Cloning: Cloning virus in plant sap
In byandell/pda: Practial Data Analysis for Designed Experiments

Description Usage Format Source References Examples

A plant scientist measured the concentration of a particular virus in plant sap using ELISA (enzyme-linked immunosorbent assay) (Novy 1992). The study included 13 potato clones (plants reproduced asexually), with 2 commercial cultivars, 5 somatic hybrids, 5 progeny of the somatic hybrids, and one clone of Solanum etuberosum (a species related to potato). Of the 5 progeny of the somatic hybrids, two were classified as susceptible and three as resistant to the virus. The scientist wants to understand the resistance to the virus among these 13 clones. Plant sap was taken from 5 inoculated plants of each clone, for a total of 65 measurements of titer. Unfortunately, one measurement was lost during processing of the samples. Figure <A HREF="clondat.s">clondat.s</A> shows the raw data by clone. The (a) figure, ordered by clone identifier, indicates considerable range in center and spread but is otherwise not very informative. The (b) figure orders by clone mean, jittered to mitigate overlap, using a separate plot symbol for each clone. The dashed identity line helps track the spread around the mean. This latter plot suggests there is less spread in titer for clones at the extremes than for those in the middle of the range.

1 2	data(Cloning) data(ClonCrit)

Cloning data frame with 64 observations on 5 variables.

[,1]	clone	factor	clone identifier
[,2]	reps	factor	replication number
[,3]	titer	numeric	concentration of virus
[,4]	code	factor	plot code
[,5]	type	factor	cell type

ClonCrit data frame with 20 observations on 6 variables.

[,1]	set	factor	all data or balanced
[,2]	means	numeric	number of means
[,3]	SNK	numeric	Student-Neuman-Kuels
[,4]	DUNCAN	numeric	Duncan's Multiple Range
[,5]	REGWQ	numeric	REGWQ
[,6]	REGWF	numeric	REGWFtype

Professor Richard G Novy (mailto:novy@prairie.nodak.edu), Plant Sciences Department, ND St U

Novy RG (1992) “Characterization of somatic hybrids between Solanum etuberosum and diploid, tuber-bearing Solanums. PhD Dissertation, Department of Plant Pathology, UW-Madison. 123 pp.

data( Cloning )

Cloning <- Cloning[ !is.na(Cloning$titer), ]
Cloning$clone <- factor(Cloning$code)

# ANOVA table
Cloning.fit <- aov( titer ~ clone, Cloning )
summary( Cloning.fit )

# estimate means
attach( Cloning )
Cloning.means <- data.frame( clone=levels(code),
   pred=c( tapply( titer, code, mean )))
Cloning.means$sd <- c( tapply( titer, code,
   function( x ){ sqrt( var( x ) ) } ))
Cloning.means$n <- c( tapply( titer, code, length ))
Cloning.means$se <- Cloning.means$sd /
   sqrt( Cloning.means$n )
Cloning.means$type <- type[ !duplicated( code ) ]
detach( )

# or try the PDA routine:
Cloning.lsm <- lsmean( Cloning.fit )

# estimate common SD
std.dev( Cloning.fit )

# preselected contrasts
aov(titer ~ clone, Cloning, 
   subset = is.na( match( Cloning$type, c("cult","etb","odd") )))

# critical values for multiple comparisons (from SAS output)
Cloning.crit <- data.frame( all=c(306,555,737,530,278),
   bal=c(254,435,527,414,232),
   row.names=c("LSD","BON","SCHEFFE","HSD","WALLER") )
for (i in names(Cloning.crit))
   names(Cloning.crit[[i]]) <- row.names(Cloning.crit)

# critical values for multi-stage testing (MST) multiple comparisons
data( ClonCrit )
Cloning.tmp <- ClonCrit$set
ClonCrit$set <- NULL
ClonCrit <- split(ClonCrit,Cloning.tmp)
rm(Cloning.tmp)

# Figure B:4.3 Cloning Data by Group
print(stripplot(titer ~ clone, Cloning, jitter = TRUE,
  panel = function(x,y,...) {
    panel.abline(v=unclass(x),lty=3,col="grey")
    panel.stripplot(x,y,...)
  },
  xlab="(a) clone identifier",ylab="titer",
  main = "Figure B:4.3" ),
  more = TRUE, split = c(1,1,2,1))

