ci.prop: Confidence Interval for Proportions

In misty: Miscellaneous Functions 'T. Yanagida'

Confidence Interval for Proportions

Description

This function computes a confidence interval for proportions for one or more variables, optionally by a grouping and/or split variable.

Usage

ci.prop(x, method = c("wald", "wilson"),
        alternative = c("two.sided", "less", "greater"), conf.level = 0.95,
        group = NULL, split = NULL, sort.var = FALSE, na.omit = FALSE,
        digits = 3, as.na = NULL, check = TRUE, output = TRUE)

Arguments

x	a numeric vector, matrix or data frame with numeric variables with 0 and 1 values, i.e., factors and character variables are excluded from x before conducting the analysis.
method	a character string specifying the method for computing the confidence interval, must be one of "wald", or "wilson" (default).
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
conf.level	a numeric value between 0 and 1 indicating the confidence level of the interval.
group	a numeric vector, character vector or factor as grouping variable.
split	a numeric vector, character vector or factor as split variable.
sort.var	logical: if TRUE, output table is sorted by variables when specifying group.
na.omit	logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion) when specifying more than one outcome variable.
digits	an integer value indicating the number of decimal places to be used.
as.na	a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to x, but not to group or split.
check	logical: if TRUE, argument specification is checked.
output	logical: if TRUE, output is shown on the console.

Details

The Wald confidence interval which is based on the normal approximation to the binomial distribution are computed by specifying method = "wald", while the Wilson (1927) confidence interval (aka Wilson score interval) is requested by specifying method = "wilson". By default, Wilson confidence interval is computed which have been shown to be reliable in small samples of n = 40 or less, and larger samples of n > 40 (Brown, Cai & DasGupta, 2001), while the Wald confidence intervals is inadequate in small samples and when p is near 0 or 1 (Agresti & Coull, 1998).

Value

Returns an object of class misty.object, which is a list with following entries:

call	function call
type	type of analysis
data	list with the input specified in x, group, and split
args	specification of function arguments
result	result table

Author(s)

Takuya Yanagida [e-mail]

References

Agresti, A. & Coull, B.A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. American Statistician, 52, 119-126.

Brown, L. D., Cai, T. T., & DasGupta, A., (2001). Interval estimation for a binomial proportion. Statistical Science, 16, 101-133.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.

Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22, 209-212.

See Also

ci.mean, ci.mean.diff, ci.median, ci.prop.diff, ci.var, ci.sd, descript

Examples

dat <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2),
                  group2 = c(1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2),
                  x1 = c(0, 1, 0, 0, 1, 1, 0, 1, NA, 0, 1, 0),
                  x2 = c(0, NA, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1),
                  x3 = c(1, 1, 1, 0, 1, NA, 1, NA, 0, 0, 0, 1))

# Two-Sided 95% CI for x1
ci.prop(dat$x1)

# Two-Sided 95% CI for x1 using Wald method
ci.prop(dat$x1, method = "wald")

# One-Sided 95% CI for x1
ci.prop(dat$x1, alternative = "less")

# Two-Sided 99% CI
ci.prop(dat$x1, conf.level = 0.99)

# Two-Sided 95% CI, print results with 4 digits
ci.prop(dat$x1, digits = 4)

# Two-Sided 95% CI for x1, x2, and x3,
# listwise deletion for missing data
ci.prop(dat[, c("x1", "x2", "x3")], na.omit = TRUE)

# Two-Sided 95% CI for x1, x2, and x3,
# analysis by group1 separately
ci.prop(dat[, c("x1", "x2", "x3")], group = dat$group1)

# Two-Sided 95% CI for x1, x2, and x3,
# analysis by group1 separately, sort by variables
ci.prop(dat[, c("x1", "x2", "x3")], group = dat$group1, sort.var = TRUE)

# Two-Sided 95% CI for x1, x2, and x3,
# split analysis by group1
ci.prop(dat[, c("x1", "x2", "x3")], split = dat$group1)

# Two-Sided 95% CI for x1, x2, and x3,
# analysis by group1 separately, split analysis by group2
ci.prop(dat[, c("x1", "x2", "x3")],
        group = dat$group1, split = dat$group2)

misty documentation built on Nov. 15, 2023, 1:06 a.m.