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)

Format

This data frame contains the following variables

trt

Treatment at 5 levels, see below.

response

Response variable.

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).

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.

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)