multcomp (version 0.4-8)

cholesterol: Cholesterol Reduction Data Set

Description

Cholesterol reduction for five treatments; data set taken from Westfall et al. (1999, p. 153). All pairwise comparisons according to Tukey in a balanced one-way layout.

Usage

data(cholesterol)

source

P. H. Westfall, R. D. Tobias, D. Rom, R. D. Wolfinger, Y. Hochberg (1999). Multiple Comparisons and Multiple Tests Using the SAS System. Cary, NC: SAS Institute Inc.

Details

See Westfall et al. (1999, p. 153). The treatment formulations are defined as: 20mg one a day (1time), 10mg twice a day (2times) and 5mg four times a day (4times). In addition, two competing drugs were used as control (drugD) and (drugE).

Examples

data(cholesterol)

# adjusted p-values for all-pairwise comparisons in a one-way layout 
# tests for restricted combinations
simtest(response ~ trt, data=cholesterol, type="Tukey",
        ttype="logical")

# adjusted p-values all-pairwise comparisons in a one-way layout 
# (tests for free combinations -> p-values will be larger)
simtest(response ~ trt, data=cholesterol, type="Tukey",
        ttype="free")


# the following lines illustrate the basic principles of
# parameter estimation used in all functions in this package
# and how the low-level functions can be used with raw parameter
# estimates.

# the full design matrix (with reduced rank!)
x <- cbind(1, 
           matrix(c(rep(c(rep(1,10), rep(0,50)), 4), 
                    rep(1, 10)), nrow = 50))
y <- cholesterol$response

xpxi   <- mginv(t(x) %*% x)
rankx  <- sum(diag((xpxi %*% (t(x) %*% x))))
n      <- nrow(x)
p      <- ncol(x)
df     <- round(n-rankx)

# parameter estimates and their correlation
parm   <- xpxi %*% t(x) %*% y
mse    <- t(y-x %*% parm) %*% (y-x %*% parm)/df
covm   <- mse[1,1]*xpxi

# the contrast matrix
contrast <- contrMat(table(cholesterol$trt), type="Tukey")

# use the work-horse directly (and add zero column for the intercept)

csimint(estpar=parm, df=df, covm=covm, cmatrix=cbind(0, contrast))    
csimtest(estpar=parm, df=df, covm=covm, cmatrix=cbind(0, contrast),
         ttype="logical")      

# only a subset of all pairwise hypotheses:
#
# * drug D versus all other formulations and
# * all pairwise comparisions for "1time", "2times" and "4times"
#
csubset = contrast[c(1,3,5,6,8,10),]
csubset
simint(response ~ trt, data=cholesterol, cmatrix = csubset)