determine if a linear fit
to the data is appropriate. The scatterplot shows you how compact or
spread apart the points are around the fitted lines, and may help you
discover outliers. The residual plot helps you determine if a linear
fit is appropriate.
Predicting new values: When you choose this option, you will be
prompted for one or more X variable values for which you wish to
predict Y variable values.
MULTIPLE REGRESSION ANALYSIS
Multiple regression is an extension of simple linear regression into
several dimensions (several independent variables). In the multiple
regression procedure, you must enter a list of the independent
variables and a single dependent variable on which you wish to perform
the regression analysis. In KWIKSTAT you may use up to 10 independent
variables in this option. Multiple regression can be complicated.
KWIKSTAT calculates and displays several results, including the
coefficients and intercept of the regression "line". A significance
test is performed to determine the significance of the contribution of
the different variables or factors to the model (mathematical
representation).
EXAMPLE MULTIPLE REGRESSION ANALYSIS (LONGLEY DATA)
Longley introduced a data set which has often been used in comparing
multiple linear regression procedures in the literature. The variables
refer to economic factors. This example uses the LONGLEY database on
the KWIKSTAT disk. Follow these steps to perform a multiple linear
regression:
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Step 1 Open the database: Open the database named LONGLEY. If you are
at the main menu, select the Open a Database option from the FILE
menu, then choose Regression and Correlation from the ANALYZE menu. If
you are in the Regression module, select "ChooSe a Database."
Step 2 Select analysis type: From the Regression menu, choose the
"Multiple Linear Regression" option.
Step 3 Select the fields to use: The LONGLEY database consists of 7
fields: DEFLATOR, GNP, UNEMP, ARMED, POP, TIME, and TOTAL. The first
six of these will be used as independent variables and the seventh,
TOTAL, is the dependent variable (the one to be predicted). Select
TOTAL as the DEPENDENT variable and DEFLATOR, GNP, UNEMP, ARMED, POP,
TIME as the INDEPENDENT variables, then select "Finished Choosing
Fields."
Step 4 View the results: KWIKSTAT will perform calculations and
display the results as shown in figure 4.22
The table at the top of the output (in Figure 4.22) tells you the
intercept value and the coefficient values for each of the independent
variables. These can be used to create an equation for prediction of
the dependent variable.
In this case, the equation is:
TOTAL = -3481930.1065 + DEFLATOR*(15.0161517122) +
GNP*(-0.03579443400) + UNEMP*(-2.0199053296) + ARMED*(-1.0332049046) +
POP*(-0.05130725587) + TIME*(1828.99249535)
Note: Although the results are reported to 8 to 9 decimal places, it
is usually not appropriate or necessary to use this many decimal
places. After viewing or printing the results, exit the viewer.
Step 5 View the Plots: From the options menu, you can choose to view
residual plots to determine if the data are linear. If the residual
plots do not show random patterns, you should determine if there is a
transformation you can perform on the data to make it linear.
Step 6 Forecast new values: From the options menu, you can choose to
predict new values from the calculated regression line.
KWIKSTAT also reports R-Square, which gives you a measure of how well
the regression "line" fits the data.
It is a good idea to view plots of residuals. The plots are helpful to
determine if regression analysis is appropriate. A pattern other than
a random horizontal band about zero indicates that the assumptions
necessary for a regression procedure may be violated.
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CORRELATION ANALYSIS
The correlation coefficient is a measure of the strength of the linear
relationship between two variables. KWIKSTAT allows you to find both
Pearson's and Spearman's (rank) correlation coefficients of two
variables. It also displays the matrix of correlation coefficients of
pairs of variables when there are more than two variables being
considered.
This example uses the Longley data described in the Multiple
Regression example above. To display the correlation matrix, use these
steps:
Step 1 Open the database: Open the database named LONGLEY.
Step 2 Select analysis type: From the Regression menu, choose the
"Correlation Matrix" option.
Step 3 Select the fields to use: The LONGLEY database consists of 7
fields: DEFLATOR, GNP, UNEMP, ARMED, POP, TIME, and TOTAL. Select all
the fields for this analysis. KWIKSTAT will perform the calculations
and display a 7 by 7 matrix.
