ci.mean.diff: Confidence Interval for the Difference in Arithmetic Means

Description

This function computes a confidence interval for the difference in arithmetic means in a one-sample, two-sample and paired-sample design with known or unknown population standard deviation or population variance for one or more variables, optionally by a grouping and/or split variable.

Usage

ci.mean.diff(x, ...)
# S3 method for default
ci.mean.diff(x, y, mu = 0, sigma = NULL, sigma2 = NULL,
             var.equal = FALSE, 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 formula
ci.mean.diff(formula, data, sigma = NULL, sigma2 = NULL,
             var.equal = FALSE, 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, ...)

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

Arguments

x: a numeric vector of data values.
...: further arguments to be passed to or from methods.
y: a numeric vector of data values.
mu: a numeric value indicating the population mean under the null hypothesis. Note that the argument mu is only used when y = NULL.
sigma: a numeric vector indicating the population standard deviation(s) when computing confidence intervals for the difference in arithmetic means with known standard deviation(s). In case of independent samples, equal standard deviations are assumed when specifying one value for the argument sigma; when specifying two values for the argument sigma, unequal standard deviations are assumed. Note that either argument sigma or argument sigma2 is specified and it is only possible to specify one value (i.e., equal variance assumption) or two values (i.e., unequal variance assumption) for the argument sigma even though multiple variables are specified in x.
sigma2: a numeric vector indicating the population variance(s) when computing confidence intervals for the difference in arithmetic means with known variance(s). In case of independent samples, equal variances are assumed when specifying one value for the argument sigma2; when specifying two values for the argument sigma, unequal variances are assumed. Note that either argument sigma or argument sigma2 is specified and it is only possible to specify one value (i.e., equal variance assumption) or two values (i.e., unequal variance assumption) for the argument sigma even though multiple variables are specified in x.
var.equal: logical: if TRUE, the population variance in the independent samples are assumed to be equal.
paired: logical: if TRUE, confidence interval for the difference of arithmetic means 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
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 giving the data values and group a numeric variable, character variable or factor with two values or factor levels giving the corresponding groups.
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.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

References

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

Examples

Run this code

#----------------------------------------------------------------------------
# One-sample design

# Example 1a: Two-Sided 95% CI for 'mpg'
# population mean = 20
ci.mean.diff(mtcars$mpg, mu = 20)

# Example 1a: One-Sided 95% CI for 'mpg'
# population mean = 20
ci.mean.diff(mtcars$mpg, mu = 20, alternative = "greater")

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

# Example 2a: Two-Sided 95% CI for 'mpg' by 'vs'
# unknown population variances, unequal variance assumption
ci.mean.diff(mpg ~ vs, data = mtcars)

# Example 2b: Two-Sided 95% CI for 'mpg' by 'vs'
# unknown population variances, equal variance assumption
ci.mean.diff(mpg ~ vs, data = mtcars, var.equal = TRUE)

# Example 2c: Two-Sided 95% CI for 'mpg' by 'vs'
# known population standard deviations, equal standard deviation assumption
ci.mean.diff(mpg ~ vs, data = mtcars, sigma = 4)

# Example 2d: Two-Sided 95% CI for 'mpg' by 'vs'
# known population standard deviations, unequal standard deviation assumption
ci.mean.diff(mpg ~ vs, data = mtcars, sigma = c(4, 5))

# Example 2e: Two-Sided 95% CI for 'mpg', 'cyl', and 'disp' by 'vs'
# unknown population variances, unequal variance assumption
ci.mean.diff(cbind(mpg, cyl, disp) ~ vs, data = mtcars)

# Example 2f: Two-Sided 95% CI for 'mpg', 'cyl', and 'disp' by 'vs'
# unknown population variances, unequal variance assumption,
# analysis by am separately
ci.mean.diff(cbind(mpg, cyl, disp) ~ vs, data = mtcars, group = mtcars$am)

# Example 2g: Two-Sided 95% CI for 'mpg', 'cyl', and 'disp' by 'vs'
# unknown population variances, unequal variance assumption,
# split analysis by am
ci.mean.diff(cbind(mpg, cyl, disp) ~ vs, data = mtcars, split = mtcars$am)

# Example 2h: Two-Sided 95% CI for the mean difference between 'group1' and 'group2'
# unknown population variances, unequal variance assumption
group1 <- c(3, 1, 4, 2, 5, 3, 6, 7)
group2 <- c(5, 2, 4, 3, 1)

ci.mean.diff(group1, group2)

#----------------------------------------------------------------------------
# Paired-sample design

dat.p <- data.frame(pre = c(1, 3, 2, 5, 7, 6), post = c(2, 2, 1, 6, 8, 9),
                    group = c(1, 1, 1, 2, 2, 2))

# Example 3a: Two-Sided 95% CI for the mean difference in 'pre' and 'post'
# unknown poulation variance of difference scores
ci.mean.diff(dat.p$pre, dat.p$post, paired = TRUE)

# Example 21: Two-Sided 95% CI for the mean difference in 'pre' and 'post'
# unknown poulation variance of difference scores
# analysis by group separately
ci.mean.diff(dat.p$pre, dat.p$post, paired = TRUE, group = dat.p$group)

# Example 22: Two-Sided 95% CI for the mean difference in 'pre' and 'post'
# unknown poulation variance of difference scores
# analysis by group separately
ci.mean.diff(dat.p$pre, dat.p$post, paired = TRUE, split = dat.p$group)

# Example 23: Two-Sided 95% CI for the mean difference in 'pre' and 'post'
# known population standard deviation of difference scores
ci.mean.diff(dat.p$pre, dat.p$post, sigma = 2, paired = TRUE)

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