Carole,

"I have been asked the following question and just can't get my head around
how to answer it, it seems to be in the wrong order to the normal sample
size calculations that I know! We have completed a mailing campaign A - it
gave us a response rate of 10%. We are about to do a mailing campaign B -
we want it to give us a response rate of 15%, but how many people do we
need to mail to ensure that our seen 15% is significantly different from
the 10% seen in mailing campaign A?"

Others may very well be able to answer this. For me, at least, this is akin
to a puzzle in which a few of the key pieces are missing.

for example. How many folks did you sample in A? What does "significantly
differerent" really mean?How do you interpret "we want it to give us a
response rate of 15%"? This, for me, is where the main conundrum lies.  Is
this over and above the 10% you got in campaign A?  Why not wish for a 100%
response rate....not at all likely, but what one like ideally like....in
any circumstance I've come across?

One can sample a million people and have a response rate from 0 to 100%.
Same for 20 people or a trillion people. The response rate usually depends
on many things: how many other surveys people have been getting in the
mail, the types (sensitivity) of questions, length of survey instrument,
etc. etc. etc factorial. One can choose a sample size to give a certain
power for example, but I'd really like to know how you design a
survey/questionnaire/whatever  to get a specific response
rate....especially if it's from a random sample. Is it a SRS?  All of this
is apart from whether the proverbial 15% is significantly different than
the 10%.

I fully realize I've just asked a lot of questions and raised a few issues.
Perhaps, my best advice : go back to the client and ask probing questions
to find out exactly what they are asking/wishing in as many specifics as
possible.

If others give you concrete answers, could you let me know. In your
words,"I can't get my head around this either."


Darryl

Darryl Bertolucci
Statistician
Federal Aviation Administration