Only half of the array is displayed since the other half is a mirror
image. The diagonal entries are also omitted since they are all one; a
variable is always perfectly correlated with itself.
Each entry in the array consists of two numbers (three numbers if the
information is printed to a printer). The first (upper) is the
Pearson's correlation coefficient for the two (row and column)
variables of that entry. The second (middle) number, in parentheses,
is the p-value of the t-test for Ho: rho = 0 vs. Ha: rho <> 0. In the
hard copy printout (if requested), the third (bottom) number, in
brackets, is the sample size, or number of paired observations used in
the calculations.
EXAMPLE GRAPHICAL CORRELATION MATRIX (LONGLEY DATA)
This example uses the Longley data used in the previous example. To
perform this analysis follow these steps:
Step 1 Open the database: Open the database named LONGLEY.
Step 2 Select analysis type: From the Regression menu, choose the
"Graphical Correlation Matrix" option.
Step 3 Select the fields to use: The LONGLEY database consists of 7
fields: DEFLATOR, GNP, UNEMP, ARMED, POP, TIME, and TOTAL. Select all
the fields for this analysis. KWIKSTAT will perform the calculations
and display the scatterplots.
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These scatterplots are a visual way of examining the relationships
between pairs of variables. It allows you to determine if a
relationship exists between the variables, and allows you to see if
that relationship is linear. You can use this graphical correlation
matrix to examine the relationships between variables before using
them in a multiple regression analysis.
USING FREQUENCY AND CROSSTABULATION PROCEDURES
The Crosstabulations, Frequencies, Chi Square module performs analyses
on categorical data, that is, data observed in categories, rather than
measurement data.
EXAMPLE: FREQUENCY TABLE, BAR AND PIE CHARTS
This example uses the EXAMPLE database file. One of the fields
(variables) in this database is STATUS referring to socioeconomic
status. Suppose you want to know how the total data set is divided up
into the five levels of STATUS. You also want to produce a visual
display of this information. To perform this analysis follow these
steps:
Step 1 Open the database: Open the database named EXAMPLE, then
choose the Crosstabulations, Frequencies, Chi Square option from the
ANALYZE menu. If you are already in the Crosstabulations, Frequencies,
Chi Square module, select the "ChooSe Database" option.
Step 2 Choose the analysis type: Select the "Frequencies" option from
the Crosstabulations, Frequencies, Chi Square module menu .
Step 3 Select field: You will be prompted to select one field
(variable) to use. Since you want to do a frequency table on STATUS,
select STATUS from the field list.
Step 4 View results: When you choose to view/print the results, a
frequency table is displayed as shown in figure 4.26. Exit the viewer
with F7.
If you select "Pie Chart," a pie chart, as described earlier in this
chapter (Graph Module) will be displayed. If you choose "Bar Chart," a
bar chart as described earlier in this chapter will appear.
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PERFORMING A GOODNESS OF FIT ANALYSIS
A goodness-of-fit test of a single population is a test to determine
if the distribution of observed frequencies in the sample data closely
matches the expected number of occurrences under a hypothetical
distribution of the population.
According to a genetic theory, crossbred pea plants show a 9:3:3:1
ratio of yellow smooth, yellow wrinkled, green smooth, green wrinkled
offspring. Out of 250 plants, under the theoretical ratio
(distribution) of 9:3:3:1, you would expect about
(9/16)x250=140.625 yellow smooth peas,
(3/16)x250=46.875 yellow wrinkled peas
(3/16)x250=46.875 green smooth peas
(1/16)x250=15.625 green wrinkled peas
After growing 250 of these pea plants, you observe that
152 have yellow smooth peas
39 have yellow wrinkled peas
53 have green smooth peas
6 have green wrinkled peas
To perform this analysis, use the following steps:
Step 1 Select the analysis type: From the Crosstabulations,
Frequencies, Chi Square menu choose the "Goodness-of-Fit" option.
Step 2 Enter the data: You will be prompted to enter the number of
categories. In this case, type 4 for the four categories of peas
(yellow smooth, yellow wrinkled, green smooth, green wrinkled) and
press Enter. You will also be asked if you want to enter the expected
ratios, or if you will be entering the actual expected values into the
table. If you choose to enter ratios, you will enter
9,3,3,1
An empty table will appear with the instructions to enter the observed
values for each category. Enter the observed values given above,
pressing Enter after each entry. For example, for the first row, enter
152 for observed (Press Enter) enter 39 (Press Enter) and so on.
