test.t: t-Test

Description

This function performs one-sample, two-sample, and paired-sample t-tests and provides descriptive statistics, effect size measure, and a plot showing error bars for (difference-adjusted) confidence intervals with jittered data points.

Usage

test.t(x, ...)
# S3 method for default
test.t(x, y = NULL, mu = 0, paired = FALSE,
       alternative = c("two.sided", "less", "greater"),
       conf.level = 0.95,  hypo = TRUE, descript = TRUE, effsize = FALSE,
       weighted = FALSE, cor = TRUE, ref = NULL, correct = FALSE,
       plot = FALSE, point.size = 4, adjust = TRUE, error.width = 0.1,
       xlab = NULL, ylab = NULL, ylim = NULL, breaks = ggplot2::waiver(),
       line = TRUE, line.type = 3, line.size = 0.8,
       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, ...)
# S3 method for formula
test.t(formula, data, alternative = c("two.sided", "less", "greater"),
       conf.level = 0.95, hypo = TRUE, descript = TRUE, effsize = FALSE,
       weighted = FALSE, cor = TRUE, 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., one-, two-, or paired 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

x: a numeric vector of data values.
...: further arguments to be passed to or from methods.
y: a numeric vector of data values.
mu: a numeric value indicating the population mean under the null hypothesis. Note that the argument mu is only used when computing a one sample t-test.
paired: logical: if TRUE, paired-samples t-test is computed.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
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 is shown on the console, see cohens.d function.
weighted: logical: if TRUE, the weighted pooled standard deviation is used to compute Cohen's d for a two-sample design (i.e., paired = FALSE), while standard deviation of the difference scores is used to compute Cohen's d for a paired-sample design (i.e., paired = TRUE).
cor: logical: if TRUE (default), paired = TRUE, and weighted = FALSE, Cohen's d for a paired-sample design while controlling for the correlation between the two sets of measurement is computed. Note that this argument is only used in a paired-sample design (i.e., paired = TRUE) when specifying weighted = FALSE.
ref: character string "x" or "y" for specifying the reference reference group when using the default test.t() function or a numeric value or character string indicating the reference group in a two-sample design when using the formula test.t() function. The standard deviation of the reference variable or reference group is used to standardized the mean difference to compute Cohen's d. Note that this argument is only used in a two-sample design (i.e., paired = FALSE).
correct: logical: if TRUE, correction factor to remove positive bias in small samples is used.
conf.level: a numeric value between 0 and 1 indicating the confidence level of the interval.
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 in a two-sample design 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.
line: logical: if TRUE (default), a horizontal line is drawn at mu for the one-sample t-test or at 0 for the paired-sample t-test.
line.type: an integer value or character string specifying the line type for the line representing the population mean under the null hypothesis, i.e., 0 = blank, 1 = solid, 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash.
line.size: a numeric value indicating the size aesthetic for the line representing the population mean under the null hypothesis.
jitter: logical: if TRUE (default), jittered data points are drawn.
jitter.size: a numeric value indicating the size aesthetic
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.
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 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.
formula: in case of two sample t-test (i.e., paired = FALSE), a formula of the form y ~ group where group is a numeric variable, character variable or factor with two values or factor levels giving the corresponding groups.
data: a matrix or data frame containing the variables in the formula formula.

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

dat1 <- data.frame(group = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2),
                   x = c(3, 1, 4, 2, 5, 3, 2, 3, 6, 6, 3, NA))

#--------------------------------------
# One-Sample Design

# Two-sided one-sample t-test
# population mean = 3
test.t(dat1$x, mu = 3)

# One-sided one-sample t-test
# population mean = 3, population standard deviation = 1.2
test.t(dat1$x, mu = 3, alternative = "greater")

# Two-sided one-sample t-test
# population mean = 3, convert value 3 to NA
test.t(dat1$x, mu = 3, as.na = 3)

# Two-sided one-sample t-test
# population mean = 3, print Cohen's d
test.t(dat1$x, sigma = 1.2, mu = 3, effsize = TRUE)

# Two-sided one-sample t-test
# population mean = 3, print Cohen's d with small sample correction factor
test.t(dat1$x, sigma = 1.2, mu = 3, effsize = TRUE, correct = TRUE)

# Two-sided one-sample t-test
# population mean = 3,
# do not print hypotheses and descriptive statistics
test.t(dat1$x, sigma = 1.2, mu = 3, hypo = FALSE, descript = FALSE)

# Two-sided one-sample t-test
# print descriptive statistics with 3 digits and p-value with 5 digits
test.t(dat1$x,  mu = 3, digits = 3, p.digits = 5)

if (FALSE) {
# Two-sided one-sample t-test
# population mean = 3, plot results
test.t(dat1$x, mu = 3, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

# Save plot, ggsave() from the ggplot2 package
ggsave("One-sample_t-test.png", dpi = 600, width = 3, height = 6)

# Two-sided one-sample t-test
# population mean = 3, extract plot
p <- test.t(dat1$x, mu = 3, output = FALSE)$plot
p

# Extract data
plotdat <- data.frame(x = test.t(dat1$x, mu = 3, output = FALSE)$data[[1]])

# Draw plot in line with the default setting of test.t()
ggplot(plotdat, aes(0, x)) +
   geom_point(stat = "summary", fun = "mean", size = 4) +
   stat_summary(fun.data = "mean_cl_normal", geom = "errorbar", width = 0.20) +
   scale_x_continuous(name = NULL, limits = c(-2, 2)) +
   scale_y_continuous(name = NULL) +
   geom_hline(yintercept = 3, linetype = 3, size = 0.8) +
   labs(subtitle = "Two-Sided 95% Confidence Interval") +
   theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5),
                      axis.text.x = element_blank(),
                      axis.ticks.x = element_blank())
}
#--------------------------------------
# Two-Sample Design

