Power and Sample Size for One-Way ANOVA — getDesignANOVA • lrstat

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.

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.

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 $\bar{\mu} = \sum_{i=1}^k r_i \mu_i$.

Author

Kaifeng Lu, kaifenglu@gmail.com

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))
#>   alpha     power   n ngroups stDev effectsize
#> 1  0.05 0.9007535 279       4   3.5 0.05164515