CHAPTER 13 STATISTICAL POTPOURRI THE ON-SCREEN CALCULATOR The SPPC System provides a complete on-screen scientific calculator. It is designed as a "Reverse Polish Notation" or RPN calculator which is very easy to use. The main thing you must remember is that all numeric values must be entered by pressing and results are obtained by entering an operator. Examples: To solve y = 2 * 3, enter the following keystrokes: 2 3 * To solve y = (2 + 3) * (4 - 5), enter: 2 3 + 4 5 - * To solve y = sqrt(16.38 * 0.55) / .05, enter: 16.38 0.55 * fs .05 / To solve y = 14.8 * cos(45), enter: 14.8 45 r tc * TRIGONOMETRIC FUNCTIONS The calculator provides the basic trigonometric functions with the tap of a key. However, you should carefully note that all trig functions require radians. This is managed quite easily by the fact that any number can be converted to radians with the press of a single key. And, when the final result is presented, in radians, it can be converted to degrees with another single keystroke. STATISTICAL FUNCTIONS The RPNC provides some very convenient statistical functions. When you wish to use the statistical functions, you should clear them by pressing the letters 'cs' for "Clear Statistics". If you do not do that, new data entries will be added to those previously entered. Thus, you may enter part of your data, carry out other operations, and then return to data entry for the statistical functions. To enter data for the statistical functions, enter Y X s (for "Summate"). Repeat those steps for each pair of Y an X values. To remove data from your statistical calculations, enter Y X n (for "Negate") and the values of Y and X will be removed from all statistical calculations. For single valued statistical functions you may enter X s. Repeat those steps for each value of X. You may then get the mean and standard deviation of X by pressing gmx (for "Get Mean of X") and gsx (for "Get Standard deviation of X"). MEMORY ARITHMETIC You may also conduct memory arithmetic using the calculator, and the rules for doing that are very simple. They are as follows: msi = "Memory Store i"; store in memory i. mri = "Memory Recall i"; recall from memory i. m+i = "Memory Add i"; add to contents of memory i. m-i = "Memory Subtract i"; subtract from contents of memory i. mxi = "Memory Multiply i"; multiply contents of memory i. m/i = "Memory Divide i"; divided contents of memory i. To clear all 21 memory registers, press cm (for "Clear Memories"). To store 15.67 in M9, press 15.67 ms9 To recall the contents of M14, press mr14 To sum 15.67 into M14, press 15.67 m+14 To multiply the contents of M8 by 7.8, press 7.8 mx8 To divide the contents of M8 by 7.8, press 7.8 m/8 To recall M4, sum it with M19 and add the result into M17, press mr4 mr19 + m+17 DATA ENCRYPTION This procedure enables you to encrypt sensitive data or text messages provided the data or messages consist of strict ASCII characters over the range from 32 to 126. ENCRYPTING A FILE In order to ENCRYPT a data file or message, choose option B from the main menu of the program. Then enter the name of the file that you wish to ENCRYPT. Then enter the name of the output file where you want the encrypted data file or message to be stored. When you have provided the input and output file names, you must provide a 'code key'. You may use any code key up to 15 characters in length. You must record or remember this code key else you cannot later decode your data file or message. The program will then ENCRYPT and store your data or message on the output file that you indicated. You may send a copy of your encrypted file to anyone who also has this program and the code key that you used. DECODING MESSAGES In order to DECODE a datafile or message, choose option C from the main menu of the program. You will then be asked to enter the name of the file that you wish to decode. You will then be asked to enter the name of the output file where you want the DECODED message to be stored. Once you have provided the input and output file names, you will be asked to provide the 'code key' which will be used to decode the input file. If you do not know the proper code key, you will obtain unintelligible results. If you enter the proper code key, the decoded data file or message will be stored in the output file that you indicated. VIEW AN ENCRYPTED FILE Option D of the menu allows you to view and encrypted file on screen without storing the decrypted version on an external file. When you choose this option you will be asked to enter the name of the file that you wish to view. You will then be asked to provide the 'code key' which will be used to decode the input file. If you do not know the proper code key, you will obtain unintelligible results. If you enter the proper code key, the decoded message will be displayed on screen. You may exit instantly by pressing the * key beside the shift key on the right side of your keyboard. This will help to insure privacy while you are viewing confidential data or messages. If someone approaches who should not see the file, just press the * key and you will return immediately to the main menu. RANDOM INTEGERS This program enables you to draw a random sample of integers from a range of values which you specify. In order to use the program you must first decide whether you wish to employ sampling with replacement or sampling without replacement. That choice is made by selecting the approriate option from the main menu of the program. Once you have chosen the sampling procedure you wish to use, you must then enter a positive integer of your choice in order to initialize or 'seed' the random number generator. After you have seeded the random number generator you must then indicate the range of values (from 'Start' to 'End') from which you wish to select N integer values. There are some restrictions. PARAMETER RESTRICTIONS The value of 'Start' cannot be less than 1. The value of 'End' cannot be greater than 99999. The value of N must be less than (End - Start + 1). N must be less than 5000. PARAMETER CHECKING The above restrictions are checked by the program so you need not worry about messing up. The program won't let you. However, you should be aware that the program could run for quite a long time if you choose sampling without replacement and your value of N represents a really large proportion of the specified range of values. That's about it. We hope the program is useful to you. It saves all the trouble of working with random number tables! RANDOM NORMAL SAMPLES This program enables you to generate any reasonable number (up to 30,000) of normally distributed random variables for any reasonable number of cases (no limit) that have a specified population mean and standard deviation. Each variable will have the same population mean and standard deviation. If you wish to create a new sample, choose Option B from the main menu. If you wish to add cases to an existing file, choose Option C from the main menu. The speed with which the program generates your sample data is dependent on the number of variables and the number of cases that you specify. For example, if you request the production of 10 variables for 100 cases, the program will require about one minute on an XT when writing to a floppy diskette and about 55 seconds when writing to your hard disk -- if you have the high speed math co-processor! If you do not have the math co-processor the program will be very slow. Thus, if you are generating a truly large sample with lots of variables, you might want to use Option C. That is, create the first part of your data using Option B. You can then add cases to your file during other computer sessions by using Option C. The output file will contain the following information: 1. A header line of your choosing. 2. A line specifying the number of cases, variables, and the letter R (for raw data). 3. Variable names which range from VAR0 to VARk where k is one less than the number of variables you requested. 4. The data values generated by the program. BASE CONVERSIONS This module enables you to convert numbers from one base to another up to base 32. If you have base 10 values which must be converted to hexidecimal values for example, you can make the conversions with enormous simplicity. Merely enter the base from which you wish to convert, the base to which you wish to convert, and then the numeric values to be converted. Outputs from this module are not saved for later printing. ASCII TABLE This module does nothing but display the ASCII characters along with their decimal, octal and hexidecimal equivalents. The ASCII Table is presented on screen only. It is not saved for printing.