Dunnett function

Dunnett Distribution

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

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, $P[X > x]$.

Returns

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

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 $\rho$

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 .

Note

The results are seed depending.

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)

See Also

qmvt pmvt dunnettTest