test.z | R Documentation |
This function performs one-sample, two-sample, and paired-sample z-tests and provides descriptive statistics, effect size measure, and a plot showing error bars for (difference-adjusted) confidence intervals with jittered data points.
test.z(x, ...)
## Default S3 method:
test.z(x, y = NULL, sigma = NULL, sigma2 = NULL, mu = 0,
paired = FALSE, alternative = c("two.sided", "less", "greater"),
conf.level = 0.95, hypo = TRUE, descript = TRUE, effsize = 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 class 'formula'
test.z(formula, data, sigma = NULL, sigma2 = NULL,
alternative = c("two.sided", "less", "greater"), conf.level = 0.95,
hypo = TRUE, descript = TRUE, effsize = 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, ...)
x |
a numeric vector of data values. |
... |
further arguments to be passed to or from methods. |
y |
a numeric vector of data values. |
sigma |
a numeric vector indicating the population standard deviation(s).
In case of two-sample z-test, equal standard deviations are
assumed when specifying one value for the argument |
sigma2 |
a numeric vector indicating the population variance(s). In
case of two-sample z-test, equal variances are assumed when
specifying one value for the argument |
mu |
a numeric value indicating the population mean under the null
hypothesis. Note that the argument |
paired |
logical: if |
alternative |
a character string specifying the alternative hypothesis,
must be one of |
hypo |
logical: if |
descript |
logical: if |
effsize |
logical: if |
conf.level |
a numeric value between 0 and 1 indicating the confidence level of the interval. |
plot |
logical: if |
point.size |
a numeric value indicating the |
adjust |
logical: if |
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 |
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 |
jitter |
logical: if |
jitter.size |
a numeric value indicating the |
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 |
check |
logical: if |
output |
logical: if |
formula |
in case of two sample z-test (i.e., |
data |
a matrix or data frame containing the variables in the formula
|
Cohen's d reported when argument effsize = TRUE
is based on the population
standard deviation specified in sigma
or the square root of the population
variance specified in sigma2
. In a one-sample and paired-sample design,
Cohen's d is the mean of the difference scores divided by the population standard
deviation of the difference scores (i.e., equivalent to Cohen's d_z
according
to Lakens, 2013). In a two-sample design, Cohen's d is the difference between
means of the two groups of observations divided by either the population standard
deviation when assuming and specifying equal standard deviations or the unweighted
pooled population standard deviation when assuming and specifying unequal standard
deviations.
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 |
plot |
ggplot2 object for plotting the results |
args |
specification of function arguments |
result |
result table |
Takuya Yanagida takuya.yanagida@univie.ac.at
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 1-12. https://doi.org/10.3389/fpsyg.2013.00863
Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.
test.t
, aov.b
, aov.w
, test.welch
,
cohens.d
, ci.mean.diff
, ci.mean
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, 4, 3, NA))
#--------------------------------------
# One-Sample Design
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
test.z(dat1$x, sigma = 1.2, mu = 3)
# Two-sided one-sample z-test
# population mean = 3, population variance = 1.44
test.z(dat1$x, sigma2 = 1.44, mu = 3)
# One-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
test.z(dat1$x, sigma = 1.2, mu = 3, alternative = "greater")
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# convert value 3 to NA
test.z(dat1$x, sigma = 1.2, mu = 3, as.na = 3)
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# print Cohen's d
test.z(dat1$x, sigma = 1.2, mu = 3, effsize = TRUE)
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# do not print hypotheses and descriptive statistics
test.z(dat1$x, sigma = 1.2, mu = 3, hypo = FALSE, descript = FALSE)
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# print descriptive statistics with 3 digits and p-value with 5 digits
test.z(dat1$x, sigma = 1.2, mu = 3, digits = 3, p.digits = 5)
## Not run:
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# plot results
test.z(dat1$x, sigma = 1.2, mu = 3, plot = TRUE)
# Load ggplot2 package
library(ggplot2)
# Save plot, ggsave() from the ggplot2 package
ggsave("One-sample_z-test.png", dpi = 600, width = 3, height = 6)
# Two-sided one-sample z-test
# population mean = 3, population standard deviation = 1.2
# extract plot
p <- test.z(dat1$x, sigma = 1.2, mu = 3, output = FALSE)$plot
