misty (version 0.4.5)

test.z: z-Test

Description

This function performs one-sample, two-sample, and paired-sample z-tests.

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"),
       hypo = TRUE, descript = TRUE, effsize = FALSE, digits = 2, p.digits = 4,
       as.na = NULL, check = TRUE, output = TRUE, ...)
# S3 method for formula
test.z(formula, data, sigma = NULL, sigma2 = NULL,
       alternative = c("two.sided", "less", "greater"), hypo = TRUE,
       descript = TRUE, effsize = FALSE, digits = 2, p.digits = 4,
       as.na = NULL, check = TRUE, output = TRUE, ...)

Arguments

x

a numeric vector of data values.

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, 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.

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 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.

...

further arguments to be passed to or from methods.

Value

Returns an object of class misty.object, which is a list with following entries: function call (call), type of analysis type, list with the input specified in x (data), specification of function arguments (args), and result table (result).

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, cohens.d, ci.mean.diff, ci.mean

Examples

# NOT RUN {
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)

#--------------------------------------
# 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)

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

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)
# }