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=========================================================== STATHELP USER'S MANUAL -- SHAREWARE VERSION =========================================================== ___________________________________ | | | WELCOME TO STATHELP | | | | Featuring | | | | WATSTAT, LOOKUP, and RANDO | | | | A Trio of Statistical Tools | | for Both Novice and Expert | | Number Crunchers | | | | From Hawkeye Softworks | |___________________________________| CONTENTS Page ======================================================= Copyright Notice & Warranty Disclaimer ---------- 1 About Shareware, the ASP, and the ASP Ombudsman -- 2 About the Shareware Version of STATHELP ---------- 2 Registration Information ------------------------- 3 General Usage Notes for All STATHELP Programs ---- 3 WATSTAT Usage Information ----------------------- 4 LOOKUP Usage Information ------------------------ 5 RANDO Usage Information ------------------------- 8 Registration Form -------------------------------- 11 ======================================================= ================ COPYRIGHT NOTICE ================ WATSTAT, LOOKUP and RANDO are Copyright 1991 by Hawkeye Softworks, 300 Golfview Ave., Iowa City, IA, 52246, All Rights Reserved. The windows and menus used in these programs were implemented with Vermont Views, a C language function library Copyright 1988, 1989 by Vermont Creative Software, All Rights Reserved. The programs were compressed and converted to a self-extracting archive file with software licensed by PKWARE, Inc., 7545 N. Port Washington Road, Glendale, WI, 53217. =================== WARRANTY DISCLAIMER =================== WATSTAT, LOOKUP, and RANDO, and the accompanying documentation carry no warranty, expressed or implied, as to their merchantability or fitness for a particular purpose. In no event will the copyright holder be liable for damages arising from the use of, or defects in, the STATHELP programs. Page 2 =============================================== ABOUT SHAREWARE, THE ASP, AND THE ASP OMBUDSMAN =============================================== Shareware is a distribution method that gives you a chance to try out and evaluate software before buying it. If you find that the software meets your needs, and if you continue to use it after a reasonable evaluation period, you are expected to REGISTER with the author and pay a set fee. Shareware authors get no compensation from the distributors of their software; they are paid for their work only through registration fees. And shareware will continue to exist only if users support it. Hawkeye Softworks is a member of the Association of Shareware Professionals (ASP), an association for shareware authors and distributors, whose goals are to set standards for the shareware system and to educate its members and the public about shareware. ASP maintains an Ombudsman office to mediate disputes between ASP members and their customers, and has published the following statement regarding its Ombudsman service: The ASP wants to make sure that the shareware principle works for you. If you are unable to resolve a shareware-related problem with an ASP member by contacting the member directly, ASP may be able to help. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegan, MI, 49442, or send a CompuServe message via CompuServe mail to ASP Ombudsman 70007,3536. ======================================= ABOUT THE SHAREWARE VERSION OF STATHELP ======================================= The STATHELP programs on this disk are Shareware programs. Whether or not you register, you may make multiple copies these programs and distribute them freely to friends, user groups, computer bulletin boards, etc., so long as the following conditions are met: 1. Anyone distributing the STATHELP programs for any kind of remuneration must first contact Hawkeye Softworks, at the address given below, for authorization. This authorization will be granted automatically to distributors recognized by The Association of Shareware Professionals as adhering to its guidelines, and such distributors may begin offering STATHELP immediately. However, they must still notify Hawkeye Softworks, to ensure that they are supplied with the latest version of STATHELP. 2. The programs must be distributed in unaltered form; program names must not changed; and copyright notices must not be removed. 