MKpower (version 1.0)

sim.power.t.test: Monte Carlo Simulations for Empirical Power of Two-sample t-Tests

Description

Simulate the empirical power and type-I-error of two-sample t-tests; i.e., classical (equal variances), Welch and Hsu t-tests.

Usage

sim.power.t.test(nx, rx, rx.H0 = NULL, ny, ry, ry.H0 = NULL, 
                 sig.level = 0.05, conf.int = FALSE, mu = 0, 
                 alternative = c("two.sided", "less", "greater"), 
                 iter = 10000)

Value

Object of class "sim.power.ttest" with the results of the three t-tests in the list elements Classical, Welch and Hsu. In addition, the simulation setup is saved in element SetUp.

Arguments

nx

single numeric, sample size of first group.

rx

function to simulate the values of first group (assuming H1).

rx.H0

NULL or function to simulate the values of first group (assuming H0).

ny

single numeric, sample size of second group.

ry

function to simulate the values of second group (assuming H1).

ry.H0

NULL or function to simulate the values of second group (assuming H0).

sig.level

significance level (type I error probability)

conf.int

logical, shall confidence intervals be computed. Increases computation time!

mu

true value of the location shift for the null hypothesis.

alternative

one- or two-sided test. Can be abbreviated.

iter

single integer, number of interations of the simulations.

Author

Matthias Kohl

Details

Functions rx and ry are used to simulate the data under the alternative hypothesis H1. If specified, functions rx.H0 and ry.H0 simulte the data unter the null hypothesis H0.

For fast computations functions from package matrixTests are used.

References

J. Hedderich, L. Sachs. Angewandte Statistik: Methodensammlung mit R. Springer 2018.

Hsu, P. (1938). Contribution to the theory of ``student's'' t-test as applied to the problem of two samples. Statistical Research Memoirs 2: 1-24.

Student (1908). The Probable Error of a Mean. Biometrika, 6(1): 1-25.

Welch, B. L. (1947). The generalization of ``Student's'' problem when several different population variances are involved. Biometrika, 34 (1-2): 28-35.

See Also

t.test, hsu.t.test, ttest

Examples

## Equal variance, small sample size
power.t.test(n = 5, delta = 2)
power.welch.t.test(n = 5, delta = 2)
power.hsu.t.test(n = 5, delta = 2)
sim.power.t.test(nx = 5, rx = rnorm, rx.H0 = rnorm,
                 ny = 5, ry = function(x) rnorm(x, mean = 2), ry.H0 = rnorm)

## Equal variance, moderate sample size
power.t.test(n = 25, delta = 0.8)
power.welch.t.test(n = 25, delta = 0.8)
power.hsu.t.test(n = 25, delta = 0.8)
sim.power.t.test(nx = 25, rx = rnorm, rx.H0 = rnorm,
                 ny = 25, ry = function(x) rnorm(x, mean = 0.8), ry.H0 = rnorm)

## Equal variance, high sample size
power.t.test(n = 100, delta = 0.4)
power.welch.t.test(n = 100, delta = 0.4)
power.hsu.t.test(n = 100, delta = 0.4)
sim.power.t.test(nx = 100, rx = rnorm, rx.H0 = rnorm,
                 ny = 100, ry = function(x) rnorm(x, mean = 0.4), ry.H0 = rnorm)

## Unequal variance, small sample size
power.welch.t.test(n = 5, delta = 5, sd1 = 1, sd2 = 3)
power.hsu.t.test(n = 5, delta = 5, sd1 = 1, sd2 = 3)
sim.power.t.test(nx = 5, rx = rnorm, rx.H0 = rnorm, 
                 ny = 5, ry = function(x) rnorm(x, mean = 5, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))
                 
## Unequal variance, moderate sample size
power.welch.t.test(n = 25, delta = 1.8, sd1 = 1, sd2 = 3)
power.hsu.t.test(n = 25, delta = 1.8, sd1 = 1, sd2 = 3)
sim.power.t.test(nx = 25, rx = rnorm, rx.H0 = rnorm, 
                 ny = 25, ry = function(x) rnorm(x, mean = 1.8, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))
                 
## Unequal variance, high sample size
power.welch.t.test(n = 100, delta = 0.9, sd1 = 1, sd2 = 3)
power.hsu.t.test(n = 100, delta = 0.9, sd1 = 1, sd2 = 3)
sim.power.t.test(nx = 100, rx = rnorm, rx.H0 = rnorm, 
                 ny = 100, ry = function(x) rnorm(x, mean = 0.9, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))
                 
## Unequal variance, unequal sample sizes
## small sample sizes
sim.power.t.test(nx = 10, rx = rnorm, rx.H0 = rnorm, 
                 ny = 5, ry = function(x) rnorm(x, mean = 5, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))
sim.power.t.test(nx = 5, rx = rnorm, rx.H0 = rnorm, 
                 ny = 10, ry = function(x) rnorm(x, mean = 3, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))

## Unequal variance, unequal sample sizes
## moderate sample sizes
sim.power.t.test(nx = 25, rx = rnorm, rx.H0 = rnorm, 
                 ny = 50, ry = function(x) rnorm(x, mean = 1.5, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))

## Unequal variance, unequal sample sizes
## high sample sizes
sim.power.t.test(nx = 100, rx = rnorm, rx.H0 = rnorm, 
                 ny = 200, ry = function(x) rnorm(x, mean = 0.6, sd = 3), 
                 ry.H0 = function(x) rnorm(x, sd = 3))