KWIKSTAT will perform the calculations (including filling in the
expected values column) and display the results.
The calculated chi-square statistic in this case is 8.97 and the
p-value is 0.031. At a 0.05 level of significance, this p-value
indicates that there is enough evidence to reject the null hypothesis
that the observed values follow the theoretical distribution. That is,
the test (at the 0.05 significance level) suggests that a 9:3:3:1
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ratio of yellow smooth:yellow wrinkled:green smooth:green wrinkled
peas is not an appropriate distribution for the population from which
these data are taken.
PERFORMING A CROSSTABULATION ANALYSIS (CHI-SQUARE)
Crosstabulations can be used to perform a chi-square test for
independence or a chi-square test for homogeneity. A two-way table is
constructed that displays the number of counts for each category.
Crosstabulation table options you may choose for constructing a table
include:
A) Frequencies only
B) Include Expected Values
C) Include Expected Values and Percents
D) Include Expected Values, Chi-Contribution and Percents
E) Include Percents
F) Include Expected Values and Chi-Contribution
Q) Quit this option
EXAMPLE: 2 BY 2 CROSSTABULATION TEST FOR INDEPENDENCE
Data for this example are observations of the number of beetles and
bugs on the upper and lower sides of leaves (Zar,1974, page 292).
2 by 2 Contingency Table Data
Beetles Bugs
---------------
Upper Leaf 12 7
Lower Leaf 2 8
Since you are given only the totals for each of the four categories,
and not the individual data for each leaf, there is no need to create
a database. Rather, you can just enter these totals from the keyboard.
To perform this analysis, follow these steps:
Step 1 Choose analysis type: From the Crosstabulations, Frequencies,
Chi Square menu, select the "Crosstabulations, Chi-Square" option. You
will be asked if you want to "Read data from the database" or "Enter
data from the keyboard." For this example, select "K" to enter data
from the keyboard.
Step 2 Select size of table: You will then be prompted to give the
size of the table. When asked for the number of rows, type 2 and press
Enter. When asked for the number of columns, again type 2 and press
Enter. An empty table will appear with the instructions to enter the
counts for each category into the appropriate cell.
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Step 3 Enter the data: Enter the values given above, pressing Enter
after each entry. KWIKSTAT will perform the calculations and display
the results.
The calculated chi-square statistic in this case is 4.89 with a
p-value of 0.028. The chi-square with Yates correction is 3.31 with a
p-value of 0.069 and the Fisher Exact Test (two tail) has a p-value of
0.050. Because one of the cells produces an expected value less than
5, KWIKSTAT gives a warning that the chi-square analysis for this data
may not be valid. Given this warning, it is best to rely on the
Fisher's Exact Test for making a decision.
EXAMPLE: ANALYZING A LARGER TABLE (SEX BY HAIR COLOR)
A generalization of the 2 by 2 table is the R by C (Rows by Columns)
table. This is an example (Zar, 1984, page 62) of a two by four
contingency table involving the variables hair color and sex. The null
hypothesis is that there is no relationship between hair color and
sex.
2 by 4 Contingency Table Data (sex by hair color)
HAIR COLOR
Sex Black Brown Blonde Red
-----------------------------------------
Male 32 43 16 9
Female 55 65 64 16
Since you are given only the totals for each of the eight categories,
and not the individual data for each person, there is no need to
create a database. Rather, you can just enter these totals from the
keyboard. To perform this analysis, follow these steps:
Step 1 Choose analysis type: From the Crosstabulations, Frequencies,
Chi Square menu, select the "Crosstabulations, Chi-Square" option. You
will be asked if you want to enter data from a (D)atabase or
(K)eyboard. Type K and press Enter.
Step 2 Select size of table: You will then be prompted to give the
size of the table. When asked for the number of rows, enter 2. When
asked for the number of columns, enter 4. An empty table will appear
with the instructions to enter the counts for each category into the
appropriate cell.