3. The file called README.1ST and the file you are now reading, called SHMANUAL.DOC, must be distributed, in unaltered form, along with the programs. If STATHELP is distributed in compressed form, as you received it, the three files called SHZIPARC.EXE, SINSTALL.BAT, and README.1ST must all be distributed together, in unaltered form. We encourage you to pass copies of STATHELP to your friends for evaluation. When you do, please encourage them to register their copies if they intend to use them regularly. Page 3 ============ REGISTRATION ============ In accord with the Shareware concept, this version of the STATHELP package gives you the opportunity to try WATSTAT, LOOKUP, and RANDO at nominal cost. If you find that you like them and continue to use them, please print and fill out the REGISTRATION FORM provided at the end of this file and send it along with the Registration fee of $20 in U.S. currency (or $10 if you are an enrolled student) to Hawkeye Softworks, at the address given on the REGISTRATION FORM. Registered users will receive: 1. The next update/revision of the STATHELP programs, as soon as available. (We expect to produce updates, with major enhancements, about once per year.) The next version of WATSTAT will provide references to standard textbooks where you can find more information about the procedures it recommends. The next LOOKUP will optionally report "critical values" for probabilities you specify and report proportions under the Normal curve between any two ordinates. The next RANDO will optionally send output to a file and allow you to merge RANDO output with your own data file. 2. A USER'S MANUAL for the revised version, containing a Glossary of all the statistical terms you'll need, as well as explaining how to use all the features of the STATHELP programs. (If you'd also like a laser-printed manual for your current version of STATHELP, which is the same as the SHMANUAL.DOC file you're now reading, just circle "YES" on the Registration Form.) 3. Free technical support, by mail or Fax, for a full year from the date your Registration is received. 4. Notices of new products from Hawkeye Softworks, at special discount prices for registered STATHELP users. ======================================================================= GENERAL USAGE NOTES FOR ALL 3 STATHELP PROGRAMS ======================================================================= You should find the STATHELP programs easy to operate. On-screen messages guide your every step and Error Messages keep you from going astray. In WATSTAT, pop-up HELP WINDOWS and an on-screen TUTORIAL give you even more extensive guidance. This manual provides more detail than you're likely to need at the outset, and it answers questions that may not occur to you until you've tried out the programs. So, we suggest that you merely skim the following sections and then print a hard copy of this file (with the DOS Print command), so you can refer to it as you experiment with the programs. The best way to learn about WATSTAT is to select "Run Tutorial" from the MENU displayed on the start-up screen. The tutorial takes only about 10 minutes, but tells you all you need to know about running WATSTAT. After completing the tutorial and doing a few practice "Consulting Sessions," you'll be ready to do serious work with WATSTAT. Page 4 The best way to learn about LOOKUP and RANDO is simply by running them: after 15 minutes or so, you should be quite proficient. Please note, however, that the STATHELP programs assume some training in statistics, and some users may need to consult a textbook to brush up on statistical terms and concepts. ======================================================================= WATSTAT USAGE INFORMATION ======================================================================= The WATSTAT program must access 4 subsidiary files, and it can't find those files unless you run it from the directory that contains them. So, before starting WATSTAT, first use DOS's CD command to change to the appropriate directory. Then, start WATSTAT by merely entering its name from the DOS prompt. At startup, WATSTAT displays a MENU that offers the following choices: ------------------ | 1 - RUN WATSTAT | | 2 - Tutorial | | 3 - Sound On/Off | | 4 - QUIT WATSTAT | ------------------ You can make menu selections in two ways: 1) by typing the number of a selection or 2) by moving the highlight with the Up/Down arrow keys and then pressing the [ENTER] key. "RUN WATSTAT" begins a "Consulting Session." When you select this option, the menu disappears and the first of a series of Choice Boxes appears to ask you about your data, design, and analytical focus. At the end of this series, WATSTAT displays a report that advises you on what statistical procedures are apt to be appropriate. At this point, you'll have the option of printing a hard copy of the Advisory Report or returning immediately to the Menu. "Tutorial," starts WATSTAT's on-screen Tutorial, which gives you complete operating instructions. The Tutorial takes only about 10 minutes and walks you through all of WATSTAT's features. "Sound On/Off" allows you to control the "OK" trill sound that WATSTAT uses to tell you that your input is acceptable and that it's proceeding to the next step. You can silence the trill and turn it back on with the Menu's "Sound On/Off" option. WATSTAT also makes a low beep sound to warn you about errors: this Error Beep can't be turned off. "QUIT WATSTAT," terminates WATSTAT and returns you to DOS. When you select this option, a Choice Box pops onto the screen and asks you to verify your intentions. If you've changed your mind, or if you chose QUIT by mistake, the Choice Box allows you to return to WATSTAT by simply pressing the [ESC]ape key. If