Posted by
Art Kendall on
Jun 13, 2011; 5:55pm
URL: http://spssx-discussion.165.s1.nabble.com/Margin-of-error-tp4481843p4485234.html
How are you using the term "margin of error"?
How are you calculating it?
Is your MOE in percentage points like the percentage result or is
is a percent of the percentage result?
When the confidence interval is close enough to symmetric the MOE
is about 1.96 * the sampling error.
Since 1000+500+71 is 1571 and not 3100, how are you using N and n?
there are 3 numbers to think about a pop size, a sample size, and
a number of (un)justified claims. These are used to find a
percentage result and a confidence interval in percentage points.
The term "margin of error" has a variety of meaning.
In planning an analysis/audit it is the largest acceptable half
width of the 95% confidence interval. When nothing else is known
about the a reasonable _subjective_ expectation of an
estimate 50% is used since it is the worst case, i.e., it has the
widest confidence interval. (highest standard error.)
"I don't want to more than x percentage points away from what we
would find if we did the whole pop." The sample size then becomes
very much a function of the worst case expected result.
In reporting results of a survey, a common way for the media to do
it is to call the widest half 95% confidence interval for any
percentage the margin of error.
It might be sated in one of these ways "All results in percentages
were within a plus or minus x percentage point 95% MOE or smaller."
"The largest 95% MOE for any resulting percentage was plus or minus
5 percentage points." "The fudge factor is +/- 5 percentage points."
"the (95%MOE was not larger than+/- 5 percentage points."
Auditing is one context where fpc's (finite population corrections)
are common but certainly not universal.
As you move farther away from a result of 50% the confidence
interval becomes less symmetric. There has been an old rule of thumb
that from 20 to 80 percent result a normal approximation is usable.
from 5% to 20% and 80 to 95% result a binomial approximation is
usable, and from 0% to 5% and 95 to 100% the Poisson approximation
is usable. If I recall correctly (and that is a big if) it comes
from Cochran. This rule of thumb comes from the days when one had to
use things called "tables" to look up coefficients, etc. These days
we use functions in software to do those things.
Search the archives for the extension command to find confidence
intervals. You probably want to use the number unjustified as the DV
since some methods
allow upper confidence limits over 100%. I do not recall whether
that command does that or if it includes the fpc.
In interpreting the results keep in mind that "justified" is not an
intrinsically dichotomous construct.
Art Kendall
Social Research Consultants
On 6/12/2011 11:36 PM, Michelle Tan wrote:
Thanks for the reply. DV is dichotomous and not the same in the three
scenarios. I am using MOE to add to the value of P to get the confidence
interval at a desired precision level.
Some background info.
The aim of the project is to conduct an audit to check if the claims
provision provided by our insurer is justified or not. So, p is the
proportion of justified cases. in my 3 scenarios, p is very lose to 1 as
expected.
There are a total of 3100 accident records which I have categorised into 3
categories of interest based on different criteria set for the 3
categories. (note that each accident may falls under more than one category
but it will only be audited once). A sample is then drawn from each
category. The findings are as follows:
N1 = 1000, n1=221, Margin of error = 1.52%
N2=500, n2=200, margin of error = 4.5%
N3=71, n3=67, Margin of error = 5.45%
i) I am using adjusted wald’s mtd to construct a Confidence interval for
each of the 3 categories and using the CI to make inferences to the total
population N in each category. is that possible? If yes, Is the sampling
error similar to Margin of error in this case? Does it sound right to use
the confidence interval obtained from sample to project to the population?
if no, what other analysis can i do?
ii) So does that means that for dichotomous data, regardless of how close
my sample size is to the pop size, the width of the margin of error only
depend on how close the estimate is to 50%?
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Art Kendall
Social Research Consultants