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