you choose to quit, WATSTAT returns you to DOS and restores what was on your screen before you started. Page 5 WATSTAT has a so-called "context-sensitive" help system, which gives you on-screen help information about the operation you're about to perform. When you're in doubt, simply press the [F1] key, and a Help Window will pop onto the screen. Some help messages are too long to fit in the Help Window, so you'll sometimes need to use the Up/Down arrow keys to scroll through and read the entire message. You can also expand the Help Window to full-screen size by pressing the [ALT] and [F1] keys, simultaneously, while a Help Window is displayed. Pressing the [ALT] and [F1] keys while Help Window is full-screen size will shrink it to its normal size. Because WATSTAT's Tutorial is so comprehensive, no further details are needed here. ======================================================================= LOOKUP USAGE INFORMATION ======================================================================= When you first start LOOKUP, you'll see the MAIN MENU, which gives you seven choices, as shown below. MAIN MENU --------------------------------------------------------------- SETUP Normal t-Dist. F-Dist. Chi-Sqr. Binomial QUIT --------------------------------------------------------------- You can make menu selections in two ways: 1) by typing the first letter of a selection or 2) by moving the highlight with the left/right arrow keys and then pressing the [ENTER] key. If you select SETUP, a Choice Box pops onto the screen, allowing you to control sound and printing. Sound -- LOOKUP makes a trill sound to tell you that it has finished a requested computation and, normally, sound should be left on. This sound is especially important on faster computers, since LOOKUP computes so quickly that you may not even notice that it has printed a new p- value. And if you hold down the "Execute" key too long, it may compute the same p-value more than once. LOOKUP also makes a low beep sound to warn you about errors: this Error Beep can't be turned off. Printer -- At your option, LOOKUP will send results to a dot matrix printer as well as to the screen. Printing is initially turned off, and you'll need to turn it on from the SETUP Choice Box. When you're finished with LOOKUP, select the QUIT option from the MENU. A Choice Box will pop onto the screen to ask you to verify your intentions. If you've changed your mind, or if you selected QUIT by mistake, the Choice Box allows you to return to LOOKUP by simply pressing the [ESC]ape key. If you choose to quit, LOOKUP returns you to DOS and restores what was on your screen before you started. Page 6 If you select one of the 5 significance test options, a DATA ENTRY FORM will appear in place of the MENU and prompt you to enter the appropriate values. A different FORM is used for each test, and each has different slots, called FIELDS, where you enter data. For example, the Normal (z-test) FORM has only one FIELD, where you enter a z- statistic, while the t-test FORM has one FIELD for a t-statistic and another for degrees of freedom. When you fill all the spaces in a given FIELD, LOOKUP jumps automatically to the next FIELD. If your entry does not fill a given FIELD, press the [ENTER] key to go to the next. If you want to jump around the FORM without changing values you've already entered, press either the [ENTER] key or the [TAB] key as many times as you wish. LOOKUP performs no calculations until you press the [F10] key: this is the "Execute" key. When a calculation is finished, LOOKUP prints the p-value and other information in the RESULTS LOG window in the middle of the screen. If SOUND is ON, you'll hear a trill sound indicating that the calculation was done successfully. If you selected PRINTER ON from the SETUP Choice Box, LOOKUP will also send the result to your printer before it trills. If your printer is turned off or is not on-line when LOOKUP tries to print, it will issue an error message telling you to get the printer back on-line. At this point, you can also tell LOOKUP to stop sending results to the printer, without returning to the SETUP Choice Box. The RESULTS LOG has room to display results from 11 calculations, but it actually stores up to 100. If you want to review results that have scrolled off the screen, press the [F2] key, as the on-screen instructions tell you. This puts the blinking cursor in the RESULTS LOG and allows you to scroll up and down, using the Up/Down Arrow keys or the PageUp/PageDn keys. The "scroll bar" on the right side of the RESULTS LOG shows your position in the LOG and will indicate when you've reached the top or bottom line. To exit the LOG and return to the ENTRY FORM, press the [ESC]ape key, as on-screen instructions tell you. Because the RESULTS LOG holds only 100 lines, it will delete early results to make room for more. Results for the z, t, F, and Chi-Square each use one line and those for the Binomial each use 2 lines. So, if you're doing a large number of calculations, it is wise to send results to your printer. After each