qDunnett {PMCMRplus}

Dunnett Distribution

Description

Distribution function and quantile function for the distribution of Dunnett's many-to-one comparisons test.

Usage

qDunnett(p, n0, n)

pDunnett(q, n0, n, lower.tail = TRUE)

Arguments

p

vector of probabilities.

n0

sample size for control group.

n

vector of sample sizes for treatment groups.

q

vector of quantiles.

lower.tail

logical; if TRUE (default), probabilities are P[X \leq x] otherwise, P[X > x].

Details

Dunnett's distribution is a special case of the multivariate t distribution.

Let the total sample size be N = n_0 + \sum_i^m n_i, with m the number of treatment groups, than the quantile T_{m v \rho \alpha} is calculated with v = N - k degree of freedom and the correlation \rho

\rho_{ij} = \sqrt{\frac{n_i n_j} {\left(n_i + n_0\right) \left(n_j+ n_0\right)}} ~~ (i \ne j).

The functions determines m via the length of the input vector n.

Quantiles and p-values are computed with the functions of the package mvtnorm.

Value

pDunnett gives the distribution function and qDunnett gives its inverse, the quantile function.

Note

The results are seed depending.

See Also

qmvt pmvt dunnettTest

Examples

## Table gives 2.34 for df = 6, m = 2, one-sided
set.seed(112)
qval <- qDunnett(p = 0.05, n0 = 3, n = rep(3,2))
round(qval, 2)
set.seed(112)
pDunnett(qval, n0=3, n = rep(3,2), lower.tail = FALSE)

## Table gives 2.65 for df = 20, m = 4, two-sided
set.seed(112)
qval <- qDunnett(p = 0.05/2, n0 = 5, n = rep(5,4))
round(qval, 2)
set.seed(112)
2 * pDunnett(qval, n0= 5, n = rep(5,4), lower.tail= FALSE)