confidence interval around a total

[Tracy Clegg]

Dear all,

 

A colleague of mine wants to estimate the total number of people in the population with a certain characteristic (X).  He has run a survey and from this has calculated the probability of X by another variable (say household type, 10 categories, hence 10 values of X), he now wants to apply these probabilities to the county population by household type.  He will then sum these totals to give a total number of people with the characteristic within each county.  What he needs to know is how to calculate the confidence interval around these totals?

Any help would be most appreciated

[Martin Holt]

Hi Tracy,

 

I'm just thinking through the logic of this approach. In the survey that your colleague ran, what was the extent of the database (given that he wants to apply the results of the survey to counties) ? A subsidiary question would be, "Can he be sure that the results of the survey are representative ?"

 

Best Wishes,

Martin Holt

[Steve Simon, P.Mean Consulting]

Tracy Clegg wrote:

If it were a single proportion, this would be trivial. If the 95%
confidence interval for a proportion goes from 0.1 to 0.3, then the
confidence interval for the total number out of one million would be
100,000 to 300,000.

It's not a single proportion, though, but a proportion estimated from 10
strata. I'm not an expert here, but the classic books on sampling
theory, such by Cochran or Kish will provide you with the formula you need.
--
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[Tracy Clegg]

Hi Martin,

 

The survey was a quota survey, I know its not the best design, but it was the best that could be done on a tight budget.  The company that ran the survey ensured it was representative for several demographic variables such as location, age, gender and social class, the overall sample size was 1250.  The final sample does have the same distribution as the census does.  

 

Tracy

 

 

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[Martin Holt]

Hi Tracy,

 

Now I'm wondering what variables were used to choose the quota, and what numbers were used to define the size of the quota, and how these relate if at all with the "certain characteristic(s)" that your colleague wishes to deal with on a county-wide basis. (It seems to me that we need to understand the experimental design before we can move on to how to present an analysis.)