misty (version 0.7.0)

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,
       plot = FALSE, adjust = TRUE, point.size = 4, errorbar.width = 0.1,
       xlab = NULL, ylab = NULL, ylim = NULL, breaks = ggplot2::waiver(),
       line = TRUE, linetype = 3, linewidth = 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 = 3, as.na = NULL, 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,
       plot = FALSE, adjust = TRUE, point.size = 4, errorbar.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 = 3, 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., 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.

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.

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.

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.

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

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.

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.

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

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.

See Also

test.t, aov.b, aov.w, test.welch, cohens.d, ci.mean.diff, ci.mean

Examples

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

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

# Example 1b: One-sided one-sample z-test
# population mean = 20, population standard deviation = 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 standard deviation = 6
# plot results
test.z(mtcars$mpg, sigma = 6, mu = 20, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

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

# Example 1d: Two-sided one-sample z-test
# population mean = 20, population standard deviation = 6
# extract plot and results
p <- test.z(mtcars$mpg, sigma = 6, mu = 20, output = FALSE)$plot
p

# Example 1e: Two-sided one-sample z-test
# Draw plot in line with the default setting of test.z()

# Extract data
plotdat <- data.frame(test.z(mtcars$mpg, sigma = 6, mu = 20, output = FALSE)$data[[1]])

# Extract results
result <- test.z(mtcars$mpg, sigma = 6, mu = 20, output = FALSE)$result

# Draw plot
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 = 20, linetype = 3, linewidth = 0.8) +
  labs(subtitle = "Two-Sided 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

# Example 2a: Two-sided two-sample z-test
# population standard deviation (SD) = 62, equal SD assumption
test.z(mpg ~ vs, sigma = 6, data = mtcars)

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

# Example 2c: One-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# print Cohen's d
test.z(mpg ~ vs, sigma = c(4, 6), data = mtcars, alternative = "greater",
       effsize = TRUE)

# Example 2d: Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# plot results
test.z(mpg ~ vs, sigma = 6, data = mtcars, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

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

# Example 2e: Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
# extract plot
p <- test.z(mpg ~ vs, sigma = 6, data = mtcars, output = FALSE)$plot
p

# Example 2f: Two-sided two-sample z-test
# population standard deviation (SD) = 1.2, equal SD assumption
test.z(c(3, 1, 4, 2, 5, 3, 6, 7), c(5, 2, 4, 3, 1), sigma = 1.2)

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

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

# Load ggplot2 package
library(ggplot2)

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

# Example 3d: Two-sided paired-sample z-test
# population standard deviation of difference score = 1.2
# extract plot
p <- test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE, output = FALSE)$plot
p

# Example 1e: Two-sided paired-sample z-test
# Draw plot in line with the default setting of test.z()

# Extract data
plotdat <- data.frame(test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE,
                      output = FALSE)$data)

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

# Extract results
result <- test.z(mtcars$drat, mtcars$wt, sigma = 1.2, paired = TRUE,
                  output = FALSE)$result

# Draw plot
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, linewidth = 0.8) +
   labs(subtitle = "Two-Sided Confidence Interval") +
   theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5),
                      axis.text.x = element_blank(),
                      axis.ticks.x = element_blank())