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P r o T A B
The Statistical Calculator
Version 1.1
Copyright 1989 -- Brad Strausbaugh
All rights reserved
Introduction
ProTAB is an easy-to-use statistical calculator for fast
quantitative analysis of small data sets. The tools
available include single and praired distribution, ANOVA,
correlation and regression, and crosstab analysis. No
knowledge of programming is required. You will need only a
basic understanding of elementary statistics.
The Shareware Concept
ProTAB is NOT free software. If you find ProTAB useful,
please register by returning the registration form found at
the end of this document, along with a one-time $20
registration fee. Your registration supports the long hours
of programming needed to provide the periodic upgrades that
keep ProTAB the #1 statistical calculator. Registered users
automatically receive all major program upgrades as they
are published.
Shareware distributors are encouraged to copy and distribute
ProTAB for the few dollars per diskett typical in the
shareware marketplace today. Charging the registration fee
mentioned above, however, is prohibited and in violation of
the copyright.
Individuals should feel free to copy ProTAB for friends and
colleagues.
Legal Liability
I have taken great care to insure that all the calculations
ProTAB makes are correct. Be advised, that by using ProTAB
you accept full responsabiliy for any and all consequences
resulting from erroneous calculations, no matter what the
cause.
Page 2
Getting Started
After extracting PROTAB.ARC you will find the following
files.
PROTAB.DOC This documentation file
PROTAB.EXE The ProTAB program
BRUN30.EXE The run-time module
T.TBL The probability tables
F1.TBL
F5.TBL
CHISQ.TBL
STUDENTS A data file for demonstration purposes
You can invoke ProTAB by setting your default device and
subdirectory to where you have these files, and entering the
following command at a DOS prompt.
C> PROTAB
After taking a few seconds to load the probability tables,
ProTAB will display the login banner. Just press any key
and you are ready to start.
How to Use ProTAB
This document uses the rather un-original example of a
junior college psychology class's test scores to illustrate
ProTAB's operation. I have included this data set (named
STUDENTS) for demonstration purposes. In the following
sections I'll show you how to Load an existing data set and
request the analysis you want. Later you'll see how to
enter, modify and store your own data sets.
Controlling the ProTAB Environment
First lets look at a few basic conventions used throughout
the ProTAB system.
1. The main menu is always present at the top of the
screen. The currently active option is highlighted in
reverse video.
2. You can change the current menu option with the left and
right arrow keys on the numeric keypad (be sure the "Num
Lock" key is off), or by entering the first letter of
the option you want. When the menu option you want is
highlighted, press the Return key to select it.
3. The Return key always advances you forward to the the
next step while the Escape key allows you to "stepback"
to the previous step.
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4. The bottom line of the screen will always display
pertinent help information.
Loading a Data Set
Lets begin by loading the STUDENTS data set. To load this
file select the Load option from the main menu. When ProTAB
asks for the file name enter STUDENTS. After taking a few
moments to load the file ProTAB will display it in the edit
window.
As you can see a data set is just a two-dimensional matrix
were each column represents a variable and each row
represents an observation, in this case, a student. I've
kept the STUDENTS file small for simplicity. Your data sets
will probably be larger. Data sets can have a maximum of
200 observations.
Now we can take a look at the analyses available.
Single Distribution Analysis
Lets begin by examining the students' mid-term exam grade
distribution. Select the Analyze Main menu option. ProTAB
will ask whether you want Distribution, ANOVA,
Correlation/Regression, or Crosstab analysis. Select
Distribution.
ProTAB then asks whether you want a Single or Paired
distribution analysis. Select Single to see the
distribution of the whole class.
ProTAB prompts for which variable to analyze. Enter
"Grade". If you enter a variable that does not exist, an
error message will appear asking you to reenter the correct
variable name.
After a few seconds ProTAB will display the Single
Distribution Analysis of the variable Grade. This screen
shows, the sample size (n), mean, median, mode, standard
deviation (StdDev), standard error of the mean (StdErr),
highest, lowest, range, variance and sum. It also shows a
grouped frequency histogram with mid-point raw score and
mid-point z score.
Notice the histogram is made up of asterisks (*), one for
each case. I should mention here that if a modal group of a
distribution exceeds 15, each asterisk will represent more
than one case. Just how many cases each asterisk represents
depends on how many multiples of 15 the modal group exceeds.
