misty (version 0.3.2)

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

Description

This function computes a confidence interval for the difference in proportions from independent and paired samples for one or more variables, optionally by a grouping and/or split variable.

Usage

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

## Default S3 method:
# S3 method for default
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,
                               check = TRUE, output = TRUE, …)
## S3 method for class 'formula'
# S3 method for 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, 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.

check

logical: if TRUE, argument specification is checked.

output

logical: if TRUE, 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 of factor levels given 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.

Value

Returns an object of class misty.object, which is a list with following entries: function call (call), type of analysis type, list with the input specified in x, group, and split (data), specification of function arguments (args), and result table (result).

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).

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

# NOT RUN {
dat.bs <- 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))

#--------------------------------------
# Between-Subject Design

# Two-Sided 95% Confidence Interval for x1 by group1
ci.prop.diff(x1 ~ group1, data = dat.bs)

# Two-Sided 95% Confidence Interval for x1 by group1
# Wald confidence interval
ci.prop.diff(x1 ~ group1, data = dat.bs, method = "wald")

# One-Sided 95% Confidence Interval for x1 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(x1 ~ group1, data = dat.bs, alternative = "less")

# Two-Sided 95% Confidence Interval for x1 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(x1 ~ group1, data = dat.bs, conf.level = 0.99)

# Two-Sided 95% Confidence Interval for y1 by group1
# # Newcombes Hybrid Score interval, print results with 3 digits
ci.prop.diff(x1 ~ group1, data = dat.bs, digits = 3)

# Two-Sided 95% Confidence Interval for y1 by group1
# # Newcombes Hybrid Score interval, convert value 0 to NA
ci.prop.diff(x1 ~ group1, data = dat.bs, as.na = 0)

# Two-Sided 95% Confidence Interval for y1, y2, and y3 by group1
# Newcombes Hybrid Score interval
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat.bs)

# Two-Sided 95% Confidence Interval 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 = dat.bs, na.omit = TRUE)

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

# Two-Sided 95% Confidence Interval 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 = dat.bs, group = dat.bs$group2,
             sort.var = TRUE)

# Two-Sided 95% Confidence Interval for y1, y2, and y3 by group1
# split analysis by group2
ci.prop.diff(cbind(x1, x2, x3) ~ group1, data = dat.bs, split = dat.bs$group2)

# Two-Sided 95% Confidence Interval 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 = dat.bs,
             group = dat.bs$group2, split = dat.bs$group3)

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

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

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

#--------------------------------------
# Within-Subject Design
dat.ws <- data.frame(pre = c(0, 1, 1, 0, 1),
                     post = c(1, 1, 0, 1, 1), stringsAsFactors = FALSE)

# Two-Sided 95% Confidence Interval for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat.ws$pre, dat.ws$post, paired = TRUE)

# Two-Sided 95% Confidence Interval for the mean difference in x1 and x2
# Wald confidence interval
ci.prop.diff(dat.ws$pre, dat.ws$post, method = "wald", paired = TRUE)

# One-Sided 95% Confidence Interval for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat.ws$pre, dat.ws$post, alternative = "less", paired = TRUE)

# Two-Sided 95% Confidence Interval for the mean difference in x1 and x2
# Newcombes Hybrid Score interval
ci.prop.diff(dat.ws$pre, dat.ws$post, conf.level = 0.99, paired = TRUE)

# Two-Sided 95% Confidence Interval for for the mean difference in x1 and x2
# Newcombes Hybrid Score interval, print results with 3 digits
ci.prop.diff(dat.ws$pre, dat.ws$post, paired = TRUE, digits = 3)
# }