pwrss (version 0.3.1)

power.t.test: Statistical Power for the Generic t Test

Description

Calculates statistical power for the generic t test with (optional) Type I and Type II error plots. Unlike other more specific functions power.t.test() function allows multiple values for one parameter at a time (only when plot = FALSE).

Usage

power.t.test(ncp, df, alpha = 0.05,
             alternative = c("not equal", "greater", "less",
                             "non-inferior", "superior", "equivalent"),
             plot = TRUE, plot.main = NULL, plot.sub = NULL,
             verbose = TRUE)

Value

power

statistical power \((1-\beta)\)

Arguments

ncp

non-centrality parameter (lambda)

df

degrees of freedom

alpha

probability of type I error

alternative

direction or type of the hypothesis test: "not equal", "greater", "less", "equivalent", "non-inferior", or "superior". The same non-centrality parameters will produce the same power rates for "greater", "less", "non-inferior", and "superior" tests. Different labels have been used merely for consistency. However, it should be noted that the non-centrality parameter should conform to the specific test type

plot

if TRUE plots Type I and Type II error

plot.main

plot title

plot.sub

plot subtitle

verbose

if FALSE no output is printed on the console. Useful for simulation, plotting, and whatnot

Examples

# power is defined as the probability of observing t-statistics
# greater than the positive critical t value OR
# less than the negative critical t value
power.t.test(ncp = 1.96, df = 99, alpha = 0.05,
             alternative = "not equal")

# power is defined as the probability of observing t-statistics
# greater than the critical t value
power.t.test(ncp = 1.96, df = 99, alpha = 0.05,
             alternative = "greater")

# power is defined as the probability of observing t-statistics
# greater than the critical t value where the non-centrality parameter
# for the alternative distribution is adjusted for the non-inferiority margin
power.t.test(ncp = 1.98, df = 99, alpha = 0.05,
             alternative = "non-inferior")

# power is defined as the probability of observing t-statistics
# greater than the critical t value where the non-centrality parameter
# for the alternative distribution is adjusted for the superiority margin
power.t.test(ncp = 1.94, df = 99, alpha = 0.05,
             alternative = "superior")

# power is defined as the probability of observing t-statistics
# less than the positive critical t value AND
# greater than the negative critical t value
# the non-centrality parameter is for the null distribution
# and is derived from the equivalence margins (lower and upper)
power.t.test(ncp = 1.96, df = 999, alpha = 0.05,
             alternative = "equivalent")
# or, define lower and upper bound with rbind()
power.t.test(ncp = rbind(-1.96, 1.96),
             df = 999, alpha = 0.05,
             alternative = "equivalent")