calculation, LOOKUP returns you to the ENTRY FORM. If you want to continue with the same FORM, merely edit whatever fields you wish and press [F10] to perform another calculation. To exit a FORM and return to the MAIN MENU, press the [ESC]ape key. WHAT p-VALUES DO YOU GET? ------------------------- For the z and t-tests, which can have either positive or negative signs, LOOKUP reports the one-tailed p-value corresponding to the sign of the test statistic. For example, if you enter a z value of 2.4, LOOKUP reports the probability of getting a z of 2.4 or greater; if you enter -2.4, it will report the probability of getting a z of -2.4 or lower. Page 7 For F and Chi-Square, which are always positive, LOOKUP always reports the upper-tail p-value. So, if you enter a Chi-Square of 5.5, it will report the probability of getting a Chi-Square statistic of 5.5 or greater, given the number of degrees of freedom you specify. For the Binomial distribution, you may specify either an upper- tail or a lower-tail p-value. This makes it useful for purposes other than significance testing. However, if you're running a Binomial test, you'd normally specify whichever tail corresponds to direction in which the observed number of "successes" deviates from the mean. For example, if you get 20 "heads" when you toss a coin 30 times, the (upper-tail) probability of getting 20 or more "heads" would be the relevant p-value. By contrast, if you get 10 "heads" in 30 tosses, the (lower-tail) probability of getting 10 or fewer "heads" would usually be what you need. Another thing to note about the Binomial FORM is the FIELD labelled "Null Hypothesis Proportion." The most common Null Hypothesis tested specifies "P=.50," which is analogous to the long-run proportion of "heads" or "tails" with a fair coin. However, LOOKUP allows you to specify proportions ranging from .002 to .999 For sample sizes up to 100, LOOKUP gives you results for an exact Binomial test, using the well-known "factorial formula" for Binomial probabilities. For samples of 101 or greater, LOOKUP reports p-values for the Normal approximation to the Binomial (without a correction for continuity). WHAT YOU CAN AND CANNOT ENTER ----------------------------- Every value you enter has an "allowable range" and LOOKUP will not allow you to enter values outside this range. In some cases, the allowable range is defined by the statistics themselves (e.g., you can't have an F or Chi-Square statistic less than 0.0). In other cases, the allowable range is arbitrarily set by the program to prevent such things as dividing by 0 or exceeding the precision of the computer. If you try to enter an out-of-range value, LOOKUP will sound a beep and issue an error message, "Field value is too large or too small." When this occurs, LOOKUP returns you to the DATA FORM so you can change the offending value. LOOKUP also traps some types of illegitimate values before you leave a FIELD. In such cases, it will sound a beep and refuse to accept your input. This will happen, for example, if you try to type a letter where a number is required or if you try to enter a minus sign or decimal point in a FIELD that requires a positive integer. PRECISION OF p-VALUES --------------------- LOOKUP will usually display p-values rounded to 4 decimal places, except for the exact Binomial test, where p-values are rounded to 8 decimal places. Sometimes, p-values are so close to 1.0 or 0.0, that LOOKUP merely reports "1" or "0." However, if too much rounding error would result, p-values are given in scientific notation, which expresses a number as the product of 1) a "base" number between 1 and 10 and 2) some power of 10. For example, the number 3.212E-005 in scientific notation translates to "3.212 times 10 to the -5th power," which is .00003212. But note that you need not do any actual Page 8 multiplication: you simply move the decimal point in the "base" number, 3.212, five places to the left, as directed by the exponent, E-005. So, if LOOKUP gives you a p-value of 4.41133E-010, you'd just shift the decimal point 10 spaces to the left and get .000000000441133. Although "pure" statisticians may require very precise p-values for their research, "applied" statisticians rarely need more than 3 decimal places of accuracy for significance tests. Thus, if a p-value is less than .001, anyone working with real-world data is sure to declare the result statistically significant. And although LOOKUP may give you p-values to as many as 16 decimal places, in scientific notation, it is wise to report such small values as "<.001." ======================================================================= RANDO USAGE INFORMATION ======================================================================= When you first start RANDO, you'll see the MAIN MENU, which gives you six choices, as shown below. MAIN MENU ----------------------------------------------------------------- 1. UNIFORMLY DISTRIBUTED NUMBERS 4. EXPERIMENTAL RANDOMIZATION 2. NORMALLY DISTRIBUTED NUMBERS 5. LOTTERY NUMBERS 3. RANDOM 1's and 0's 6. QUIT ----------------------------------------------------------------- You can select from the MENU in two ways: 1) by typing the NUMBER of your selection or 2) by highlighting your selection with the Up, Down, Left, and Right arrow keys and then pressing the [ENTER] key. Here's what happens when you select each of the six items: 1. The UNIFORMLY DISTRIBUTED NUMBERS option simulates random sampling from a Uniformly Distributed Population, in which all possible numbers occur the same number of times, so that all numbers have an equal chance of being drawn. When you select this option, a Sub-Menu pops onto the screen, allowing you to specify one of two further options: 1) Integers ("whole numbers") with any minimum and maximum values you want, within a possible range of 0 to 32,776. 2) Decimal Numbers ranging from 0.0 to 1.0. 2. The NORMALLY DISTRIBUTED NUMBERS option simulates random sampling from a Normally Distributed Population, in which the chance of drawing any given number varies inversely with its distance from the mean. When you select this option, a Sub-Menu pops onto the screen, allowing you to specify one of two further options: 1) Random Numbers with a Mean of 0.0 and a Standard Deviation of 1.0. 2) Random Numbers with any Mean and Standard Deviation you wish. In either case, the Mean and Standard Deviation of the resulting numbers will only APPROXIMATE those you request, but the approximation should be adequate for most practical purposes. Page 9 3. The RANDOM 1's and 0's option simulates random sampling from a Dichotomous Population, i.e., one which has only two possible values. When you select this option, a Sub-Menu pops onto the screen, allowing you to specify one of two further options: 1) The Approximate Proportion of 1's you want, within an allowable range of .01 to .99. 2) The Exact Proportion of 1's you want, within an allowable range of .01 to .99. If you choose this option, RANDO will increment your SEED until it finds a new SEED that produces a proportion of 1's within +/-.01 of the proportion you want. In its printout, RANDO will tell you what SEED it actually used. In either case, the obtained proportion of 1's will depend on the quantity of numbers you request. You'll get closer to the proportion you want if you request a large quantity of numbers (say, 1000) and if the quantity is evenly divisible by the proportion you specify, e.g., you can divide 100 numbers into .65 1's and .35 0's, but you can't get these exact proportions if you ask for 115 numbers. 4. The EXPERIMENTAL RANDOMIZATION option simulates the random ordering of numbers from 1 to N, where N may range from 3 to 20. As its name implies, this type of random process is used in experiments where each subject gets all N treatments and where treatments are administered in a different order across subjects. Random ordering serves to justify significance tests as well as to protect against "order effects" that might result if certain treatments always follow certain others. 5. The LOTTERY NUMBERS option simulates lotteries in which numbered cards or Ping-Pong balls are randomly drawn by hand or by a machine. When you select this option, a Sub-Menu pops onto the screen, allowing you to specify one of two further options: 1) The STANDARD LOTTERY option simulates the type of drawing used in most state lotteries (often called "Lotto"), where you pick X different numbers ranging from 1 to N and where the order of your picks is irrelevant. For example, you may pick X=6 different numbers, in any order, that fall in the range of 1 to N=54. 2) The PICK DIGIT SEQUENCE (0-9) option simulates the type of lottery that some states run as a "Daily Game." Here, you may pick duplicate digits in the 0 to 9 range and you must match not only the digits but the order of digits generated by the lottery machines. For example, in a "Pick 4" game, you may pick 0,0,4,5, and you'll win only if the lottery machines pick the same digits in exactly the same order. 6. The QUIT option tells RANDO that you want to quit and return to DOS. When you select this option, a Choice Box pops onto the screen, asking you to verify your intentions. If you've changed your mind, or if you selected this option by mistake, you can press the [ESC]ape key and return to the MAIN MENU. If you choose to quit, RANDO returns you to DOS and restores what was on your screen before you started. Page 10 Once you've made your menu selections, RANDO displays a DATA ENTRY FORM just below the MENU and prompts you to enter the appropriate values. A different FORM is used for each type of random number, and each has different slots, called FIELDS, where you enter data. However, all forms have a FIELD labelled "Set Seed (Any Number, 1 to 65535)," which is explained in the next section. When you fill all the spaces in a given FIELD, RANDO jumps automatically to the next FIELD. If your entry does not fill a given FIELD, press the [ENTER] key to go to the next FIELD. If you want to jump around the FORM without changing values you've already entered, press either the [ENTER] key or the [TAB] key as many