Empirical power of a t-test

Source: R/a3_power.R

This function takes a reference mean value, sample size, mean, standard deviation, significance level and computes the empirical power of R randomly drawn normally distributed samples with mean mu, standard deviation sd and sample size n. The function can compute the power of one-sample t-tests and two-sample t-tests (variance is always assumed to be equal). This function will always return the data it generates internally because its focus is not on efficiency but rather reproducibility

emp_power(n, mu, mu0, sd, alpha = 0.05, R = 1000, type = c("one_sample",
  "two_sample"), ...)

Arguments

n

numeric. sample size
mu

mean value used to draw random normal samples. See ?rnorm() for more information
mu0

numeric. mean of control group if running a two-sample t-test or, if type = "one_sample", a value indicating the true value of the mean (or difference in means if you are performing a one sample test). See ?t.test() for more information
sd

standard deviation used to draw random normal samples
alpha

significance level
R

number of replications
type

string. if 'one_sample', then a one-sample t-test, else a two-sample t-test
...

optional arguments. You may pass selected parameters from the t.test() function. You may also pass the following parameters:

  • n0: numeric. sample size of control group if running a two-sample t-test. If not supplied then the function will use the value of n defined above.

  • sd0: numeric. standard deviation of control group if running a two-sample t-test. If not supplied then the function will use the value of sd defined above.

  • alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. See ?t.test() for more information

Note that you are required to either pass all parameters related to the control group (n0, mu0, sd0) or a parameter related to the reference mean (ref_mu).

Value

list containing:

  • inputs: list. user input values

  • data: matrix. values of R samples of size n with mean mu and standard deviation sd drawn from a normal distribution using rnorm()

  • p_values: vector. resulting p-values of R tests comparing the samples against the reference mean ref_mu

  • power: vector. power calculated by taking the proportion of p-values for which the value falls below or is equal to the significance level alpha

  • se :standard error of the power estimate. Calculated using the SE formula of a proportion. For more information, see the reference to Rizzo below.

See also

Rizzo, Maria L. 'Statistical Computing with R. Chapman and Hall/CRC, 2007'. (pp. 167-169)