Cloning$pred <- jitter( predict( Cloning.fit))
print( xyplot( titer ~ pred, Cloning, groups = code,
  type = "p", cex = 1, pch = levels( Cloning$code ),
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    panel.abline( 0, 1, lty = 2 )
  },
  xlab="(b) clone mean",ylab="titer",
  main = "Cloning Data by Group" ),
  split = c(2,1,2,1))

# Figure B:4.4 Plot of Clone Mean vs SD
print( xyplot( sd ~ pred, Cloning.means, groups = clone,
  type = "p", pch = levels( Cloning.means$clone ), cex = 2,
  xlab="(a) mean by clone identifier", ylab="clone SD",
  main = "Figure B:4.4" ),
  more = TRUE, split = c(1,1,2,1))
print( xyplot( sd ~ pred, Cloning.means, groups = type,
  type = "p", pch = levels( Cloning.means$type ), cex = 2,
  xlab="(b) mean by type", ylab="clone SD",
  main = "Clone Mean vs SD" ),
  split = c(2,1,2,1))

# Figure B:4.7 95% Critical Values by Groups
ci.plot( Cloning.fit, lsm = Cloning.lsm,
  rdf=df.resid( Cloning.fit), sort=TRUE, ylim = c(-150,2000),
  xlab = "", ylab = "(a) with common S",
  main = "Figure B:4.7",
  panelf = function(...) {
    panel.abline( h = 0, lty = 2 )
  },
  more = TRUE, split = c(1,1,2,1) )

ci.plot( Cloning.fit, lsm = Cloning.means,
  rdf = Cloning.means$n-1, sort=TRUE, ylim = c(-150,2000),
  xlab = "", ylab = "(b) with group SDs",
  main = "Cloning 95 % CIs",
  panelf = function(...) {
    panel.abline( h = 0, lty = 2 )
  },
  split = c(2,1,2,1) )

# Figure B:6.2 Cloning Unbalanced Multiple Comparisons
# critical values for Cloning data with all 13 groups
Cloning.x <- c( 2, max( ClonCrit$all$means ))
Cloning.y <- range( unlist( c( Cloning.crit$all,
   ClonCrit$all[,-1] )))
Cloning.tmp <- round( mean( Cloning.x ) )
Cloning.zaxis <- seq( 1.5, 5, .5 )
Cloning.z <- Cloning.zaxis * sqrt(2/5)*239

plot( Cloning.x, Cloning.y, type="n",
   xlab="(a) based on F test", ylab="" )
title( "Figure B:6.2(a) Unbalanced Comparisons" )
axis( 4, Cloning.z,
   labels = as.character( Cloning.zaxis ))
for ( i in c("LSD","BON","SCHEFFE","WALLER") ) {
	abline( Cloning.crit[i,"all"], 0, lty=2 )
	text( Cloning.tmp, Cloning.crit[i,"all"], i )
}
for ( i in c("REGWF") ) {
	lines( ClonCrit$all$means, ClonCrit$all[[i]] )
	text( Cloning.tmp, ClonCrit$all[[i]][Cloning.tmp], i )
}

plot( Cloning.x, Cloning.y, type="n",
   xlab = "(b) based on range", ylab = "critical value" )
title( "Figure B:6.2(b) Unbalanced Comparisons" )
axis( 4, Cloning.z, labels = as.character( Cloning.zaxis ))

Cloning.p <- NULL
for ( i in c("LSD","HSD") )
	Cloning.p[i] <- Cloning.crit[i,"all"]
for ( i in c("REGWQ","SNK","DUNCAN") )
	Cloning.p[i] <- ClonCrit$all[[i]][Cloning.tmp]
Cloning.p["SNK"] <- Cloning.p["SNK"] - 25
Cloning.p["HSD"] <- Cloning.p["HSD"] + 25
for ( i in c("LSD","HSD")) {
	abline( Cloning.crit[i,"all"], 0, lty=2 )
	text( Cloning.tmp, Cloning.p[i], i )
}
for ( i in c("REGWQ","SNK","DUNCAN") ) {
	lines( ClonCrit$all$means, ClonCrit$all[[i]] )
	text( Cloning.tmp, Cloning.p[i], i )
}
rm( Cloning.tmp, Cloning.x, Cloning.y, Cloning.p, Cloning.z )

