power: power for two independent groups when population standard...

In yelleKneK/SMSD: Sequential Methods for Study Design

power for two independent groups when population standard deviation known

Description

This function calculates the probability of Type II error when the sample size is known, and the required sample size to achieve a preassigned Type II error probability (beta) for a test of two independent groups. This function uses the $z$-distribution (note the more commonly used $t$-distribution) is used.

Usage

power(
  mu0,
  mu1,
  sigma,
  alpha,
  n = NULL,
  n1 = NULL,
  n2 = NULL,
  n_vals = NULL,
  beta = NULL,
  method = c("sample_size", "type_2", "type_2_seq")
)

Arguments

mu0	Population mean of group 0 (e.g., control).
mu1	Population mean of group 1 (e.g., experimental).
sigma	The population standard deviation, assumed equal across groups.
alpha	The Type I error rate.
n	The number of samples, used to calculate Type II error for a given sample size.
n1	The lowest number of samples to consider when generating a sequence of Type II errors.
n2	The highest number of samples to consider when generating a sequence of Type II errors.
n_vals	The number of samples to generate Type II error for.
beta	The desired Type II error rate, used when calculating the necessary sample size.
method	What should the function calculate, (1) "sample_size" returns the calculated sample size necessary to achieve a specified Type II error rate. (2) "type_2" returns the calculated Type II error rate for a given sample size. (3) "type_2_seq" returns a series of length "n_vals" of calculated type II error rates from n1 to n2.

Value

Depending on the method chosen the function returns either the necessary sample size to achieve a certain type II error, the type II error for a given sample size or a sequence of type II errors for different sample sizes.

References

Mukhopadhyay, N., \& de Silva, B. M. (2009). Sequential Methods and Their Applications. New York: CRC Press.

Examples

# Set parameter values
mu0 <- 0
mu1 <- 1
sigma <- 2
alpha <- 0.05
n <- 16

# Calculate type II error
t2 <- power(mu0 = mu0, mu1 = mu1, sigma = sigma,
            alpha = alpha , n = n, method="type_2")
t2

# Calculate sample size
beta <- 0.361
size <- power(mu0 = mu0, mu1 = mu1, sigma = sigma,
              alpha = alpha, beta = beta, method = "sample_size")
size

# Return sequence of type II errors
n1 <- 5
n2 <- 50
n_vals <- 10
seq_vals <- power(mu0 = mu0, mu1 = mu1, sigma=sigma, alpha = alpha,
                  n1 = n1, n2 = n2, n_vals = n_vals,
                  method = "type_2_seq")
seq_vals

yelleKneK/SMSD documentation built on Nov. 23, 2022, 6:40 p.m.