ci.prop.diff: Confidence Interval for the Difference in Proportions

In misty: Miscellaneous Functions 'T. Yanagida'

Confidence Interval for the Difference in Proportions

Description

This function computes a confidence interval for the difference in proportions in a two-sample and paired-sample design for one or more variables, optionally by a grouping and/or split variable.

Usage

ci.prop.diff(x, ...)

## Default S3 method:
ci.prop.diff(x, y, method = c("wald", "newcombe"), paired = FALSE,
             alternative = c("two.sided", "less", "greater"), conf.level = 0.95,
             group = NULL, split = NULL, sort.var = FALSE, digits = 2,
             as.na = NULL, write = NULL, append = TRUE,
             check = TRUE, output = TRUE, ...)

## S3 method for class 'formula'
ci.prop.diff(formula, data, method = c("wald", "newcombe"),
             alternative = c("two.sided", "less", "greater"), conf.level = 0.95,
             group = NULL, split = NULL, sort.var = FALSE, na.omit = FALSE,
             digits = 2, as.na = NULL, write = NULL, append = TRUE,
             check = TRUE, output = TRUE, ...)

Arguments

x	a numeric vector with 0 and 1 values.
...	further arguments to be passed to or from methods.
y	a numeric vector with 0 and 1 values.
method	a character string specifying the method for computing the confidence interval, must be one of "wald", or "newcombe" (default).
paired	logical: if TRUE, confidence interval for the difference of proportions in paired samples is computed.
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. Note that a grouping variable can only be used when computing confidence intervals with unknown population standard deviation and population variance.
split	a numeric vector, character vector or factor as split variable. Note that a split variable can only be used when computing confidence intervals with unknown population standard deviation and population variance.
sort.var	logical: if TRUE, output table is sorted by variables when specifying group.
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.
write	a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.
append	logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check	logical: if TRUE (default), argument specification is checked.
output	logical: if TRUE (default), output is shown on the console.
formula	a formula of the form y ~ group for one outcome variable or cbind(y1, y2, y3) ~ group for more than one outcome variable where y is a numeric variable with 0 and 1 values and group a numeric variable, character variable or factor with two values or factor levels giving the corresponding group.
data	a matrix or data frame containing the variables in the formula formula.
na.omit	logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion) when specifying more than one outcome variable.

Details

The Wald confidence interval which is based on the normal approximation to the binomial distribution are computed by specifying method = "wald", while the Newcombe Hybrid Score interval (Newcombe, 1998a; Newcombe, 1998b) is requested by specifying method = "newcombe". By default, Newcombe Hybrid Score interval is computed which have been shown to be reliable in small samples (less than n = 30 in each sample) as well as moderate to larger samples(n > 30 in each sample) and with proportions close to 0 or 1, while the Wald confidence intervals does not perform well unless the sample size is large (Fagerland, Lydersen & Laake, 2011).

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

Fagerland, M. W., Lydersen S., & Laake, P. (2011) Recommended confidence intervals for two independent binomial proportions. Statistical Methods in Medical Research, 24, 224-254.

Newcombe, R. G. (1998a). Interval estimation for the difference between independent proportions: Comparison of eleven methods. Statistics in Medicine, 17, 873-890.

Newcombe, R. G. (1998b). Improved confidence intervals for the difference between binomial proportions based on paired data. Statistics in Medicine, 17, 2635-2650.

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

See Also

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

Examples

dat1 <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
                              1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2),
                   group2 = c(1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2,
                              1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2),
                   group3 = c(1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
                              1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2),
                   x1 = c(0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, NA, 0, 0,
                          1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0),
                   x2 = c(0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1,
                          1, 0, 1, 0, 1, 1, 1, NA, 1, 0, 0, 1, 1, 1),
                   x3 = c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0,
                          1, 0, 1, 1, 0, 1, 1, 1, 0, 1, NA, 1, 0, 1))

#-------------------------------------------------------------------------------
# Two-sample design

# Example 1: Two-Sided 95% CI for x1 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(x1 ~ group1, data = dat1)

# Example 2: Two-Sided 95% CI for x1 by group1
# Wald CI
ci.prop.diff(x1 ~ group1, data = dat1, method = "wald")

# Example 3: One-Sided 95% CI for x1 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(x1 ~ group1, data = dat1, alternative = "less")

# Example 4: Two-Sided 99% CI for x1 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(x1 ~ group1, data = dat1, conf.level = 0.99)

# Example 5: Two-Sided 95% CI for y1 by group1
# Newcombes Hybrid Score interval, print results with 3 digits
ci.prop.diff(x1 ~ group1, data = dat1, digits = 3)

# Example 6: Two-Sided 95% CI for y1 by group1
# Newcombes Hybrid Score interval, convert value 0 to NA
ci.prop.diff(x1 ~ group1, data = dat1, as.na = 0)

# Example 7: Two-Sided 95% CI for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1)

# Example 8: Two-Sided 95% CI for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval, listwise deletion for missing data
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1, na.omit = TRUE)

# Example 9: Two-Sided 95% CI for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval, analysis by group2 separately
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2)

# Example 10: Two-Sided 95% CI for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval, analysis by group2 separately, sort by variables
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2,
             sort.var = TRUE)

# Example 11: Two-Sided 95% CI for y1, y2, and y3 by group1
# split analysis by group2
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1, split = dat1$group2)

# Example 12: Two-Sided 95% CI for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval, analysis by group2 separately, split analysis by group3
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat1,
             group = dat1$group2, split = dat1$group3)

#-----------------

group1 <- c(0, 1, 1, 0, 0, 1, 0, 1)
group2 <- c(1, 1, 1, 0, 0)

# Example 13: Two-Sided 95% CI for the mean difference between group1 amd group2
# Newcombes Hybrid Score interval
ci.prop.diff(group1, group2)

#-------------------------------------------------------------------------------
# Paires-sample design

dat2 <- data.frame(pre = c(0, 1, 1, 0, 1),
                   post = c(1, 1, 0, 1, 1))

# Example 14: Two-Sided 95% CI for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat2$pre, dat2$post, paired = TRUE)

# Example 15: Two-Sided 95% CI for the mean difference in x1 and x2
# Wald CI
ci.prop.diff(dat2$pre, dat2$post, method = "wald", paired = TRUE)

# Example 16: One-Sided 95% CI for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat2$pre, dat2$post, alternative = "less", paired = TRUE)

# Example 17: Two-Sided 99% CI for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat2$pre, dat2$post, conf.level = 0.99, paired = TRUE)

# Example 18: Two-Sided 95% CI for for the mean difference in x1 and x2
# Newcombes Hybrid Score interval, print results with 3 digits
ci.prop.diff(dat2$pre, dat2$post, paired = TRUE, digits = 3)

misty documentation built on Oct. 24, 2024, 5:10 p.m.