Random: Random Data Examples

In byandell/pda: Practial Data Analysis for Designed Experiments

Description

Consider a population of classes, say the counties of Wisconsin, with an arbitrary class in this population labeled by u. This class represents a sub-population of elements, say the population of farms in county u. If this class is selected for the experiment, an independently selected random sample of its elements (farms) would be selected for measurement, for instance of annual milk production per farm. The key questions concern estimating the average response across the population (state) and understanding the sources of variation in this measurement. Note that a different way to run the experiment would be to take a random sample of all elements (all farms in the state), without regard to which class (county) they come from. This latter design structure is completely randomized, while the former has two stages of randomization. Substantial variation among classes (counties) would be confounded with element-to-element variation (among farms) in the latter design.

Usage

data( Random )

See Also

Rantwo

Examples

data( Random )

# Figure G:19.1 Random model histograms
tmpdata = list( "(c) centered element values" = mean( Random ) +
    unlist( apply( Random, 2, function(x){x-mean(x)} )),
  "(b) class means" = apply( Random, 2, mean ),
  "(a) responses" = unlist( Random ))
tmpg = NULL
for( i in names( tmpdata ))
  tmpg = c( tmpg, rep( i, length( tmpdata[[i]] )))
tmpdata = data.frame( x = unlist( tmpdata ), g = tmpg )
histogram( ~ x | g, tmpdata, layout=c(1,3), nint = 30 )

# Figure G:19.2 Random model boxplots and tree diagram
tmp <- order( apply( Random, 2, median ) )
boxplot( as.list( Random[ , tmp ] ) )
#axis( 1, tmp, names( Random ) )
mtext( "(a) box-plots by class", 1, 2 )

plot( c(0.5,3.5), range( Random ), type = "n",
   xaxt = "n", xlab = "", ylab = "" )
mtext( c("mean","class","element"), 1, 0.5, at = 1:3 )
mtext( "(b) tree diagram", 1, 2 )
mtext( "response", 2, 2 )

Random.mean <- mean(unlist(Random))
Random.class <- apply(Random,2,mean)
points( 1, Random.mean )
points( rep( 2, length( Random ) ), Random.class )
points( rep( 3, length( unlist( Random ) ) ), unlist( Random ) )
branch( Random.mean, Random.class, 1:2, flip = TRUE )
for ( i in names( Random ) )
   branch( mean( Random[[i]] ), Random[[i]], 2:3, flip = TRUE )

# set up data for formal analysis
Random.frame <- data.frame( response = c( as.matrix( Random )))
Random.frame$class <- factor( rep( 1:10, rep( 10,10 )))

# one-factor anova (using aov() and fixed effects )
summary( aov( response ~ class, Random.frame ))
# one-factor anova (using aov() and random effects )
Random.ranaov <- aov( response ~ Error(class), Random.frame )

# one-factor anova (using lme() and random effects )
library( lme4 )
Random.lme <- lmer(response ~ 1 + (1|class), Random.frame )
summary( Random.lme )
VarCorr( Random.lme )

byandell/pda documentation built on May 13, 2019, 9:27 a.m.