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 error bars for difference-adjusted confidence intervals with jittered data points.

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,
           plot = FALSE, point.size = 4, adjust = TRUE, error.width = 0.1,
           xlab = NULL, ylab = NULL, ylim = NULL, breaks = ggplot2::waiver(),
           jitter = TRUE, jitter.size = 1.25, jitter.width = 0.05,
           jitter.height = 0, jitter.alpha = 0.1, title = "",
           subtitle = "Confidence Interval", digits = 2, p.digits = 4,
           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
sample: type of sample, i.e., two- or multiple sample
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: 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.
plot: logical: if TRUE, a plot showing error bars for confidence intervals is drawn.
point.size: a numeric value indicating the size aesthetic for the point representing the mean value.
adjust: logical: if TRUE (default), difference-adjustment for the confidence intervals is applied.
error.width: a numeric value indicating the horizontal bar width of the error bar.
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.
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.
title: a character string specifying the text for the title for the plot.
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.
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.
...: further arguments to be passed to or from methods.
subtitle: a character string specifying the text for the subtitle for the plot.

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