Step 3 Enter the data: Enter the values given above, pressing Enter
after each entry. KWIKSTAT will perform the calculations and display
the results.
Step 4 Analyze the results: The calculated chi-square statistic in
this case is 8.99 with a p-value of 0.03. A decision can be made using
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this p-value of the test. A low p-value (less than the chosen
significance level) is usually taken to indicate rejection of the null
hypothesis.
CREATING A 3-D BAR CHART
As an option when performing a Crosstabulation, KWIKSTAT allows you to
draw a 3-dimensional bar chart of data for a contingency table
(crosstabulation), and then to focus in on a part of it if desired.
Data for the 3-dimensional bar chart must be entered first, either
from the keyboard or a database, by using the "Crosstabulations,
Chi-Square" option.
MCNEMAR'S TEST
McNemar's test is appropriate for use with paired, dichotomous data.
This test is sometimes called a test for related samples or a test for
the significance of changes. It is useful for comparing paired or
related observations in which the response is dichotomous, that is,
the response is one of only two possible outcomes. McNemar's test is
the 2 by 2 version of Cochran's Q test described in the section on
non-parametric tests. The test assumes that any pair of observations
is independent of any other pair of observations, although clearly the
observations within a pair are not independent of each other.
LIFE TABLES AND SURVIVAL ANALYSIS
Survival Analysis is used to analyze the survival experience of a
group of persons or components. In medical research, survival analysis
is helpful is studying the survival of patients under one or more
conditions. In industry, the survival may be that of a component such
as an electronic switch or a gear. To perform a survival analysis, the
data must be in the following form:
1) a TIME variable which contains a time (e.g., minutes, days, years,
etc.) in which the subject or component has been observed to be alive
(not failed).
2) a CENSOR variable which must take on the values 0 or 1, where 1
means the subject has died (failed), and a 0 means the subject was
still alive (not failed) at the last available time period.
3) optionally, a GROUPING variable which may have up to ten values
(numeric or character), i.e., the data may be in groups.
KWIKSTAT allows you to choose from two types of life tables, Actuarial
or Kaplan-Meier. The Actuarial method uses fixed length intervals in
the table, and the Kaplan-Meier table uses intervals based on the
data.
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Once the data are entered into the program, a life table for each
group is produced which includes, for each time interval, the number
entered, withdrawn, lost, dead, exposed, the proportion dead,
proportion surviving, cumulative proportion surviving, and other
information.
A plot is given for the cumulative proportion surviving in the
group(s) against time. If more than one group is entered, a
Mantel-Haenszel log-rank test is performed to test the hypothesis of
equal survival patterns for the groups. A reference to how this test
is developed is covered in Matthews and Farewell (1988).
EXAMPLE: ACTUARIAL LIFE TABLE ANALYSIS
The data for this example are in the LIFE database on the KWIKSTAT
disk. These data are from Prentice (1973). To perform this analysis,
follow these steps:
Step 1 Open the database: If you are at the main KWIKSTAT menu, choose
the Open Database option from the FILE menu and select the database
LIFE, then choose the Life Table and Survival Analysis option from the
ANALYZE menu. If you are already in the Life module, open the LIFE
database by selecting the "ChooSe database to open" option.
Step 2 Choose the analysis type: Select the "Actuarial Life Table
Analysis" option from the Life Table and Survival Analysis menu. Step
3 Choose fields to use: The LIFE database consists of 3 fields:
SURVIVAL, CENSOR, and GROUP. A portion of the LIFE database is shown
here:
SURVIVAL CENSOR GROUP
72 1 1
411 1 1
228 1 1
11 1 1
25 0 1
144 1 1
etc...
The first column is the SURVIVAL field with entries of length of life,
or length of survival. The second column is the CENSOR field, an
indicator of whether the subject has failed (died) or not at the last
observed time period. 1 means failed, 0 means not failed (still
alive).
The third column contains a grouping variable. In this case it is
either 1 or 2. Group 1 may represent one treatment, while group 2
represents another kind of treatment. The objective is to compute
survival curves to see if the treatments provide different average
survival distributions.
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Select SURVIVAL as the TIME variable, CENSOR as the censor variable
and GROUP as the grouping variable.
