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I am calculating the relative median income of census tracts with respect to the CBSA (essentially the metropolitan area) that contains them. I am using ecdf in R to get the percentiles for each set of census tracts within nearly 1000 CBSAs . The trouble is that some CBSAs are very small, with less than 30 census tracts (some even smaller). I have read about plotting ecdfs with confidence envelopes, but I need a way to determine if my ecdf function for a given CBSA is within bounds for a given significance level. If not, then I can pursue a different method for the small CBSAs. How can I determine if a CBSA is too small for the ecdf method outlined above?

D. Kresta
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  • You don't seem to provide enough information for there to be an answerable question here. You can obtain confidence intervals for any percentile no matter what size the data set: see https://stats.stackexchange.com/questions/99829. In what sense, then, do you intend us to understand your meaning of "too small"? – whuber Sep 08 '18 at 21:48
  • "Too small" in the sense that I suspect for some of the smaller CBSAs, the confidence interval of the percentile calculation will be very large. Trouble is, I don't know how to determine if a C.I for a percentile is too large. – D. Kresta Sep 08 '18 at 22:31
  • OK: that shows us you need to give us a quantitative statement of what "very large" means. Without that, there's no answer. Can you tell us, *numerically,* how large is too large? – whuber Sep 08 '18 at 23:41
  • thank you, you are helping get to the root of my actual question. My experience with C.I's is in the context of hypothesis testing, so that if the CI contains zero, you cannot reject the null. In the case of CIs for a percentile, I don't know how to interpret them. I read the article you provided, but I'm still scratching my head. – D. Kresta Sep 09 '18 at 01:05

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