MATLAB: Confidence interval for single proportion with exact method

statistics

I am trying to compute confidence interval for single proportion using exact method based on binomial distribution with matlab. For example, if you look at chapter 510 on the NCSS user manual it describes (<http://www.ncss.com/pdf/manuals/NCSSUG5.pdf>) what I am trying calculate. I would think that the statistics toolbox would have this capability, but I can't seem to locate it. Please let me know if you this function, or how I might be able to replicate it with Matlab and the stats toolbox. Thanks.

Best Answer

Sounds like you want the binofit() function. It uses the Clopper-Pearson method to calculate the confidence intervals. This Wikipedia page has info on the method, and the extent to which it is "exact": http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval.

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probplot doesn't have any confidence interval. If you are trying to fit your data to a probability distribution, the demo Fitting a Univariate Distribution Using Cumulative Probabilities might help you.

MATLAB: Confidence interval using binofit

The binofit function computes confidence intervals using the Clopper-Pearson method.

I believe what you're seeing is because the distribution is very coarse for N*p values on the order of 1. With N=1000 and p=1/500,

>> binocdf(4:5,1000,1/500)
ans =
    0.9475    0.9835

So in order for the confidence interval to have at least a 95% chance of including p=1/500, the intervals based on x=4 and x=5 would both have to include p. So the coverage probability will be over 98%.

Try increasing to N=100000 in your example and see if the results match.

Best Answer

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