Calculate confidence limits for a sample proportion

Input Values

  

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.

Sample size :
Number positive :
Confidence level:
Confidence interval method:
Decimal places in answer :

Confidence limits for a proportion

Analysed: Sat Jan 20, 2018 @ 01:47

Inputs

Sample size 9210
Number positive 27
Confidence level 0.99
CI method All


Results

 Number positive   Sample size   Proportion/Prevalence   Lower 99% CL  Upper 99% CL 
Normal approx. 27 9210 0.002932 0.001480 0.004383
Clopper-Pearson exact 27 9210 0.002932 0.001683 0.004719
Wilson 27 9210 0.002932 0.001795 0.004784
Jeffreys 27 9210 0.002932 0.001724 0.004651
Agresti-Coull 27 9210 0.002932 0.001753 0.004826


CI plot

Download excel file of results

Download

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