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Problem: Estimate coefficient of variation for the mean expenditures for a number of groups. For each group, I have a sample of totals and the counts of people. E.g., for group A, I have totals (people): 1000(200), 1100(205), 1113 (199), and so on.

Based on the CLT, the means should be approximately normally distributed for large enough sample sizes. I can then use the estimator given here.

My question is how should I handle the estimation for groups where the sample size is small? For example, I have some groups with only 4 data points. Would this be a good case for resampling techniques like bootstrapping?

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  • $\begingroup$ How would you resample with 4 observations only? There is no point in that..maybe try to merge this with another group, look for more data...in 4 data points, there is just no information at all $\endgroup$ – Jan Sila Aug 24 '16 at 20:20
  • $\begingroup$ Thanks for the response. Merging similar groups is definitely something I will consider. The groups range in sample size from 4 to 100. I've seen elsewhere that 1. bootstrapping should be done on samples of at least 20, and 2. the CLT is valid for samples of 30 or more. How do you recommend I estimate the CV? Is it unreasonable to estimate the CV for groups with sample under 30? Should I use resampling for some groups? $\endgroup$ – drj3122 Aug 24 '16 at 20:38
  • $\begingroup$ Is this for school or work? If for school, I would just put my answer as in that case it is inconclusive (maybe your teacher is testing blind use of formulas without thinking about it)...those CLT/bootstrap size numbers are just rule of thumb, if your data 'clearly' form a shape of a distribution and make sense, then use 30 and dont really need to resample - you do that to check that distribution of the statistic is quite narrow..as bootstrapping is often used to sort out outliers, have a look at your data if there are any distinctive outliers and if yes, use bootstrap.. $\endgroup$ – Jan Sila Aug 24 '16 at 20:58
  • $\begingroup$ It's for work. I'm reviewing some previous work and I'm skeptical that it is statistically sound; e.g. estimating CVs based on small samples. $\endgroup$ – drj3122 Aug 24 '16 at 21:06
  • $\begingroup$ Yh in that case I would not take them into account really! :) $\endgroup$ – Jan Sila Aug 25 '16 at 9:28
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Such a small sample of 4 cannot give any good estimate of mean or standard deviation of the population, hence the Coefficient of variation will have a massive error. To remedy, I suggest to merge low-observation group with a similar one to increase the sample size.

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