https://github.com/cran/mratios
Tip revision: 2b6c94f552ca2e80d2e1fe52ed99dbef97d5a778 authored by Frank Schaarschmidt on 22 October 2008, 00:00:00 UTC
version 1.3.9
version 1.3.9
Tip revision: 2b6c94f
simtest.ratio.Rd
\name{simtest.ratio}
\alias{simtest.ratio}
\alias{simtest.ratioI}
\title{ Simultaneous tests for ratios of normal means }
\description{
Performs simultaneous tests for several ratios of linear combinations of treatment means in the normal one-way ANOVA model with homogeneous variances.
}
\usage{
simtest.ratio(formula, data, type = "Dunnett", base = 1,
alternative = "two.sided", Margin.vec = NULL, FWER = 0.05,
Num.Contrast = NULL, Den.Contrast = NULL, names = TRUE)
}
\arguments{
\item{formula}{ A formula specifying a numerical response and a grouping factor (e.g., response ~ treatment) }
\item{data}{ A dataframe containing the response and group variable }
\item{type}{ type of contrast, with the following options:
\itemize{
\item \bold{"Dunnett":} many-to-one comparisons, with control in the denominator
\item \bold{"Tukey":} all-pair comparisons
\item \bold{"Sequen":} comparison of consecutive groups, where the group with lower order is the denomniator
\item \bold{"AVE":} comparison of each group with average of all others, where the average is taken as denominator
\item \bold{"GrandMean":} comparison of each group with grand mean of all groups, where the grand mean is taken as denominator
\item \bold{"Changepoint":} ratio of averages of groups of higher order divided by averages of groups of lower order
\item \bold{"Marcus":} Marcus contrasts as ratios
\item \bold{"McDermott":} McDermott contrasts as ratios
\item \bold{"Williams":} Williams contrasts as ratios
\item \bold{"UmbrellaWilliams":} Umbrella-protected Williams contrasts as ratios
}
Note: type is ignored if Num.Contrast and Den.Contrast are specified by the user (See below).
}
\item{base}{ a single integer specifying the control (i.e. denominator) group for the Dunnett contrasts, ignored otherwise }
\item{alternative}{ a character string:
\itemize{
\item \bold{"two.sided":} for two-sided tests
\item \bold{"less":} for lower tail tests
\item \bold{"greater":} for upper tail tests
}}
\item{Margin.vec}{ a single numerical value or vector of Margins under the null hypotheses, default is 1 }
\item{FWER}{ a single numeric value specifying the family-wise error rate to be controlled }
\item{Num.Contrast}{ Numerator contrast matrix, where columns correspond to groups and rows correspond to contrasts }
\item{Den.Contrast}{ Denominator contrast matrix, where columns correspond to groups and rows correspond to contrasts }
\item{names}{ a logical value: if TRUE, the output will be named according to names of user defined contrast or factor levels }
}
\details{
Given a one-way ANOVA model, the interest is in simultaneous tests for several ratios of linear combinations of the treatment means.
Let us denote the ratios by \eqn{\gamma_i, i=1,...,r}, and let \eqn{\psi_i, i=1,...,r}, denote the relative margins against which we compare the ratios.
For example, upper-tail simultaneous tests for the ratios are stated as
\deqn{H_0i: \gamma_i <= \psi_i }
versus
\deqn{H_1i: \gamma_i > \psi_i, i=1,...,r}.
The associated likelihood ratio test statistic \eqn{T_i} has a t-distribution.
For multiplicity adjustments, we use the joint distribution of the \eqn{T_i} , \eqn{i=1,...,r},
which under the null hypotheses follows a central r-variate t-distribution.
Adjusted p-values can be calculated by adapting the results of Westfall et al. (1999) for ratio formatted hypotheses.
}
\value{
An object of class simtest.ratio containing:
\item{estimate }{a (named) vector of estimated ratios}
\item{teststat }{ a (named) vector of the calculated test statistics}
\item{Num.Contrast }{the numerator contrast matrix}
\item{Den.Contrast }{the denominator contrast matrix}
\item{CorrMat }{the correlation matrix of the multivariate t-distribution calculated under the null hypotheses}
\item{critical.pt }{the equicoordinate critical value of the multi-variate t-distribution for a specified FWER}
\item{p.value.raw }{a (named) vector of unadjusted p-values}
\item{p.value.adj }{a (named) vector of p-values adjusted for multiplicity}
\item{Margin.vec }{the vector of margins under the null hypotheses}
and some other input arguments.
}
\references{
Dilba, G., Bretz, F., and Guiard, V. (2006): Simultaneous confidence sets and confidence intervals for multiple ratios. Journal of Statistical Planning and Inference 136, 2640-2658.
Westfall, P.H., Tobias, R.D., Rom, D., Wolfinger, R.D., and Hochberg, Y. (1999): Multiple comparisons and multiple tests using the SAS system. SAS Institute Inc. Cary, NC, 65-81.
}
\author{
Gemechis Dilba, Frank Schaarschmidt }
\seealso{ While \code{print.simtest.ratio} produces a small default print-out of the results,
\code{summary.simtest.ratio} can be used to produce a more detailed print-out, which is recommended if user-defined contrasts are used,
\code{sci.ratio} for constructing simultaneous confidence intervals for ratios in oneway layout
See \code{summary.glht(multcomp)} for multiple tests for parameters of \code{lm}, \code{glm}.
}
\examples{
library(mratios)
# # #
# User-defined contrasts for comparisons
# between Active control, Placebo and three dosage groups:
data(AP)
AP
boxplot(pre_post~treatment, data=AP)
# Test whether the differences of doses 50, 100, 150 vs. Placebo
# are non-inferior to the difference of Active control vs. Placebo
# User-defined contrasts:
# Numerator Contrasts:
NC <- rbind(
"(D100-D0)" = c(0,-1,1,0,0),
"(D150-D0)" = c(0,-1,0,1,0),
"(D50-D0)" = c(0,-1,0,0,1))
# Denominator Contrasts:
DC <- rbind(
"(AC-D0)" = c(1,-1,0,0,0),
"(AC-D0)" = c(1,-1,0,0,0),
"(AC-D0)" = c(1,-1,0,0,0))
NC
DC
noninf <- simtest.ratio(pre_post ~ treatment, data=AP,
Num.Contrast=NC, Den.Contrast=DC, Margin.vec=c(0.9,0.9,0.9),
alternative="greater")
summary( noninf )
# # #
# Some more examples on standard multiple comparison procedures
# stated in terms of ratio hypotheses:
# Comparisons vs. Control:
many21 <- simtest.ratio(pre_post ~ treatment, data=AP,
type="Dunnett")
summary(many21)
# Let the Placebo be the control group, which is the second level
# in alpha-numeric order. A simultaneous test for superiority of
# the three doses and the Active control vs. Placebo could be
# done as:
many21P <- simtest.ratio(pre_post ~ treatment, data=AP,
type="Dunnett", base=2, alternative="greater", Margin.vec=1.1)
summary(many21P)
# All pairwise comparisons:
allpairs <- simtest.ratio(pre_post ~ treatment, data=AP,
type="Tukey")
summary(allpairs)
# # #
# Comparison to grand mean of all strains
# in the Penicillin example:
data(Penicillin)
CGM <- simtest.ratio(diameter~strain, data=Penicillin, type="GrandMean")
CGM
summary(CGM)
}
\keyword{ htest }
\concept{ratio}
\concept{multiple testing}