# Figure B: Critical Values for Comparison of 9 Clones
# critical values for Cloning data with 9 groups
Cloning.x <- c( 2, max( ClonCrit$bal$means) )
Cloning.y <- range( unlist( c( Cloning.crit$bal,
   ClonCrit$bal[,-1] ) ) )
Cloning.tmp <- round( mean( Cloning.x ) )
Cloning.z <- Cloning.zaxis * sqrt( 2 / 4.91) * 198

plot( Cloning.x, Cloning.y, type="n",
   xlab="(a) based on F test", ylab="" )
title( "Figure B:6.3(a) Balanced Comparisons" )
axis(4, Cloning.z, lab = as.character( Cloning.zaxis ) )
for ( i in c("LSD","BON","SCHEFFE","WALLER") ) {
	abline( Cloning.crit[i,"bal"], 0, lty=2 )
	text( Cloning.tmp, Cloning.crit[i,"bal"], i )
}
for ( i in c("REGWF") ) {
	lines( ClonCrit$bal$means, ClonCrit$bal[[i]] )
	text( Cloning.tmp, ClonCrit$bal[[i]][Cloning.tmp], i )
}

plot( Cloning.x, Cloning.y, type="n",
   xlab="(b) based on range", ylab="critical value" )
title( "Figure B:6.3(b) Balanced Comparisons" )
axis(4, Cloning.z, labels = as.character( Cloning.zaxis ))
Cloning.p <- NULL
for ( i in c("LSD","HSD") )
	Cloning.p[i] <- Cloning.crit$bal[i]
for ( i in c("REGWQ","SNK","DUNCAN") )
	Cloning.p[i] <- ClonCrit$bal[[i]][Cloning.tmp]
Cloning.p["SNK"] <- Cloning.p["SNK"] - 25
Cloning.p["HSD"] <- Cloning.p["HSD"] + 25
for ( i in c("LSD","HSD") ) {
	abline( Cloning.crit[i,"bal"], 0, lty=2 )
	text( Cloning.tmp, Cloning.p[i], i )
}
for ( i in c("REGWQ","SNK","DUNCAN") ) {
	lines( ClonCrit$bal$means, ClonCrit$bal[[i]] )
	text( Cloning.tmp, Cloning.p[i], i )
}
rm( Cloning.tmp, Cloning.x, Cloning.y, Cloning.p, Cloning.z,
   Cloning.zaxis )

# Figure B:6.4 Critical Value by Number of Groups

Cloning.groups <- 2:20
Cloning.alpha <- .05

plot( range(Cloning.groups), c(1,6), type="n",
	xlab="number of groups", ylab="critical value" )
title( "Figure B:6.4 Critical Value by Number of Groups" )
axis(1,c(2,13))
# SCHEFFE
lines( Cloning.groups, sqrt( qchisq( 1 - Cloning.alpha,
   Cloning.groups - 1 ) ), lty=2 )
text( 13, 5, "SCHEFFE" )
# TUKEY's HSD
lines( Cloning.groups,
   c(2.77,3.32,3.63,3.86,4.03,4.17,4.29,4.39,4.47,4.55,4.62,
   4.68,4.74,4.8,4.84,4.89,4.93,4.97,5.01) / sqrt(2), lty=3 )
text( 13, 3, "HSD" )
# BON
Cloning.comp <- Cloning.groups * ( Cloning.groups - 1 )
lines( Cloning.groups,
   qnorm( 1 - Cloning.alpha / Cloning.comp ) )
text( 13, 3.8, "BONFERRONI" )
# LSD
lines( c(2,20), rep( qnorm( 1 - Cloning.alpha / 2), 2 ) )
text( 13, 1.6, "LSD" )

rm( Cloning.alpha, Cloning.groups, Cloning.comp )

# Figure B:6.5 Bonferroni Comparisons to Match Scheffe' Method

Cloning.groups <- 2:20
Cloning.alpha <- .05

# equivalent comparisons between B and S
Cloning.a <- log( Cloning.alpha / ( 2 * ( 1 - pnorm( sqrt(
   qchisq( .95, Cloning.groups - 1 ))))))
plot(Cloning.groups, Cloning.a, type="l", yaxt="n",
	xlab="number of groups", ylab="comparisons" )
title( "Figure B:6.5 Match of Bonferroni to Scheffe" )
axis( 1, c(2,13) )
axis( 2, log( c(1,10,78,1000,10000,100000,1000000) ),
	c("1","10","78","1000","10^4","10^5","10^6"), adj=1 )
axis( 2, log(100), FALSE )
lines( c(13,13), c(0,Cloning.a[12]), lty=2 )
lines( c(2,13), rep(log(78),2), lty=2 )

rm( Cloning.groups, Cloning.alpha, Cloning.a )