# Two-sided two-sample t-test
test.t(x ~ group, data = dat1)

# One-sided two-sample t-test
test.t(x ~ group, data = dat1, alternative = "greater")

# Two-sided two-sample t-test
# print Cohen's d with weighted pooled SD
test.t(x ~ group, data = dat1, effsize = TRUE)

# Two-sided two-sample t-test
# print Cohen's d with unweighted pooled SD
test.t(x ~ group, data = dat1, effsize = TRUE, weighted = FALSE)

# Two-sided two-sample t-test
# print Cohen's d with weighted pooled SD and
# small sample correction factor
test.t(x ~ group, data = dat1, effsize = TRUE, correct = TRUE)

# Two-sided two-sample t-test
# print Cohen's d with SD of the reference group 1
test.t(x ~ group, data = dat1, effsize = TRUE,
       ref = 1)

# Two-sided two-sample t-test
# print Cohen's d with weighted pooled SD and
# small sample correction factor
test.t(x ~ group, data = dat1, effsize = TRUE,
       correct = TRUE)

# Two-sided two-sample t-test
# do not print hypotheses and descriptive statistics,
test.t(x ~ group, data = dat1, descript = FALSE, hypo = FALSE)

# Two-sided two-sample t-test
# print descriptive statistics with 3 digits and p-value with 5 digits
test.t(x ~ group, data = dat1, digits = 3, p.digits = 5)

if (FALSE) {
# Two-sided two-sample t-test
# Plot results
test.t(x ~ group, data = dat1, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

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

# Two-sided two-sample t-test
# extract plot
p <- test.t(x ~ group, data = dat1, output = FALSE)$plot
p

# Extract data used to plot results
plotdat <- test.t(x ~ group, data = dat1, output = FALSE)$data

# Draw plot in line with the default setting of test.t()
ggplot(plotdat, aes(factor(group), x)) +
   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) + scale_y_continuous(name = "y") +
   labs(title = "", subtitle = "Two-Sided 95% Confidence Interval") +
   theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5))
}

#-----------------

group1 <- c(3, 1, 4, 2, 5, 3, 6, 7)
group2 <- c(5, 2, 4, 3, 1)

# Two-sided two-sample t-test
test.t(group1, group2)

#--------------------------------------
# Paired-Sample Design

dat2 <- data.frame(pre = c(1, 3, 2, 5, 7),
                   post = c(2, 2, 1, 6, 8))

# Two-sided paired-sample t-test
test.t(dat2$pre, dat2$post, paired = TRUE)

# One-sided paired-sample t-test
test.t(dat2$pre, dat2$post, paired = TRUE,
       alternative = "greater")

# Two-sided paired-sample t-test
# convert value 1 to NA
test.t(dat2$pre, dat2$post, as.na = 1, paired = TRUE)

# Two-sided paired-sample t-test
# print Cohen's d based on the standard deviation of the difference scores
test.t(dat2$pre, dat2$post, paired = TRUE, effsize = TRUE)

# Two-sided paired-sample t-test
# print Cohen's d based on the standard deviation of the difference scores
# with small sample correction factor
test.t(dat2$pre, dat2$post, paired = TRUE, effsize = TRUE,
       correct = TRUE)

# Two-sided paired-sample t-test
# print Cohen's d controlling for the correlation between measures
test.t(dat2$pre, dat2$post, paired = TRUE, effsize = TRUE,
       weighted = FALSE)

# Two-sided paired-sample t-test
# print Cohen's d controlling for the correlation between measures
# with small sample correction factor
test.t(dat2$pre, dat2$post, paired = TRUE, effsize = TRUE,
       weighted = FALSE, correct = TRUE)

# Two-sided paired-sample t-test
# print Cohen's d ignoring the correlation between measures
test.t(dat2$pre, dat2$post, paired = TRUE, effsize = TRUE,
       weighted = FALSE, cor = FALSE)

# Two-sided paired-sample t-test
# do not print hypotheses and descriptive statistics
test.t(dat2$pre, dat2$post, paired = TRUE, hypo = FALSE, descript = FALSE)

# Two-sided paired-sample t-test
# population standard deviation of difference score = 1.2
# print descriptive statistics with 3 digits and p-value with 5 digits
test.t(dat2$pre, dat2$post, paired = TRUE, digits = 3,
       p.digits = 5)

if (FALSE) {
# Two-sided paired-sample t-test
# Plot results
test.t(dat2$pre, dat2$post, paired = TRUE, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

# Save plot, ggsave() from the ggplot2 package
ggsave("Paired-sample_t-test.png", dpi = 600, width = 3, height = 6)

# Two-sided paired-sample t-test
# Extract plot
p <- test.t(dat2$pre, dat2$post, paired = TRUE, output = FALSE)$plot
p

# Extract data used to plot results
plotdat <- data.frame(test.t(dat2$pre, dat2$post, paired = TRUE, output = FALSE)$data)

# Difference score
plotdat$diff <- plotdat$y - plotdat$x

# Draw plot in line with the default setting of test.t()
ggplot(plotdat, aes(0, diff)) +
   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) + scale_y_continuous(name = NULL) +
   geom_hline(yintercept = 0, linetype = 3, size = 0.8) +
   labs(subtitle = "Two-Sided 95% Confidence Interval") +
   theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5),
                      axis.text.x = element_blank(),
                      axis.ticks.x = element_blank())
}

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