test.z: z-Test

Description

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.

Usage

test.z(x, ...)
# S3 method for default
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,
       digits = 2, p.digits = 3, as.na = NULL, plot = FALSE, bar = TRUE,
       point = FALSE, ci = TRUE, line = TRUE, jitter = FALSE, adjust = TRUE,
       point.size = 4, errorbar.width = 0.1, xlab = NULL, ylab = NULL,
       ylim = NULL, ybreaks = ggplot2::waiver(), linetype = 3, linewidth = 0.8,
       jitter.size = 1.25, jitter.width = 0.05, jitter.height = 0,
       jitter.alpha = 0.1, title = "", 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, ...)
# S3 method for 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, digits = 2, p.digits = 3,
       as.na = NULL, plot = FALSE, bar = TRUE, point = FALSE, ci = TRUE,
       line = TRUE, jitter = FALSE, adjust = TRUE, point.size = 4, errorbar.width = 0.1,
       xlab = NULL, ylab = NULL, ylim = NULL, ybreaks = ggplot2::waiver(),
       linetype = 3, linewidth = 0.8, jitter.size = 1.25, jitter.width = 0.05,
       jitter.height = 0, jitter.alpha = 0.1, title = "",
       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
formula: formula
data: data frame with the outcome and grouping variable
args: specification of function arguments
plot: ggplot2 object for plotting the results
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.
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 sigma; when specifying two values for the argument sigma, unequal standard deviations are assumed. Note that either argument sigma or argument sigma2 is specified.
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 sigma2; when specifying two values for the argument sigma, unequal variance are assumed. Note that either argument sigma or argument sigma2 is specified.
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 z-test.
paired: logical: if TRUE, paired-sample z-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 (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 is shown on the console.
conf.level: a numeric value between 0 and 1 indicating the confidence level of the interval.
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 bar plots with 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.
line: logical: if TRUE (default), a horizontal line is drawn at mu for the one-sample z-test or at 0 for the paired-sample z-test.
adjust: logical: if TRUE (default), difference-adjustment for the confidence intervals in a two-sample design 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.
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.
linetype: 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.
linewidth: a numeric value indicating the linewidth aesthetic for the line representing the population mean under the null hypothesis.
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 between 0 and 1 for specifying the alpha argument in the geom_jitter function for controlling 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.
filename: a character string indicating the filename argument (default is "NA_Pattern.pdf") including the file extension for 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 file argument.
width: a numeric value indicating the width argument (default is the size of the current graphics device) for the ggsave function.
height: a numeric value indicating the height argument (default is the size of the current graphics device) for the ggsave function.
units: a character string indicating the units argument (default is in) for the ggsave function.
dpi: a numeric value indicating the dpi argument (default is 600) for 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.
formula: in case of two sample z-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

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.

References

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.

Examples

Run this code

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

# Example 1a: Two-sided one-sample z-test, population mean = 20, population SD = 6
test.z(mtcars$mpg, sigma = 6, mu = 20)

# Example 1b: One-sided one-sample z-test, population mean = 20, population SD = 6,
# print Cohen's d
test.z(mtcars$mpg, sigma = 6, mu = 20, alternative = "greater", effsize = TRUE)

# Example 1c: Two-sided one-sample z-test, population mean = 20, population SD = 6,
# plot results
test.z(mtcars$mpg, sigma = 6, mu = 20, plot = TRUE)

if (FALSE) {
# Example 1d: Two-sided one-sample z-test, save plot
test.z(mtcars$mpg, sigma = 6, mu = 20, plot = TRUE, filename = "One-sample_z-test.png",
       width = 4, height = 5)}

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

# Example 2a: Two-sided two-sample z-test, population SD = 6, equal SD assumption
test.z(mpg ~ vs, data = mtcars, sigma = 6)

# Example 2b: Two-sided two-sample z-test, alternative specification
test.z(c(3, 1, 4, 2, 5, 3, 6, 7), c(5, 2, 4, 3, 1), sigma = 1.2)

# Example 2c: Two-sided two-sample z-test, population SD = 4 and 6, unequal SD assumption
test.z(mpg ~ vs, data = mtcars, sigma = c(4, 6))

# Example 2d: One-sided two-sample z-test, population SD = 4 and 6, unequal SD assumption
# print Cohen's d
test.z(mpg ~ vs, data = mtcars, sigma = c(4, 6), alternative = "greater",
       effsize = TRUE)

# Example 2e: Two-sided two-sample z-test, population SD = 6, equal SD assumption
# plot results
test.z(mpg ~ vs, data = mtcars, sigma = 6, plot = TRUE)

if (FALSE) {
# Example 2f: Two-sided two-sample z-test, save plot
test.z(mpg ~ vs, data = mtcars, sigma = 6, plot = TRUE, filename = "Two-sample_z-test.png",
       width = 5, height = 6)}

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

# Example 3a: Two-sided paired-sample z-test, population SD of difference score = 1.2
test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE)

# Example 3b: One-sided paired-sample z-test, population SD of difference score = 1.2,
# print Cohen's d
test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE,
       alternative = "greater", effsize = TRUE)

# Example 3c: Two-sided paired-sample z-test, population SD of difference score = 1.2,
# plot results
test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE, plot = TRUE)

if (FALSE) {
# Example 3d: Two-sided paired-sample z-test, save plot
test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE, plot = TRUE,
       filename = "Paired-sample_z-test.png", width = 4, height = 5)}

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