In such cases the histogram may show a group with a
frequency of one or more but no asterisks. The histogram
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should be used only to get a general picture of the
distribution curve.
I should also mention that if the distribution is not
unimodal, the mode statistic will be zero.
If you want to send this display to your printer select the
Print option from the line-2 menu. The Print option is
available for all analysis screens. When you are finished
select the Menu option, or just press the Escape key to
stepback to the Distribution menu.
Paired Distribution Analysis
You can compare the mid-term grades of male and female
students. From the Distribution menu select Paired.
At the appropriate prompts enter "Sex" as the independent
variable, and "Grade" as the dependent variable. For the
independent group x enter "F" (Female), and the independent
group y enter "M" (Male).
After a few seconds ProTAB will display the Paired
Distribution Analysis of Grade by Sex.
In addition to the statistics we saw in the Single
Distribution Analysis, we also see the t ratio, degree of
freedom (d.f.) and p for both the one and two tailed
probability distributions. The histogram shows occurrences
of the x variables as "x", the y variable as "y", and were
both occur, "#".
Analysis of Variance
We can compare grades across high schools. Since there are
more than two high schools represented in this junior
college class we use ANOVA.
Stepback to the main menu and select Analyze then ANOVA from
the Analyze menu. Enter "HighSchool" as the independent
variable and "Grade" as the dependent.
After computing for a few seconds ProTAB displays the
Analysis of Variance Summary Table which includes the within
and between groups sum of squared deviations from the mean
(SS), degree of freedom (d.f.), mean square (MS), F ratio,
and p.
If you want to see statistics for each group of students by
high school, select GroupDetail from the ANOVA menu. This
display shows each group's n, mean, standard deviation, and
standard error of the mean.
Page 5
When you are using ANOVA on your own data, keep in mind that
the maximum number of independent groups allowed is ten.
Correlation Analysis
Suppose you want to know the extent to which you can predict
a student's mid-term exam grade from his or her GPA.
Select the main menu option Analyze, then select the Analyze
menu option Correlation/Regression. ProTAB will prompt for
which correlation coefficient to use, Pearson or Spearman.
Since Grades and GPA are interval data we select Pearson.
Using Spearman for anything other than ranked data will
yield unpredictable results.
ProTAB will ask for which display you want. Select Detail
(We'll look at the others in a moment). ProTAB then prompts
for which variables to use. Enter "GPA" as the Independent
(predictor) variable, and "Grade" as the dependent variable.
After a few seconds ProTAB displays the Pearson Correlation
Analysis. This display includes the Pearson Correlation
coefficient (r), r Square, standard error of prediction
(StdErr), degree of freedom, t ratio, regression line slope
and Y intersect. It also shows a brief scatterplot where
points are represented as ".", ":", "+", or "#" depending on
their frequencies.
Now we can predict a student's likely mid-term exam score
from his or her GPA. Select the line-2 menu option Predict,
then enter the GPA of a student whose Grade you want to
predict, say, "3.2". ProTAB will display the predicted
Grade (Y Prime) along with the Grade high, low, and range
for the 99%, 95%, 90%, and 80% confidence levels.
You can compare one numeric variable with all others. Lets
stepback to the Correlation menu using the Escape key,
select the Pearson coefficient again, and now select the
OneToAll display. At the independent variable prompt, enter
"Grade". ProTAB now displays statistics showing how Grade
correlates to all other numeric variables.
And finally we can see how all numeric variables correlate
to all others. Proceed to the Display prompt as before, and
this time select AllToAll. ProTAB will display the
correlation coefficient of all numeric variables to all
others.
Crosstab Analysis
We can examine the contingency of two variables. Suppose we
want to compare the frequency of male vs female students
from each high school. Use the Escape key to stepback to
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the Analysis menu and select Crosstab. Enter "HighSchool"
as the X variable and "Sex" as the Y variable. After
computing for a few seconds, ProTAB will display the
Crosstab Analysis screen, with each cell containing the
observed (O) and theoretical (T) frequencies; and it will
show the degree of freedom, chi-square, and p.
When you use Crosstab analysis on your data keep in mind
that each variable can have no more than ten groups.
Sorting
You can sort the data array by any number of variables. For
example, suppose you want to sort the students by
HighSchool, and within each HighSchool you want to sort by
Grade.
