ci.var: Confidence Interval for the Variance

In misty: Miscellaneous Functions 'T. Yanagida'

Confidence Interval for the Variance

Description

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

Usage

ci.var(x, method = c("chisq", "bonett"),
       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, matrix or data frame with numeric variables, 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 "chisq", or "bonett" (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 confidence interval based on the chi-square distribution is computed by specifying method = "chisq", while the Bonett (2006) confidence interval is requested by specifying method = "bonett". By default, the Bonett confidence interval interval is computed which performs well under moderate departure from normality, while the confidence interval based on the chi-square distribution is highly sensitive to minor violations of the normality assumption and its performance does not improve with increasing sample size. Note that at least four valid observations are needed to compute the Bonett confidence interval.

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

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

Bonett, D. G. (2006). Approximate confidence interval for standard deviation of nonnormal distributions. Computational Statistics and Data Analysis, 50, 775-782. https://doi.org/10.1016/j.csda.2004.10.003

See Also

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

Examples

dat <- 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),
                  x1 = c(3, 1, 4, 2, 5, 3, 2, 3, 6, 4, 3, NA, 5, 3,
                         3, 2, 6, 3, 1, 4, 3, 5, 6, 7, 4, 3, 5, 4),
                  x2 = c(4, NA, 3, 6, 3, 7, 2, 7, 3, 3, 3, 1, 3, 6,
                         3, 5, 2, 6, 8, 3, 4, 5, 2, 1, 3, 1, 2, NA),
                  x3 = c(7, 8, 5, 6, 4, 2, 8, 3, 6, 1, 2, 5, 8, 6,
                         2, 5, 3, 1, 6, 4, 5, 5, 3, 6, 3, 2, 2, 4))

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

# Two-Sided 95% CI for x1 using chi square distribution
ci.var(dat$x1, method = "chisq")

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

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

# Two-Sided 95% CI, print results with 3 digits
ci.var(dat$x1, digits = 3)

# Two-Sided 95% CI for x1, convert value 4 to NA
ci.var(dat$x1, as.na = 4)

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

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

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