p
# Extract data
plotdat <- data.frame(test.z(dat1$x, sigma = 1.2, mu = 3, output = FALSE)$data[[1]])
# Extract results
result <- test.z(dat1$x, sigma = 1.2, mu = 3, output = FALSE)$result
# Draw plot in line with the default setting of test.z()
ggplot(plotdat, aes(0, x)) +
geom_point(data = result, aes(x = 0L, m), size = 4) +
geom_errorbar(data = result, aes(x = 0L, y = m, ymin = m.low, ymax = m.upp),
width = 0.2) +
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())
## End(Not run)
#--------------------------------------
# Two-Sample Design
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
test.z(x ~ group, sigma = 1.2, data = dat1)
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2 and 1.5, unequal SD assumption
test.z(x ~ group, sigma = c(1.2, 1.5), data = dat1)
# Two-sided two-sample z-test
# population variance (Var) = 1.44 and 2.25, unequal Var assumption
test.z(x ~ group, sigma2 = c(1.44, 2.25), data = dat1)
# One-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
test.z(x ~ group, sigma = 1.2, data = dat1, alternative = "greater")
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# print Cohen's d
test.z(x ~ group, sigma = 1.2, data = dat1, effsize = TRUE)
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# do not print hypotheses and descriptive statistics,
# print Cohen's d
test.z(x ~ group, sigma = 1.2, data = dat1, descript = FALSE, hypo = FALSE)
# Two-sided two-sample z-test
# population mean = 3, population standard deviation = 1.2
# print descriptive statistics with 3 digits and p-value with 5 digits
test.z(x ~ group, sigma = 1.2, data = dat1, digits = 3, p.digits = 5)
## Not run:
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# plot results
test.z(x ~ group, sigma = 1.2, data = dat1, plot = TRUE)
# Load ggplot2 package
library(ggplot2)
# Save plot, ggsave() from the ggplot2 package
ggsave("Two-sample_z-test.png", dpi = 600, width = 4, height = 6)
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# extract plot
p <- test.z(x ~ group, sigma = 1.2, data = dat1, output = FALSE)$plot
p
## End(Not run)
#-----------------
group1 <- c(3, 1, 4, 2, 5, 3, 6, 7)
group2 <- c(5, 2, 4, 3, 1)
# Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
test.z(group1, group2, sigma = 1.2)
#--------------------------------------
# Paired-Sample Design
dat2 <- data.frame(pre = c(1, 3, 2, 5, 7),
post = c(2, 2, 1, 6, 8), stringsAsFactors = FALSE)
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE)
# Two-sided paired-sample z-test
# population variance of difference score = 1.44
test.z(dat2$pre, dat2$post, sigma2 = 1.44, paired = TRUE)
# One-sided paired-sample z-test
# population standard deviation of difference score = 1.2
test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE,
alternative = "greater")
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# convert value 1 to NA
test.z(dat2$pre, dat2$post, sigma = 1.2, as.na = 1, paired = TRUE)
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# print Cohen's d
test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE, effsize = TRUE)
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# do not print hypotheses and descriptive statistics
test.z(dat2$pre, dat2$post, sigma = 1.2, mu = 3, paired = TRUE,
hypo = FALSE, descript = FALSE)
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# print descriptive statistics with 3 digits and p-value with 5 digits
test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE,
digits = 3, p.digits = 5)
## Not run:
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# plot results
test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE, plot = TRUE)
# Load ggplot2 package
library(ggplot2)
# Save plot, ggsave() from the ggplot2 package
ggsave("Paired-sample_z-test.png", dpi = 600, width = 3, height = 6)
# Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# extract plot
p <- test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE, output = FALSE)$plot
p
# Extract data
plotdat <- data.frame(test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE,
output = FALSE)$data)
# Difference score
plotdat$diff <- plotdat$y - plotdat$x
# Extract results
result <- test.z(dat2$pre, dat2$post, sigma = 1.2, paired = TRUE,
output = FALSE)$result
# Draw plot in line with the default setting of test.t()
ggplot(plotdat, aes(0, diff)) +
geom_point(data = result, aes(x = 0, m.diff), size = 4) +
geom_errorbar(data = result,
aes(x = 0L, y = m.diff, ymin = m.low, ymax = m.upp), width = 0.2) +
scale_x_continuous(name = NULL, limits = c(-2, 2)) +
scale_y_continuous(name = "y") +
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())
## End(Not run)
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