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From |
Alexander Cavallo <[email protected]> |

To |
[email protected] |

Subject |
st: svy and hypergeometric distribution |

Date |
Mon, 17 Jan 2005 17:19:41 -0600 |

I have some statistics questions. I am refering to Cochran's famous book, "Sampling Techniques". 1. Does Stata have a routine to compute a confidence interval for a proportion using the hypergeometric distribution? 2. Does svyprop use the normal approximation to compute CIs for the proportion? 3. How can I generalize the exact hypergeometric calculation to account for weights? 4. How can I generalize the exact hypergeometric calculation to include weights and strata? Background - normal approximation for CI for proportion To compute a confidence interval for a proportion under simple random sampling, the normal approximation can be used. The confidence interval is p +- {t * sqrt(1-f) * sqrt[p * (1-p) / (n-1)] + 1/(2*n) where p is the sample proportion q = 1 - p t is standard normal z score for desired significance level n is sample size f = n / N is the sampling rate Background - hypergeometric distribution for CI for proportion I understand that if p is too close to 0 or 1, then I should use the hypergeometric distribution to compute an exact confidence interval (which may be non-symmetric). Let H(x, n-x, A, N-A) be the hypergeometric probability for finding in a sample of size n from a population of size N: x occurences in the sample and A occurences in the population. H(x, n-x, A, N-A) = [A choose x] * [(N-A) choose (n-x)] / [N choose n] The upper 95% CI for the population number of occurences, A is given by finding the smallest integer Au such that sum from j=0 to x {H(j, n-j, Au, N-Au)}<= 0.025. The lower limit Al for the 95% CI on population occurences is given by the largest integer Al such that sum from j=x to n {H(j, n-j, Al, N-Al)}<= 0.025. Proposal - weighted hypergeometric calculation Here is what I propose for the svy hypergeometric calculation. Replace x (number of occurences) with the weighted version. Replace n with the sum of weights. Round new x and new n to integers and solve the same equations for Au and Al. But how would I extend this to stratified analysis? Thanks! --Alex Cavallo Navigant Consulting, Inc. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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