getDesignANOVA {lrstat}

Power and sample size for one-way ANOVA

Description

Obtains the power and sample size for one-way analysis of variance.

Usage

getDesignANOVA(
  beta = NA_real_,
  n = NA_real_,
  ngroups = 2,
  means = NA_real_,
  stDev = 1,
  allocationRatioPlanned = NA_real_,
  rounding = TRUE,
  alpha = 0.05
)

Arguments

beta

The type II error.

n

The total sample size.

ngroups

The number of treatment groups.

means

The treatment group means.

stDev

The common standard deviation.

allocationRatioPlanned

Allocation ratio for the treatment groups. It has length ngroups - 1 or ngroups. If it is of length ngroups - 1, then the last treatment group will assume value 1 for allocation ratio.

rounding

Whether to round up sample size. Defaults to 1 for sample size rounding.

alpha

The two-sided significance level. Defaults to 0.05.

Details

Let \{\mu_i: i=1,\ldots,k\} denote the group means, and \{r_i: i=1,\ldots,k\} denote the randomization probabilities to the k treatment groups. Let \sigma denote the common standard deviation, and n denote the total sample size. Then the F-statistic

F = \frac{SSR/(k-1)}{SSE/(n-k)} \sim F_{k-1, n-k, \lambda},

where

\lambda = n \sum_{i=1}^k r_i (\mu_i - \bar{\mu})^2/\sigma^2

is the noncentrality parameter, and \bar{\mu} = \sum_{i=1}^k r_i \mu_i.

Value

An S3 class designANOVA object with the following components:

• power: The power to reject the null hypothesis that there is no difference among the treatment groups.

• alpha: The two-sided significance level.

• n: The number of subjects.

• ngroups: The number of treatment groups.

• means: The treatment group means.

• stDev: The common standard deviation.

• effectsize: The effect size.

• allocationRatioPlanned: Allocation ratio for the treatment groups.

• rounding: Whether to round up sample size.

Author(s)

Kaifeng Lu, [e-mail]

Examples

(design1 <- getDesignANOVA(
  beta = 0.1, ngroups = 4, means = c(1.5, 2.5, 2, 0),
  stDev = 3.5, allocationRatioPlanned = c(2, 2, 2, 1),
  alpha = 0.05))