Step 4 Select interval length: KWIKSTAT reports the names and sizes of
the groups and then asks you to specify the length of each interval
for the table to be produced. You can specify a desired interval
length or you can use the default length by simply pressing Enter. For
this example, press Enter to select the default length.
Step 5 Analyze the results: KWIKSTAT will perform the calculations and
display an options menu. If you choose the View/Print option two sets
of tables, one for each group will be displayed. The first table
includes the numbers of subjects entered alive, withdrawn, dead,
exposed, the proportion dead, proportion alive, cumulative survival
proportion and standard error for the first group. The second table
includes 95% confidence limits on the cumulative survival proportion.
From the table, you can see that, in the first group, 22 of 37
exposed, or 59.5% died in the first interval (0.0-99.0) and two were
withdrawn. In the second group, 12 of 23.5 exposed (51.1%) died and
one was withdrawn in the first interval. Exit the viewer by selecting
F7/Exit.
Comparing Survival Curves: At the end of the report, KWIKSTAT reports
the results of the Mantel-Haenszel comparison of the two curves. The
hypotheses being tested are:
Ho: The survival curves are the same.
Ha: The survival curves are not the same.
In this example, the Mantel-Haenszel comparison procedure results in a
chi-square statistic of 0.7191 and a p-value of 0.397. This p-value is
much too large to reject the hypothesis of equal curves. This
indicates that the two distributions are not statistically
significantly different - thus neither treatment is superior in terms
of survival distributions.
Displaying Survival Curves: From the options menu, you can choose to
display survival curves. This is a graphical representation of the
cumulative proportion surviving from the life table. The survival
curve for this analysis is shown.
The Kaplan-Meier life table contains most of the same information as
the Actuarial Life Table. However, instead of the time intervals being
fixed, the time intervals are based on time values from the data.
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==========
REFERENCES
==========
Box, Jenkins, and Reinsel, Time Series Analysis - Forecasting and
Control, Prentice-Hall, 1994.
Deming, W.E., Out of Crisis, Cambridge, MA: Massachusetts Institute
of Technology, Center for Advanced Engineering Study, 1986
Dixon, W.J. and Massey, F.J., Introduction to Statistical Analysis,
McGraw-Hill Book Company, New York, 1969.
Elliott, A.C. and Woodward, W.A.,"Analysis of an Unbalanced Two-Way
ANOVA on the Microcomputer", Communications in Statistics, Volume B15,
Number 1, 1986.
Gunst, R.F., and Mason, R.L., Regression Analysis and its
Applications, Marcel Dekker, New York, 1980.
Granger, C.W.J. and Newbold, P., Forecasting Economic Time Series,
Academic Press, 1977.
Hoaglin, D.C., Mosteller, F., Tukey, J.W., Understanding Robust and
Exploratory Data Analysis, John Wiley & Sons, Inc. New York, 1983.
(Box and Whiskers Plots, Stem and Leaf Displays)
Kennedy, W. J., Jr., and Gentle, J.E., Statistical Computing, Marcel
Dekker, Inc, New York, 1980.
Larsen, R.J. and Marx, M.L., Statistics, Prentice-Hall, 1990.
Lehmann, E.L. Nonparametrics: Statistical Methods Based on Ranks,
Holden-Day, Inc, Oakland, Ca, 1975.
Longley, J.W. "An appraisal of least squares programs for the electronic
computer from the point of view of the user." JASA, 1967, 62, 819-831.
Montgomery, D.C., Introduction to Statistical Quality Control, John
Wiley and Sons, 1991.
Neter, J., Wasserman, W., and Kutner, M. H., Applied Linear
Statistical Models, Richard D. Irwin, Inc., 1990, Third Edition.
Prentice, R.L. "Exponential survivals with censoring and explanatory
variables.", Biometrika 60, 1973, 279-288.
Ryan, Thomas P. Statistical Methods for Quality Improvement, John
Wiley & Sons, New York, 1989. Tukey, J.W., Exploratory Data Analysis,
Addison-Wesley, 1977.
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Tsay, R.S., and Tiao, G.C., "Consistent Estimates of Autoregressive
Parameters and Extended Sample Autocorrelation Functions for
Stationary and Nonstationary ARMA Models," JASA 79, 84-96, 1981.
