test.welch: Welch's Test

Description

This function performs Welch's two-sample t-test and Welch's ANOVA including Games-Howell post hoc test for multiple comparison and provides descriptive statistics, effect size measures, and a plot showing bars representing means for each group and error bars for difference-adjusted confidence intervals.

Usage

test.welch(formula, data, alternative = c("two.sided", "less", "greater"),
           posthoc = FALSE, conf.level = 0.95, hypo = TRUE, descript = TRUE,
           effsize = FALSE, weighted = FALSE, ref = NULL, correct = FALSE,
           digits = 2, p.digits = 3, as.na = NULL, plot = FALSE, bar = TRUE,
           point = FALSE, ci = TRUE, jitter = FALSE, adjust = TRUE,
           point.size = 3, errorbar.width = 0.1, jitter.size = 1.25,
           jitter.width = 0.05, jitter.height = 0, jitter.alpha = 0.1,
           xlab = NULL, ylab = "y", ylim = NULL, ybreaks = ggplot2::waiver(),
           title = NULL, subtitle = "Confidence Interval", filename = NULL,
           width = NA, height = NA, units = c("in", "cm", "mm", "px"),
           dpi = 600, 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
sample: type of sample, i.e., one-, two-, or paired sample
data: data frame with the outcome and grouping variable
formula: formula
args: specification of function arguments
plot: ggplot2 object for plotting the results
result: result 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.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". Note that this argument is only used when conducting Welch's two-sample t-test.
posthoc: logical: if TRUE, Games-Howell post hoc test for multiple comparison is conducted when performing Welch's ANOVA.
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.
effsize: logical: if TRUE, effect size measure Cohen's d for Welch's two-sample t-test (see cohens.d), \(\eta^2\) and \(\omega^2\) for Welch's ANOVA and Cohen's d for the post hoc tests are shown on the console.
weighted: logical: if TRUE, the weighted pooled standard deviation is used to compute Cohen's d.
ref: a numeric value or character string indicating the reference group. The standard deviation of the reference group is used to standardized the mean difference to compute Cohen's d.
correct: logical: if TRUE, correction factor to remove positive bias in small samples is used.
digits: an integer value indicating the number of decimal places to be used for displaying descriptive statistics and confidence interval.
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.
plot: logical: if TRUE, a plot showing error bars for confidence intervals is drawn.
bar: logical: if TRUE (default), bars representing means for each groups are drawn.
point: logical: if TRUE, points representing means for each groups are drawn.
ci: logical: if TRUE (default), error bars representing confidence intervals are drawn.
jitter: logical: if TRUE, jittered data points are drawn.
adjust: logical: if TRUE (default), difference-adjustment for the confidence intervals is applied.
point.size: a numeric value indicating the size aesthetic for the point representing the mean value.
errorbar.width: a numeric value indicating the horizontal bar width of the error bar.
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 between 0 and 1 for specifying the alpha argument in the geom_jitter function for controlling the opacity of the jittered data points.
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.
ybreaks: 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 of the plot.
subtitle: a character string specifying the text for the subtitle of the plot.
filename: a character string indicating the filename argument including the file extension in the ggsave function. Note that one of ".eps", ".ps", ".tex", ".pdf" (default), ".jpeg", ".tiff", ".png", ".bmp", ".svg" or ".wmf" needs to be specified as file extension in the filename argument. Note that plots can only be saved when plot = TRUE.
width: a numeric value indicating the width argument (default is the size of the current graphics device) in the ggsave function.
height: a numeric value indicating the height argument (default is the size of the current graphics device) in the ggsave function.
units: a character string indicating the units argument (default is in) in the ggsave function.
dpi: a numeric value indicating the dpi argument (default is 600) in the ggsave function.
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.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

Effect Size Measure: By default, Cohen's d based on the non-weighted standard deviation (i.e., weighted = FALSE) which does not assume homogeneity of variance is computed (see Delacre et al., 2021) when requesting an effect size measure (i.e., effsize = TRUE). Cohen's d based on the pooled standard deviation assuming equality of variances between groups can be requested by specifying weighted = TRUE.

References

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

Delacre, M., Lakens, D., Ley, C., Liu, L., & Leys, C. (2021). Why Hedges' g*s based on the non-pooled standard deviation should be reported with Welch's t-test. https://doi.org/10.31234/osf.io/tu6mp

Examples

Run this code

#----------------------------------------------------------------------------
# Two-Sample Design

# Example 1a: Two-sided two-sample Welch-test
test.welch(mpg ~ vs, data = mtcars)

# Example 1b: One-sided two-sample Welch-test
test.welch(mpg ~ vs, data = mtcars, alternative = "greater")

# Example 1c: Two-sided two-sample Welch-test, print Cohen's d
test.welch(mpg ~ vs, data = mtcars, effsize = TRUE)

# Example 1d: Two-sided two-sample Welch-test, plot results
test.welch(mpg ~ vs, data = mtcars, plot = TRUE)

#----------------------------------------------------------------------------
# Multiple-Sample Design

# Example 2a: Welch's ANOVA
test.welch(mpg ~ gear, data = mtcars)

# Example 2b: Welch's ANOVA, Games-Howell post hoc test
test.welch(mpg ~ gear, data = mtcars, posthoc = TRUE)

# Example 2c: Welch's ANOVA, print eta-squared and omega-squared
test.welch(mpg ~ gear, data = mtcars, effsize = TRUE)

# Example 2d: Welch's ANOVA, plot results
test.welch(mpg ~ gear, data = mtcars, plot = TRUE)

if (FALSE) {
# Example 2e: Welch's ANOVA, save plot
test.welch(mpg ~ gear, data = mtcars, plot = TRUE,
           filename = "Multiple-sample_Welch-test.png", width = 6, height = 5)
}

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