misty (version 0.5.0)

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 = TRUE, 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, 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 code"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, null and alternative hypothesis are shown on the console.

descript

logical: if TRUE, 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.

check

logical: if TRUE, argument specification is checked.

output

logical: if TRUE, 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

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

See Also

test.t, test.z, test.levene, aov.b, cohens.d, ci.mean.diff, ci.mean

Examples

dat1 <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2),
                   group2 = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3),
                   y = c(3, 1, 4, 2, 5, 3, 2, 3, 6, 6, 3, NA))

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

# Two-sided two-sample Welch-test
test.welch(y ~ group1, data = dat1)

# One-sided two-sample Welch-test
test.welch(y ~ group1, data = dat1, alternative = "greater")

# Two-sided two-sample Welch-test
# print Cohen's d with weighted pooled SD
test.welch(y ~ group1, data = dat1, effsize = TRUE)

# Two-sided two-sample Welch-test
# print Cohen's d with unweighted pooled SD
test.welch(y ~ group1, data = dat1, effsize = TRUE, weighted = FALSE)

# Two-sided two-sample Welch-test
# print Cohen's d with weighted pooled SD and
# small sample correction factor
test.welch(y ~ group1, data = dat1, effsize = TRUE, correct = TRUE)

# Two-sided two-sample Welch-test
# print Cohen's d with SD of the reference group 1
test.welch(y ~ group1, data = dat1, effsize = TRUE,
           ref = 1)

# Two-sided two-sample Welch-test
# print Cohen's d with weighted pooled SD and
# small sample correction factor
test.welch(y ~ group1, data = dat1, effsize = TRUE,
           correct = TRUE)

# Two-sided two-sample Welch-test
# do not print hypotheses and descriptive statistics,
test.welch(y ~ group1, data = dat1, descript = FALSE, hypo = FALSE)

# Two-sided two-sample Welch-test
# print descriptive statistics with 3 digits and p-value with 5 digits
test.welch(y ~ group1, data = dat1, digits = 3, p.digits = 5)

if (FALSE) {
# Two-sided two-sample Welch-test
# plot results
test.welch(y ~ group1, data = dat1, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

# Save plot, ggsave() from the ggplot2 package
ggsave("Two-sample_Welch-test.png", dpi = 600, width = 4, height = 6)

# Two-sided two-sample Welch-test
# extract plot
p <- test.welch(y ~ group1, data = dat1, output = FALSE)$plot
p

# Extract data
plotdat <- test.welch(y ~ group1, data = dat1, output = FALSE)$data

# Draw plot in line with the default setting of test.welch()
ggplot(plotdat, aes(factor(group), y)) +
  geom_point(stat = "summary", fun = "mean", size = 4) +
  stat_summary(fun.data = "mean_cl_normal", geom = "errorbar", width = 0.20) +
  scale_x_discrete(name = NULL) +
  labs(subtitle = "Two-Sided 95% Confidence Interval") +
  theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5))
}
#--------------------------------------
# Multiple-Sample Design

# Welch's ANOVA
test.welch(y ~ group2, data = dat1)

# Welch's ANOVA
# print eta-squared and omega-squared
test.welch(y ~ group2, data = dat1, effsize = TRUE)

# Welch's ANOVA
# do not print hypotheses and descriptive statistics,
test.welch(y ~ group2, data = dat1, descript = FALSE, hypo = FALSE)

if (FALSE) {
# Welch's ANOVA
# plot results
test.welch(y ~ group2, data = dat1, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

# Save plot, ggsave() from the ggplot2 package
ggsave("Multiple-sample_Welch-test.png", dpi = 600, width = 4.5, height = 6)

# Welch's ANOVA
# extract plot
p <- test.welch(y ~ group2, data = dat1, output = FALSE)$plot
p

# Extract data
plotdat <- test.welch(y ~ group2, data = dat1, output = FALSE)$data

# Draw plot in line with the default setting of test.welch()
ggplot(plotdat, aes(group, y)) +
  geom_point(stat = "summary", fun = "mean", size = 4) +
  stat_summary(fun.data = "mean_cl_normal", geom = "errorbar", width = 0.20) +
  scale_x_discrete(name = NULL) +
  labs(subtitle = "Two-Sided 95% Confidence Interval") +
  theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5))
}