Quantiles for Dunnett's Comparisons with Control

DESCRIPTION:

Computes a quantile of Dunnett's pivotal quantity for use in multiple comparisons.

USAGE:

qdunnett(p, k, df, nvec, control, two.sided=T) 

REQUIRED ARGUMENTS:

p
the probability lying below the desired quantile.
k
a scalar, the number of treatments or quantities to be compared (including the control); missing values and Inf's are not accepted.
df
a scalar, the error degrees of freedom. Inf is accepted (though specifying df=Inf will result in the use of df=1000). Missing values are not allowed.
nvec
a vector of length k whose values are proportional to the treatment sample sizes (or more generally, to the inverses of the variances of the estimators).
control
an integer specifying which of the treatments is to be considered the control.

OPTIONAL ARGUMENTS:

two.sided
a logical value, if TRUE a value for two-sided comparisons is returned.

VALUE:

the pth quantile of the distribution of the pivotal quantity specified below.

DETAILS:

Suppose X1, X2, ... Xk are independent normal variables with means 0 and variances proportional to the entries of 1/nvec. Let U be a random variable independent of the X's, such that df*U^2 is Chisquare with df degrees of freedom. The two-sided pivotal quantity is defined to be D = max{1<=i<=k,i!=c: |Xi-Xc|/(U*sqrt(1/nvec(i)+1/nvec(c))) }, where c denotes the control's subscript. The one-sided pivotal quantity is the above without absolute values. The function obtains the critical point by numerical integration and a secant method.

REFERENCES:

Hochberg, Y. and Tamhane, A. C.(1987). Multiple Comparison Procedures. Wiley, New York.

Hsu, Jason C. (1996). Multiple Comparisons: Theory and Methods. Chapman and Hall, London.

SEE ALSO:

, , , .

EXAMPLES:

qdunnett(.99, 10, 20, rep(3, 10), 10, two.side=F) 
qdunnett(.99, 10, 26, c(3, 3, 3, 3, 3, 3, 3, 3, 3, 9), 10, two.side=F)