test.levene: Levene's Test for Homogeneity of Variance

In misty: Miscellaneous Functions 'T. Yanagida'

Levene's Test for Homogeneity of Variance

Description

This function performs Levene's test for homogeneity of variance across two or more independent groups.

Usage

test.levene(formula, data, method = c("median", "mean"), conf.level = 0.95,
            hypo = TRUE, descript = TRUE, plot = TRUE, violin.alpha = 0.3,
            violin.trim = FALSE, box = TRUE, box.alpha = 0.2, box.width = 0.2,
            jitter = TRUE, jitter.size = 1.25, jitter.width = 0.05,
            jitter.height = 0, jitter.alpha = 0.2, gray = FALSE,
            start = 0.9, end = 0.4, color = NULL, xlab = NULL, ylab = NULL,
            ylim = NULL, breaks = ggplot2::waiver(), title = "",
            subtitle = "", digits = 2, p.digits = 3, as.na = NULL,
            check = TRUE, output = TRUE)

Arguments

formula	a formula of the form y ~ group where y is a numeric variable giving the data values and group a numeric variable, character variable or factor with two or more than two values or factor levels giving the corresponding groups.
data	a matrix or data frame containing the variables in the formula formula.
method	a character string specifying the method to compute the center of each group, i.e. method = "median" (default) to compute the Levene's test based on the median (aka Brown-Forsythe test) or method = "mean" to compute the Levene's test based on the arithmetic mean.
conf.level	a numeric value between 0 and 1 indicating the confidence level of the interval.
hypo	logical: if TRUE, null and alternative hypothesis are shown on the console.
descript	logical: if TRUE, descriptive statistics are shown on the console.
plot	logical: if TRUE, a plot showing violin plots with boxplots is drawn.
violin.alpha	a numeric value indicating the opacity of the violins.
violin.trim	logical: if TRUE, the tails of the violins to the range of the data is trimmed.
box	logical: if TRUE (default), boxplots are drawn.
box.alpha	a numeric value indicating the opacity of the boxplots.
box.width	a numeric value indicating the width of the boxplots.
jitter	logical: if TRUE (default), jittered data points are drawn.
jitter.size	a numeric value indicating the size aesthetic for the jittered data points.
jitter.width	a numeric value indicating the amount of horizontal jitter.
jitter.height	a numeric value indicating the amount of vertical jitter.
jitter.alpha	a numeric value indicating the opacity of the jittered data points.
gray	logical: if TRUE, the plot is drawn in gray scale.
start	a numeric value between 0 and 1, graphical parameter to specify the gray value at the low end of the palette.
end	a numeric value between 0 and 1, graphical parameter to specify the gray value at the high end of the palette.
color	a character vector, indicating the color of the violins and the boxes. By default, default ggplot2 colors are used.
xlab	a character string specifying the labels for the x-axis.
ylab	a character string specifying the labels for the y-axis.
ylim	a numeric vector of length two specifying limits of the limits of the y-axis.
breaks	a numeric vector specifying the points at which tick-marks are drawn at the y-axis.
title	a character string specifying the text for the title for the plot.
subtitle	a character string specifying the text for the subtitle for the plot.
digits	an integer value indicating the number of decimal places to be used for displaying results.
p.digits	an integer value indicating the number of decimal places to be used for displaying the p-value.
as.na	a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis.
check	logical: if TRUE, argument specification is checked.
output	logical: if TRUE, output is shown.

Details

Levene's test is equivalent to a one-way analysis of variance (ANOVA) with the absolute deviations of observations from the mean of each group as dependent variable (center = "mean"). Brown and Forsythe (1974) modified the Levene's test by using the absolute deviations of observations from the median (center = "median"). By default, the Levene's test uses the absolute deviations of observations from the median.

Value

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

call	function call
type	type of analysis
formula	formula of the current analysis
data	data frame specified in data
plot	ggplot2 object for plotting the results
args	specification of function arguments
result	list with result tables, i.e., descript for descriptive statistics and test for the ANOVA table

Author(s)

Takuya Yanagida [e-mail]

References

Brown, M. B., & Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69, 364-367.

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

See Also

aov.b, test.t, test.welch

Examples

dat <- data.frame(y = c(2, 3, 4, 5, 5, 7, 8, 4, 5, 2, 4, 3),
                  group = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3))

# Levene's test based on the median with 95% confidence interval
test.levene(y ~ group, data = dat)

# Levene's test based on the arithmetic mean  with 95% confidence interval
test.levene(y ~ group, data = dat, method = "mean")

# Levene's test based on the median with 99% confidence interval
test.levene(y ~ group, data = dat, conf.level = 0.99)

## Not run: 
# Levene's test based on the median with 95% confidence interval
# plot results
test.levene(y ~ group, data = dat, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

# Save plot, ggsave() from the ggplot2 package
ggsave("Levene-test.png", dpi = 600, width = 5, height = 6)

# Levene's test based on the median with 95% confidence interval
# extract plot
p <- test.levene(y ~ group, data = dat, output = FALSE)$plot
p

# Extract data
plotdat <- test.levene(y ~ group, data = dat, output = FALSE)$data

# Draw violin and boxplots in line with the default setting of test.levene()
ggplot(plotdat, aes(group, y, fill = group)) +
  geom_violin(alpha = 0.3, trim = FALSE) +
  geom_boxplot(alpha = 0.2, width = 0.2) +
  geom_jitter(alpha = 0.2, width = 0.05, size = 1.25) +
  theme_bw() + guides(fill = "none")

## End(Not run)

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