
PORPORTION CONFIDENCE LIMITSName:
In Dataplot, you define a success by entering the command
before entering the PROPORTION CONFIDENCE LIMITS command. That is, you specify the lower and upper values that define a success. Then the estimate for the proportion of successes is simply the number of points in the success region divided by the total number of points. In most applications, successes are defined by 1's and failures by 0's. The default limits are 0.5 and 1.5, so if your data is defined by 0 and 1 values the ANOP LIMITS command can be omitted. Several methods have been proposed for the confidence limits for a binomial proportion. The following methods are currently supported in Dataplot
NORMAL/EXACT> The default is the Wilson method. The Brown, Cai, and DasGupta paper studied the coverage properties of various methods. They specifically recommend the Wilson, the adjusted Wald, and the Jeffreys method as having the best coverage properties. Specifically, they recommend the Wilson and Jeffreys methods for n ≤ 40. For n > 40, these three methods have comparable performance. Although the normal approximation and exact binomial methods are not typically recommended, Dataplot provides them since they are still used in practice.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
PROPORTION CONFIDENCE LIMITS Y
ANOP LIMITS 0.80 1.0
with BINPPF denoting the percent point function of the binomial distribution.
Brown, L. D. Cai, T. T. and DasGupta, A. (2001), "Interval estimation for a binomial proportion," Statistical Science, 16(2), 101133. Wilson (1927), "Probable inference, the law of succession, and statistical inference," Journal of the American Statistical Association, Vol. 22, pp. 209212. Snedecor and Cochran, 1989, "Statistical Methods," Eigth Edition, Iowa State University Press, pp. 121124.
2017/11: Change method for determining the confidence interval . Create a binary variable with 30 rows . with 8 successes. . let n = 30 let nsuc = 8 let y = 0 for i = 1 1 n let y = 1 for i = 1 1 nsuc . . Now do proportions confidence interval . set write decimals 6 set binomial method wilson proportion confidence interval y set binomial method adjusted wald proportion confidence interval y set binomial method jeffreys proportion confidence interval y set binomial method exact proportion confidence interval y set binomial method normal proportion confidence interval yThis command generated the following output: TwoSided Confidence Limits for a Proportion (Wilson Method) Response Variable: Y Sample: Number of Observations: 30 Number of Successes: 8 Proportion of Successes: 0.266667 Standard Error: 0.080737  Confidence Lower Upper Value (%) Limit Limit  50.000 0.215992 0.324313 75.000 0.185098 0.367950 90.000 0.157323 0.414615 95.000 0.141827 0.444480 99.000 0.116046 0.501805 99.900 0.092558 0.564537 99.990 0.077142 0.612690 99.999 0.066181 0.651056 TwoSided Confidence Limits for a Proportion (Adjusted Wald Method) Response Variable: Y Sample: Number of Observations: 30 Number of Successes: 8 Proportion of Successes: 0.266667 Standard Error: 0.080737  Confidence Lower Upper Value (%) Limit Limit  50.000 0.217582 0.326788 75.000 0.188962 0.376021 90.000 0.163909 0.432706 95.000 0.150238 0.471347 99.000 0.128339 0.551032 99.900 0.110551 0.646995 99.990 0.101710 0.727092 99.999 0.098343 0.794898 TwoSided Confidence Limits for a Proportion (Bayesian with Jeffreys Prior Method) Response Variable: Y Sample: Number of Observations: 30 Number of Successes: 8 Proportion of Successes: 0.266667 Standard Error: 0.080737  Confidence Lower Upper Value (%) Limit Limit  50.000 0.217637 0.325518 75.000 0.184464 0.367317 90.000 0.153145 0.412052 95.000 0.134941 0.440996 99.000 0.103386 0.497902 99.900 0.073387 0.563271 99.990 0.053383 0.616478 99.999 0.039406 0.661171 TwoSided Confidence Limits for a Proportion (Exact Binomial Method) Response Variable: Y Sample: Number of Observations: 30 Number of Successes: 8 Proportion of Successes: 0.266667 Standard Error: 0.080737  Confidence Lower Upper Value (%) Limit Limit  50.000 0.202418 0.342833 75.000 0.170298 0.385007 90.000 0.140185 0.429934 95.000 0.122795 0.458894 99.000 0.092892 0.515598 99.900 0.064818 0.580375 99.990 0.046392 0.632814 99.999 0.033699 0.676670 TwoSided Confidence Limits for a Proportion (Normal Approximation Method) Response Variable: Y Sample: Number of Observations: 30 Number of Successes: 8 Proportion of Successes: 0.266667 Standard Error: 0.080737  Confidence Lower Upper Value (%) Limit Limit  50.000 0.212210 0.321123 75.000 0.173791 0.359543 90.000 0.133866 0.399468 95.000 0.108424 0.424909 99.000 0.058701 0.474632 99.900 0.000998 0.532335 99.990 0.000000 0.580783 99.999 0.000000 0.623298  
Date created: 06/05/2001 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 