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Summarise categorical or continuous data

Calculate confidence limits for a sample proportion

This utility calculates confidence limits for a population proportion for a specified level of confidence.

Inputs are the sample size and number of positive results, the desired level of confidence in the estimate and the number of decimal places required in the answer.

The program outputs the estimated proportion plus upper and lower limits of the specified confidence interval, using 5 alternative calculation methods decribed and discussed in Brown, LD, Cat, TT and DasGupta, A (2001). Interval Estimation for a proportion. Statistical Science 16:101-133:

  1. Asymptotic (Wald) method based on a normal approximation;
  2. Binomial (Clopper-Pearson) "exact" method based on the beta distribution;
  3. "Wilson" Score interval;
  4. "Agresti-Coull" (adjusted Wald) interval; and
  5. "Jeffreys" interval.

The Wald interval often has inadequate coverage, particularly for small n and values of p close to 0 or 1. Conversely, the Clopper-Pearson Exact method is very conservative and tends to produce wider intervals than necessary. Brown et al. recommends the Wilson or Jeffreys methods for small n and Agresti-Coull, Wilson, or Jeffreys, for larger n as providing more reliable coverage than the alternatives. Also note that the point estimate for the Agresti-Coull method is slightly larger than for other methods because of the way this interval is calculated.