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

Description

Determines the power, the non-centrality parameter, or the degrees of freedom for the generic t-Test with (optional) Type 1 and Type 2 error plots.

Usage

power.t.test(
  power = NULL,
  ncp = NULL,
  req.sign = "+",
  null.ncp = 0,
  df = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided", "two.one.sided"),
  plot = TRUE,
  verbose = 1,
  utf = FALSE
)

Value

power: statistical power \((1-\beta)\).
ncp: non-centrality parameter under alternative.
null.ncp: non-centrality parameter under null.
df: degrees of freedom.
alpha: type 1 error rate (user-specified).
t.alpha: critical value(s).
beta: type 2 error rate.
type.s: type S error rate (only for two-tailed test).
type.m: type M error rate (only for two-tailed test).

Arguments

power: statistical power \((1 - \beta)\); either power, ncp or df needs to be NULL (and is then estimated).
ncp: non-centrality parameter for the alternative; ; either power, ncp or df needs to be NULL (and is then estimated).
req.sign: whether ncp is expected to be greater '+1', less than '-1', or within '0' the null.ncp bounds; only relevant if ncp is to be estimated.
null.ncp: non-centrality parameter for 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).
df: degrees of freedom; either power, ncp or df needs to be NULL (and is then estimated).
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
alternative: character; the direction or type of the hypothesis test: "two.sided", "one.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: 1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.
utf: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Examples

Run this code

# two-sided
# power defined as the probability of observing test statistics greater
# than the positive critical value OR less than the negative critical value
power.t.test(ncp = 1.96, df = 100, alpha = 0.05, alternative = "two.sided")
power.t.test(power = 0.80, df = 100, alpha = 0.05, alternative = "two.sided")

# one-sided
# power is defined as the probability of observing a test statistic greater
# than the critical value
power.t.test(ncp = 1.96, df = 100, alpha = 0.05, alternative = "one.sided")
power.t.test(power = 0.80, df = 100, 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.t.test(ncp = 0, null.ncp = c(-2, 2), df = 100, alpha = 0.05,
             alternative = "two.one.sided")
power.t.test(power = 0.80, req.sign = "0", null.ncp = c(-2, 2),
             df = 100, 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.t.test(ncp = 2, null.ncp = c(-1, 1), df = 100, alpha = 0.05,
             alternative = "two.one.sided")
power.t.test(power = 0.80, req.sign = "+", null.ncp = c(-1, 1),
             df = 100, alpha = 0.05, alternative = "two.one.sided")

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