Winer, B.J., Statistical Principles in Experimental Design, Second
Edition, McGraw-Hill Book Company, 1971.
Woodward, W.A., Elliott, A.C., Gray, H.L and Matlock, D.C., Directory
of Statistical Microcomputer Software, Marcel Dekker, New York, 1988.
Woodward, W.A., and Gray, H.L., "On the relationship between the
S-array and the Box-Jenkins Method of ARMA Model Identification," JASA
76, 579-587, 1981.
Zar, J.H., Biostatistical Analysis, Prentice Hall, Inc, 1974 and 1984
editions.
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===========
APPENDIX A
===========
INTERPRETING ERROR CODES
While every precaution is taken in writing software, all possibilities
of use cannot be anticipated. If the program encounters a problem it
does not know how to resolve, it will usually display an error
message. This message will contain an error code and a reference code.
If you encounter an error message, write it down and refer to this
list to see if you can figure out how to resolve the problem. If you
are unable to resolve the problem, please write down the steps you
took before the error was encountered, and send it to TexaSoft on the
Problem Report Form. We will try to resolve the problem as quickly as
possible.
Error Number 5 = Illegal function call
Error Number 6 = Overflow
Error Number 7 = Out of Memory
Error Number 9 = Subscript out of range
Error Number 11 = Division by zero
Error Number 14 = Out of String Space
Error Number 24 = Device Timeout
Error Number 25 = Device fault
Error Number 27 = Out of Paper
Error Number 50 = FIELD overflow
Error Number 51 = Internal Error
Error Number 52 = Bad filename or number
Error Number 53 = File not found
Error Number 54 = Bad file mode
Error Number 55 = File already open
Error Number 57 = Device I/O error
Error Number 58 = File already exists
Error Number 61 = Disk full
Error Number 62 = Input past end of file
Error Number 63 = Bad record number
Error Number 64 = Bad filename
Error Number 67 = Too many files
Error Number 68 = Device unavailable
Error Number 70 = Permission denied
Error Number 71 = Disk not ready
Error Number 72 = Disk media error
Error Number 74 = Rename across disks
Error Number 75 = Path/File access error
Error Number 76 = Path not found
Error Number 81 = Invalid filename
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PROBLEM REPORT FORM: KWIKSTAT
Please explain in detail the problem that occurred. If possible, send
a printout of the results or Print Screen if possible.
KWIKSTAT VERSION#_____________ RELEASE#________________
(see opening screen)
KWIKSTAT module where problem occurred:______________________
(It is often helpful if you can indicate the precise commands you
used leading up to the problem.)
Your computer brand/model_____________________________________
(Also indicate if it is a 8088, 286, 386, 486, Pentium)
Monitor type: (circle one) EGA, or VGA (including SuperVGA)
Amount of free memory available:____________________
(use the MEM or CHKDSK command to find this out.)
Version of DOS you are using:____________________________________
(Use the VER command to find this out.)
Memory resident program in use:__________________________________
Running KWIKSTAT from (i.e DOS, Windows, DOS SHELL):__________
PROBLEM:
Mail to:TexaSoft, P.O. Box 1169, Cedar Hill, Texas 75106-1169. Or fax to
214-291-3400, or send E-Mail to Compuserve 70721,3145 or Internet
70721.3145@compuserve.com.
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USER'S BALLOT
Please indicate your preference for improvements in KWIKSTAT. On a
scale of 0 to 10
0 = Very Low priority for this change
10 = Very High priority for this change
Vote Proposed item of change
---- ---------------------------------------------------------
____ Windows version
____ Add more ANOVA types - example:___________
____ Add more Non-parametric statistical tests
____ Add General Linear Model
____ Make Report more flexible
____ Add more Quality Control options
____ Cluster Analysis
____ Discriminant Analysis
____ Add other types of analysis - example:__________
____ _____________________________________________
____ _____________________________________________
____ _____________________________________________
____ _____________________________________________
Other Comments:(Your ideas are very important us.)
Mail to:TexaSoft, P.O. Box 1169, Cedar Hill, Texas 75106-1169. Fax
to:214-291-3400 or send E-Mail to Compuserve 70721,3145 or Internet
70721.3145@compuserve.com.
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