To do this, stepback to the main menu and select the Sort
option. ProTAB will prompt for the variables or "keys" to
sort by. Enter "HighSchool" and "Grade" for keys 1 and 2
respectively. When ProTAB prompts for key 3, just press
Return.
After a few seconds ProTAB will display the array in the
sort order requested.
Printing the Data Array
To list the entire data array on your printer just select
the Print main menu option. The array will be printed out
in the current sort order with the variables names appearing
across the top and line numbers down the left side.
Defining an Array
By way of illustration, let us define a new array containing
information on our students in the junior college psychology
class. Initially we will define only the first two
variables, Grade and Sex; we'll enter a few observations;
then add a third variable, HighSchool, and add that data.
I'm presenting it this way to show the flexability available
in defining, entering, and changing data.
We begin by selecting the Define option from the main menu.
If the STUDENTS array is still in the edit window, ProTAB
will ask it you want to Create a new array or Modify the
current one. Select Create. Next, if you've Sorted the
STUDENTS array per the discussion above, or changed it in
any way, ProTAB asks it you want to save it. Answer "N"
(No) to this question.
ProTAB will clear the edit window and start asking you
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questions about the first variable in the new array. The
first variable we want to define is Grade, and the first
question ProTAB asks is the width for that column. Keep the
following points in mind when you select a width.
1. Variables can be from 1 to 10 characters wide (8 is the
default). This includes decimal points and signs. Be
sure you choose a width that will hold the maximum value
you expect in your data.
2. The width you select to accomodate the variable's data
will also be the maximum width allowed for the
variable's name.
Lets make this variable 8 characters wide. Since 8 is the
default we can just press the Return key at the Width
prompt.
Next, ProTAB asks for the name we want to give this
variable. Notice the space available to enter the variable
name is only 8 characters wide, the same as our width
selection. Enter the variable name "Grade".
Finally ProTAB asks whether Grade is a text or numeric
variable. Data for numeric variables is right justified and
available for math operations, while data for text variables
is left justified and cannot be summed, or averaged, etc.
Since we want to perform calculations on Grade, enter "N"
for numeric.
Now our first variable has been defined and its name appears
in the upper left corner of the edit window. ProTAB now
asks if we want to define another variable. We still have
to define a variable to identify each student's sex, so
enter "Y" for Yes. We want the width for this variable to
be 3 characters wide, the name to be "Sex" and the data type
to be Text. Go ahead and define the variable Sex.
Remember, the help line is always present at the bottom of
the screen if you get stuck.
This time when ProTAB asks if you want to define a third
variable, enter "N" for No. ProTAB will return you to the
main menu.
Entering Data
With an array defined, we are now ready to enter our
students' data. Select the Edit option from the main menu.
ProTAB prompts for the grade of the first student. It also
highlights the corresponding cell in the edit window. The
first student's mid-term exam grade was 96%, so enter "96"
at the prompt, then press Return (never enter the percent
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sign, and never enter a dollar sign or a pound sign. The
only valid characters for a numeric variable are the digits
0 to 9, a decimal point, and sign if needed).
ProTAB then prompts for the same student's Sex. Enter "M"
for Male, then press Return.
ProTAB is now awaiting data for the second student. Go
ahead and enter data for a few students (see the list below
for the data in our STUDENTS example). If you make a
mistake and need to change the data in a certain cell, use
the arrow keys to move to that cell, then enter the correct
data. If you get in trouble, remember the help line at the
bottom of the screen.
Define Edit Save Load Sort Analyze Print Quit
+- Grade -Sex--------
1 96 M
2 80 F
3 84 F
4 90 M
5 88 F
6 78 M
7 86 M
8 88 F
9 92 M
10 90 F
11 84 F
12 88 F
13 68 M
14 74 F
15 100 M
16
17
+-------------------
When you are finished press the Escape key to stepback to
the main menu. At this point you could select the Analyze
main menu option to study this data, but lets not and say we
did. We are only concerned here with demonstrating the use
of the editor.
Adding New Variables To The Current Data Array
Now we can add a new variable to the array. We will name it
"HS" for High School. Although I spelled out HighSchool in
the earlier example for clarity, you will probably find
yourself using short abbreviations like this in your work.
