Date: Thu, 24 May 2001 10:20:22 -0400
Reply-To: Peter Flom <peter.flom@NDRI.ORG>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Peter Flom <peter.flom@NDRI.ORG>
Subject: Re: sample size and sampling error?
How accurate your results are depends MUCH more on how good your response rate is, and on how representative the respondents are, compared to the total population.
IF your respondents (as opposed to those you mail out the survey to) are a random sample, then you can get fairly good estimates with relatively small samples. Exactly how accurate the result will be depends on exactly what you are trying to measure. From what you say, it sounds like you are estimating proportions. For which are not very close to 0 or 1, the SE formula is (pq/n)^ .5; where p is the proportion saying "yes" (or whatever), and q = 1 - p. So, for example, if you had 1000 respondents, and 500 said "yes" your standard error = (.5*.5/1000)^.5 = .0158. With 10,000 respondents, it only goes down to .005 (unless I've pushed the wrong button somewhere)
But if your respondents are NOT random, then no sample size is going to help. SO, I'd recommend allocating resources to get as many people to respond as possible
Peter L. Flom, Ph.D.
Principal Research Associate
National Development and Research Institutes, Inc.
2 World Trade Center
New York, NY 10048
(212) 845-4698 (fax)
>>> Mike Tonkovich <takeadoe@FROGNET.NET> 05/24/01 09:50AM >>>
Sounds as though this may be a reasonable question for the list. Hope so at least. Would greatly appreciate any feedback you might have on the subject.
We have an estimated 479,000 hunters in Ohio and we want to conduct a survey
to estimate such things as hunter success rates, participation rates, and
opinions on various issues related to deer management. The first question
of course, is how large of a sample? My former boss conducted a similar
survey and ended up with 3800 (actually he mailed surveys to 6700 hunters,
apparently he new that the response rate would be down around 45-55% and
took this into consideration when calculating the necessary sample size)
useable responses. I'm now getting ready to conduct a similar survey and
the question of sample size once again needs to be addressed. There was
little documentation on how he arrived at 6,700 or 3,800 for that matter, so
I'm left with coming up with my own estimate and of course justifying it.
In all of the STATS text books that I've been able to lay my hands on, they
all deal with minimum sample sizes for estimating the mean for a given
variable or a proportion. In each case, you're asked to specify a
confidence level (typically 95%) and also the bound or error that you are
willing to accept, for instance plus/minus 2.5lbs in the case of the average
weight of a particular strain of egg plant. In this survey that I plan on
running, I'm going to ask 40 questions. Am I to do this for every variable
and take the maximum sample size needed to achieve the desired level of
confidence or what? If not, is there a similar formula that one uses in
situations such as mine to come up with a sample size required for x-level
On a related note, after discussing this issue with a statistician in
Virginia, he sent me an excel spreadsheet that asked for 2 inputs - the size
of the sample and the size of the population and the output was the maximum
% sampling error. The inputs and outputs are presented below.
Population Size Sample Size Max Sampling Error (95% CI) Percent Error
479000.00 3800.00 0.0158345305 1.583453047
I'm having a tough time grasping just exactly what the 1.58% means (in
simple terms that adminstrators can understand!). Does that mean that in
repeated sampling of n=3800, 95 times out of 100, the sample mean plus or
minus 1.58% of the mean will contain the actual population mean? How, or
should I say, does this relate in anyway to the standard error and CV. I
know that the CV is actually a percentage (the SE expressed as a percent of
the mean). Is this 1.58% the maximum CV for all variables in the survey?
If anyone can help me sort this out, I would greatly appreciate it.
Thanks in advance for any assitance you might be able to offer.
Michael J. Tonkovich, Ph.D.
Wildlife Research Biologist
ODNR, Division of Wildlife