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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. Page 3 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 Page 4 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 Page 6 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 Page 7 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 Page 8 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 Page 9 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 Page 10 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. Page 11 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.