DM Calc ======== Copyright 1992, Vincent Wilhelm: CIS-ID: 72500,3547 This program may be copied and distributed without restriction, as long as this documentation accompanies it. To order a copy by mail, send $4.50 to cover disk duplication and postage to Vincent Wilhelm 17 New Street Allendale, NJ 07401 This program is designed to 1. Calculate the target response rate for a direct mail program 2. Calculate the confidence interval for a given mail quantity/response rate 3. Calculate how many pieces of mail need to be sent to achieve a certain confidence level To start the program, copy the file DMCALC.EXE to the directory of your choice on your disk drive, log onto that directory and type DMCALC. NOTE: All percentages should be entered as whole numbers. Decimal points should only be used to show a fraction of a percent. ======================================================== INTERVAL When testing a direct mail program, it is important to realize that the "TRUE" response rate will be plus or minus X "standard errors" from the test sample result. The value of "X" depends on the degree of confidence we wish to have in the interval we calculate. Hence, the higher the degree of confidence, the wider the interval. Degree of Confidence Value of "X" -------------------- ------------ 80% 1.282 90% 1.645 95% 1.960 99% 2.580 The STANDARD ERROR = the square root of the response rate times (1 - response rate) divided by the test mail quantity. Thus, the CONFIDENCE INTERVAL is calculated as follows: CI = test response rate +/- X times the standard error. EXAMPLE: If we mailed 5,000 pieces to an Nth name sample of a mailing list and obtained a 1.2 percent response, we could be 95% certain that the response rate for the entire list would be Standard Error = square root of [0.012 X (1 - 0.012) divided by 5,000] = square root of 0.00000237 = 0.001539 = 0.154 percent If we are satisfied with a 95% degree of certainty in our confidence interval calculation, the value of "X" becomes 1.96, and the Confidence Interval is 1.2 percent, plus or minus 1.96 X 0.154 percent, or +/- 0.3018 percent. Thus, we are 95% confident that the "true" response rate will be somewhere between 0.8982% and 1.5108%. =========================================================== QUANTITY To calculate how many pieces of mail are necessary for a direct mail test, the same calculation is solved by providing a desired "precision level" -- that is, how far (plus or minus) from the test response rate are we willing for the "true" response rate to be. Essentially, the precision level is 1/2 the confidence interval. If the response rate is 1.2 percent, and we wanted to be 95% certain that the "true" response rate was between 1.0% and 1.4%, we would specify a precision level of 0.2%. Thus, 0.002 = 1.96 times the Standard Error. As in the example above, the standard error would be calculated as Standard Error = square root of [0.012 times (1 - 0.012)] divided by mail quantity] So, 0.002 = 1.96 times the square root of [0.012 times (1 - 0.012)] divided by the mail quantity Divide both sides of this equation by 1.96, then square each side ... 0.00000104 = [0.012 X (1 - 0.012)] divided by the mail quantity 0.00000104 = 0.011856 divided by the mail quantity mail quantity = 0.011856 divided by 0.00000104 mail quantity = 11,400 ============================================================ RESPONSE RATE The target response rate is calculated on the basis of an "allowable" -- the amount, per unit, that could be allocated to advertising and profit. This is determined by subtracting all the direct costs associated with the sale of each unit: manufacturing cost, royalty payment, and fulfillment cost -- as well as any provision for bad debt and overhead. To determine the breakeven response rate, simply divide the allowable into the mailing cost. To learn more about these calculations, I highly recommend a book entitled THE NEW DIRECT MARKETING, by David Shapard Associates, Inc. Copyright 1990, Dow Jones-Irwin, Homewood, Illinois.