tTestAlpha.RdCompute the Type I Error level necessary to achieve a specified power for a one- or two-sample t-test, given the sample size(s) and scaled difference.
numeric vector of sample sizes. When sample.type="one.sample",
n.or.n1 denotes \(n\), the number of observations in the single sample. When sample.type="two.sample", n.or.n1 denotes \(n_1\), the number
of observations from group 1.
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.
numeric vector of sample sizes for group 2. The default value is the value of
n.or.n1. This argument is ignored when sample.type="one.sample".
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.
numeric vector specifying the ratio of the true difference (\(\delta\)) to the population standard deviation (\(\sigma\)). This is also called the “scaled difference”.
numeric vector of numbers between 0 and 1 indicating the power
associated with the hypothesis test. The default value is power=0.95.
character string indicating whether to compute power based on a one-sample or
two-sample hypothesis test. When sample.type="one.sample", the computed
power is based on a hypothesis test for a single mean. When sample.type="two.sample", the computed power is based on a hypothesis test
for the difference between two means. The default value is sample.type="one.sample" unless the argument n2 is supplied.
character string indicating the kind of alternative hypothesis. The possible values
are "two.sided" (the default), "greater", and "less".
logical scalar indicating whether to compute the power based on an approximation to
the non-central t-distribution. The default value is FALSE.
numeric scalar indicating the tolerance argument to pass to the
uniroot function.
The default value is tol=1e-7.
positive integer indicating the maximum number of iterations
argument to pass to the uniroot function. The default value is
maxiter=1000.
Formulas for the power of the t-test for specified values of
the sample size, scaled difference, and Type I error level are given in
the help file for tTestPower. The function tTestAlpha
uses the uniroot search algorithm to determine the
required Type I error level for specified values of the sample size, power,
and scaled difference.
numeric vector of Type I error levels.
See tTestPower.
See tTestPower.
# Look at how the required Type I error level for the one-sample t-test
# decreases with increasing sample size. Set the power to 80% and
# the scaled difference to 0.5.
seq(5, 30, by = 5)
#> [1] 5 10 15 20 25 30
#[1] 5 10 15 20 25 30
alpha <- tTestAlpha(n.or.n1 = seq(5, 30, by = 5),
power = 0.8, delta.over.sigma = 0.5)
round(alpha, 2)
#> [1] 0.65 0.45 0.29 0.18 0.11 0.07
#[1] 0.65 0.45 0.29 0.18 0.11 0.07
#----------
# Repeat the last example, but use the approximation.
# Note how the approximation underestimates the power
# for the smaller sample sizes.
#----------------------------------------------------
alpha <- tTestAlpha(n.or.n1 = seq(5, 30, by = 5),
power = 0.8, delta.over.sigma = 0.5, approx = TRUE)
round(alpha, 2)
#> [1] 0.63 0.46 0.30 0.18 0.11 0.07
#[1] 0.63 0.46 0.30 0.18 0.11 0.07
#----------
# Look at how the required Type I error level for the two-sample
# t-test decreases with increasing scaled difference. Use
# a power of 90% and a sample size of 10 in each group.
seq(0.5, 2, by = 0.5)
#> [1] 0.5 1.0 1.5 2.0
#[1] 0.5 1.0 1.5 2.0
alpha <- tTestAlpha(10, sample.type = "two.sample",
power = 0.9, delta.over.sigma = seq(0.5, 2, by = 0.5))
round(alpha, 2)
#> [1] 0.82 0.35 0.06 0.01
#[1] 0.82 0.35 0.06 0.01
#----------
# Look at how the required Type I error level for the two-sample
# t-test increases with increasing values of required power. Use
# a sample size of 20 for each group and a scaled difference of
# 1.
alpha <- tTestAlpha(20, sample.type = "two.sample", delta.over.sigma = 1,
power = c(0.8, 0.9, 0.95))
round(alpha, 2)
#> [1] 0.03 0.07 0.14
#[1] 0.03 0.07 0.14
#----------
# Clean up
#---------
rm(alpha)