Confidence Intervals for Difference of Two Binomial Proportions
This function can be used to compute confidence intervals for the difference of two binomial proportions. It includes methods for the independent and the paired case.
binomDiffCI(a, b, c, d, conf.level = 0.95, paired = FALSE, method = ifelse(paired, "wilson-cc", "wilson"), R = 9999, bootci.type = "all", alternative = c("two.sided", "less", "greater"), ...)
a: independent: number of successes of group 1; paired: number of cases with success in group 1 and 2.b: independent: number of successes of group 2; paired: number of cases with success in group 1 and failure in group 2.c: independent: number of failures of group 1; paired: number of cases with failure in group 1 and success in group 2.d: independent: number of failures of group 2; paired: number of cases with failure in group 1 and 2.conf.level: confidence levelpaired: a logical value indicating whether the two groups are paired.method: character string specifing which method to use; see details.R: number of bootstrap replicates.bootci.type: type of bootstrap interval; see boot.ci.alternative: a character string specifying one- or two-sided confidence intervals. Must be one of "two.sided" (default), "greater" or "less" (one-sided intervals). You can specify just the initial letter....: further arguments passed to function boot, e.g. for parallel computing.The Wald intervals (independent and paired) are obtained by applying the normal approximation. There are also Wald intervals with continuity correction.
The Wilson intervals are recommended by Newcombe and Altman (2000); see Chapter 6 of Altman et al. (2000). In the paired case, the continuity corrected version of the interval is recommended. The intervals are proposed in Newcombe (1998a) and Newcombe (1998b).
The bootstrap interval is calculated by using function boot.ci.
A list with class "confint" containing the following components: - estimate: the estimated probability of success.
D. Altman, D. Machin, T. Bryant, M. Gardner (eds). Statistics with Confidence: Confidence Intervals and Statistical Guidelines, 2nd edition. John Wiley and Sons 2000.
R.G. Newcombe (1998a). Interval estimation for the difference between independent proportions: comparison of eleven methods. Stat Med, 17 (8), 873-890.
R.G. Newcombe (1998b). Improved confidence intervals for the difference between binomial proportions based on paired data. Stat Med, 17 (22), 2635-2650.
Matthias Kohl Matthias.Kohl@stamats.de
prop.test, boot.ci
## Example 1: Altman et al. (2000, p. 49) ## the confidence interval computed by prop.test prop.test(c(63, 38), c(93, 92))$conf.int ## wald / simple asymptotic interval binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "wald") ## wald / simple asymptotic interval with continuity correction binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "wald-cc") ## wilson binomDiffCI(a = 63, b = 38, c = 30, d = 54) ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 999) ## one-sided binomDiffCI(a = 63, b = 38, c = 30, d = 54, alternative = "greater") ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 999, bootci.type = "bca", alternative = "greater") ## Example 2: Altman et al. (2000, p. 50) ## the confidence interval computed by prop.test prop.test(c(5, 0), c(56, 29))$conf.int ## wald / simple asymptotic interval binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "wald") ## wald / simple asymptotic interval with continuity correction binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "wald-cc") ## wilson binomDiffCI(a = 5, b = 0, c = 51, d = 29) ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "boot", R = 999) ## one-sided binomDiffCI(a = 5, b = 0, c = 51, d = 29, alternative = "less") ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "boot", R = 999, bootci.type = "perc", alternative = "less") ## Example 3: Altman et al. (2000, p. 51) ## wald / simple asymptotic interval binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wald") ## wald / simple asymptotic interval with continuity correction binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wald-cc") ## wilson binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wilson") ## wilson with continuity correction binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE) ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "boot", R = 999) ## Example 4: Altman et al. (2000, p. 51) ## wald / simple asymptotic interval binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wald") ## wald / simple asymptotic interval with continuity correction binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wald-cc") ## wilson binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wilson") ## wilson with continuity correction binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE) ## bootstrap intervals (R = 999 to reduce computation time for R checks) binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "boot", bootci.type = c("norm", "basic", "stud", "perc"), R = 999) ## type = "bca" gives error binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 9999, parallel = "multicore", ncpus = 2)