



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.