times as you wish. As you enter each FIELD, the MESSAGE BOX at the bottom of the screen tells you what to type in that FIELD. Each FIELD has an Allowable Range of values, and RANDO will complain if you try to enter an out-of-range value. Sometimes it will merely sound a low-pitched "Error Beep," as when you type a letter in a FIELD that requires numbers. Sometimes it will also display an Error Message in the MESSAGE BOX, as when you tell it to pick 20 Lottery numbers and you have specified a maximum possible number of only 15. You'll also get an Error Message if your printer is turned off or is off-line when RANDO tries to print. RANDO generates no random numbers until you press the [F10] key: this is the "Execute" key. RANDO sends all of its output to your printer and, when it's finished printing, makes an "OK" trill sound to tell you it's ready to continue. (Note: If your printer has a built-in buffer, RANDO will be ready to continue while the printer is still working.) If you want to continue with the same FORM, merely edit whatever fields you wish and press [F10] to generate more random numbers. To exit a FORM and return to the MAIN MENU, press the [ESC]ape key. THE SEED -------- RANDO generates random numbers with mathematical algorithms that always begin with an arbitrary number called the SEED. This SEED may be any number between 1 and 65,535, which is the largest "unsigned integer" your machine can store. The numbers RANDO generates are called "Pseudo-Random Numbers," because the same sequence of numbers is generated for any given SEED. In virtually all practical applications, Pseudo-Random numbers may be used in place of "True" random numbers and, because a sequence of Pseudo-Random numbers can be duplicated, they are often more desirable. If you want to duplicate a sequence of numbers, use the same SEED; if you want a different sequence, change the SEED. Other than this, there are no "rules" for specifying a "correct" SEED. Your birth date, your "lucky" number, or something as dull as "123456" are equally appropriate. But, if you ask for a new set of numbers (by changing the SEED) after studying the first set, you should be aware that you are committing a statistical sin known as "Capitalizing on Chance" Note: RANDO sends all its output to a printer, and it requires a dot matrix or other printer equipped with a tractor feed. Because it sends no page-breaks, it won't work with lasers or other sheet-fed printers. Page 11 The form below is for your convenience in registering. Just print it on a dot-matrix printer, fill it out, and send it along with $20 in US dollars ($10 for currently enrolled students) to the address given on the form. If you can't print the form, a hand-drawn facsimile will do. ------------------------------------------------------------------------------ ========================== Mail to: Hawkeye Softworks STATHELP REGISTRATION FORM 300 Golfview Avenue ========================== Iowa City, IA 52246 NAME ________________________________________________ DATE: ________ ADDRESS __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ PHONE (Optional) __________________________ Would you like a laser-printed copy of SHMANUAL? YES NO (circle one) What is the Version Number displayed on your screen when you run: WATSTAT _______ LOOKUP _______ RANDO _______ [If you don't have the most current version, we'll automatically send one, in addition to the next upgrade.] Where did you get your shareware version of the STATHELP programs? [If from a dealer, please give their name & approximate purchase date.] __________________________________________________________________ What features would you like to see in subsequent versions of STATHELP? [Use reverse side or attach additional pages if needed. We value your views] _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ ------------------------------------------------------------------------------ When registering, feel free to include comments about the STATHELP programs and suggestions for improving them. If you are an instructor or student in a statistics course, please send information about your textbook, so we can include references to it in the next version of WATSTAT. User input will guide further development of the STATHELP programs and, we hope, lead to new programs to be added to the package. Whether or not you register, please also report any bugs you may find and provide as much detail as you can about them. That is, besides describing symptoms of a bug, explain what you were doing just before it occurred, whether it always occurs under certain conditions, what brand and model of computer and printer you have, what DOS version you're using, and what other software (particularly TSR's) may have been in your computer's memory at the time. If possible, print copies of your AUTOEXEC.BAT and CONFIG.SYS files and send those too. =================================================================== End -- WE TRUST THAT YOU'LL ENJOY USING WATSTAT, LOOKUP, AND RANDO ===================================================================