MadSci Network: Other

Re: calculating confidence rates in samples. (Statistics)

Date: Sun Nov 26 13:52:05 2000
Posted By: Paul Thompson, Faculty, Biostatistics, Med School
Area of science: Other
ID: 971719916.Ot

Well, it isn't as simple as all that.  If there are just red and blue cars,
and no other colors, then it is quite simple.

You are interested in a CONFIDENCE INTERVAL around that proportion.  NOTE PLEASE 
that it is the proportion, not the red cars, that we are putting the CI around. 
 RED VS. BLUE, not RED ALONE.  This is a binomial situation.  Let p be the 
proportion of red cars, q = 1 - p, n = sample size.

p +- 1.645 * sqrt(p * q / n),

This breaks down when p or q are <= .05.  Special other formulae must be used 
then.  See Fleiss Statistical Methods for Rates and proportions.

When there are red, blue and green cars, we get more complicated, although it 
can be simplified to red and non-red (see above).  If it can't be simplified to 
red and non-red, this is the multinomial situation and it is harder to do this.

You are always 90% confident of your answer.  If you rephrase this way:
I wish to be 90% confident that the answer is within .05 of the sample
proportion, then we are dealing with a power question, and we can answer it.

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