Stepback to the main menu with the Escape key and select
Define. Since ProTAB now has our current array in memory,
it asks whether we want to Create a new array or Modify the
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current one. We want to add a variable to the current array
so select Modify. Then ProTAB asks if we want to Add a new
variable or Delete an existing one. Select Add.
Subsequent prompts should look familiar. They are the
Width, Name, and Text/Numeric prompts we've seen before.
Define the new high school variable as Width: 2, Name: HS,
and data type: T (text).
Now stepback to the main menu and select the Edit option.
Using the arrow keys to position the active cell on line 1
under the HS variable, enter the data into the new variable
as shown below. Again, just enter a few observations until
you are comfortable with the editor.
Terminate each entry with the Down Arrow key instead of the
Return key to stay in the HS column.
Use "WY" for West York, "EY" for East York, and "C" for
Central.
Define Edit Save Load Sort Analyze Print Quit
+- Grade -Sex-HS-------
1 96 M EY
2 80 F C
3 84 F C
4 90 M WY
5 88 F EY
6 78 M C
7 86 M C
8 88 F WY
9 92 M WY
10 90 F EY
11 84 F WY
12 88 F EY
13 68 M EY
14 74 F C
15 100 M WY
16
17
+-----------------------
When you have entered the high schools, stepback to the main
menu with the Escape key.
Saving Arrays to Disk
In practice it's a good habit to save new data to disk
immediately after you leave the Edit mode. In the event of
a system failure you can recover simply by reloading the
array from disk. And if you are entering a particularly
large array you may want to save the array after entering
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every twenty lines or so.
To save your current array to disk. Use the Escape key to
stepback to the main menu, then select the Save option.
ProTAB asks for a name to identify the array when it's on
disk. Enter the array name "CLASS". ProTAB will then save
your array to disk.
To Quit from ProTAB
You can terminate your ProTAB interactive session and return
to DOS by selecting the Quit main menu option. If the
current data array has been changed but not saved to disk, a
warning will appear, asking if you want to save it before
quitting.
Analyzing Data Output by Other Programs
You can use ProTAB to analyze data you already have on disk
from other programs. This data must have the
characteristics outlined here. See the example of our
STUDENTS file below.
1. Variables cannot be more than 10 characters wide.
2. Variables must be separated by one space.
3. On the first line, an "N" for numeric or "T" for text
must appear, left justified, over each variable.
4. On the second line, the variable name must appear, left
justified, over each variable.
5. On the third line, hyphens must appear across the width
of each variable. This tells ProTAB each variable's
start and end position.
6. From the forth line on the data should appear. Numeric
data must be right justified within each variable, and
text data must be left justified.
7. ProTAB allows a maximum of 200 lines of data.
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Any deviation from these characteristics can have
unpredictable results. You can use your favorite text
editor to make the necessary modifications to your file. If
you are using a word processor, be sure it is set to
non-document mode.
N T T N N
Grade Sex HighSchool GPA SAT
-------- --- ---------- -------- --------
96 M EASTYORK 3.6 1300
80 F CENTRAL 3.3 1166
84 F CENTRAL 3.4 1210
90 M WESTYORK 3.4 1280
88 F EASTYORK 3.5 1277
78 M CENTRAL 2.7 1120
86 M CENTRAL 3.5 1260
88 F WESTYORK 3.4 1256
92 M WESTYORK 3.6 1380
90 F EASTYORK 2.8 1390
84 F WESTYORK 3.0 1250
88 F EASTYORK 3.1 1310
68 M EASTYORK 2.3 824
74 F CENTRAL 2.4 1022
100 M WESTYORK 3.8 1498
Page 12
Registration Form
If your find ProTAB useful in meeting your needs for fast
quantitative analysis of small data sets, please fill out
this registration form and send it, along with your $20
registration fee, to ...
Brad Strausbaugh
350 E. Del Mar Blvd #125
Pasadena, Ca 91101
Registered users will automatically receive all major
upgrades of ProTAB as they become available. Thanks in
advance for your registration.
Full Name:_____________________________________________
Company:_____________________________________________
Street:_____________________________________________
City/State/Zip:_____________________________________________
Phone:_______________________
Comments
User feedback is the most important determinant of the
direction for future ProTAB upgrades. Please use the rest
of this page (and the back if needed) to jot down any
enhancements you'd like to see.