test.levene: 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 = FALSE, 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,
            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
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

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 (default), null and alternative hypothesis are shown on the console.
descript: logical: if TRUE (default), 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.
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.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

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.

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.

Examples

Run this code

# Example 1: Levene's test based on the median
test.levene(mpg ~ gear, data = mtcars)

# Example 2: Levene's test based on the arithmetic mean
test.levene(mpg ~ gear, data = mtcars, method = "mean")

if (FALSE) {
# Example 3: Write results into a text file
test.levene(mpg ~ gear, data = mtcars, write = "Levene.txt")}

# Example 4: Levene's test based on the median,
# plot results
test.levene(mpg ~ gear, data = mtcars, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

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

# Levene's test based on the median
# extract plot
p <- test.levene(mpg ~ gear, data = mtcars, output = FALSE)$plot
p

# Example 5: Levene's test based on the median
# Draw violin and boxplots in line with the default setting of test.levene()

# Extract data
plotdat <- test.levene(mpg ~ gear, data = mtcars, output = FALSE)$data

# Draw violin and boxplots
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")

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