generic.z.test: Statistical Power for the Generic Z-Test

In pwrss: Statistical Power and Sample Size Calculation Tools

Statistical Power for the Generic Z-Test

Description

Calculates power for the generic Z-Test with (optional) Type 1 and Type 2 error plots.

Usage

power.z.test(mean = NULL, sd = 1, null.mean = 0, null.sd = 1,
             alpha = 0.05, alternative = c("two.sided",
                                           "one.sided", "two.one.sided"),
             plot = TRUE, verbose = TRUE, pretty = FALSE, ...)

Arguments

mean	mean of the alternative.
sd	standard deviation of the alternative. Do not change this value except when some sort of variance correction is applied (e.g. as in logistic and Poisson regressions).
null.mean	mean of the null. When alternative = "two.one.sided", the function expects two values in the form c(lower, upper). If a single value is provided, it is interpreted as the absolute bound and automatically expanded to c(-value, +value).
null.sd	standard deviation of the null. Do not change this value except when some sort of correction is applied.
alpha	type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \alpha.
alternative	character; direction or type of the hypothesis test: "one.sided", "two.sided", or "two.one.sided". "two.one.sided" is used for equivalence and minimal effect testing.
plot	logical; FALSE switches off Type 1 and Type 2 error plot. TRUE by default.
verbose	logical; whether the output should be printed on the console. TRUE by default.
...	legacy inputs will be mapped to their corresponding arguments (silent). e.g. ncp
pretty	logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

mean	mean of the alternative distribution.
sd	standard deviation of the alternative distribution.
null.mean	mean of the null distribution.
null.sd	standard deviation of the null distribution.
z.alpha	critical value(s).
power	statistical power (1-\beta).

Examples

# two-sided
# power defined as the probability of observing z-statistics
# greater than the positive critical t value OR
# less than the negative critical t value
power.z.test(mean = 1.96, alpha = 0.05,
             alternative = "two.sided")

# one-sided
# power is defined as the probability of observing z-statistics
# greater than the critical t value
power.z.test(mean = 1.96, alpha = 0.05,
             alternative = "one.sided")

# equivalence
# power is defined as the probability of observing a test statistic
# greater than the upper critical value (for the lower bound) AND
# less than the lower critical value (for the upper bound)
power.z.test(mean = 0, null.mean = c(-2, 2), alpha = 0.05,
             alternative = "two.one.sided")

# minimal effect testing
# power is defined as the probability of observing a test statistic
# greater than the upper critical value (for the upper bound) OR
# less than the lower critical value (for the lower bound).
power.z.test(mean = 2, null.mean = c(-1, 1), alpha = 0.05,
             alternative = "two.one.sided")

pwrss documentation built on Sept. 16, 2025, 9:11 a.m.