Tukey: Tukey & Mandel Interactions

In byandell/pda: Practial Data Analysis for Designed Experiments

Description

A plant geneticist wanted to compare the growth characteristics of two inbred lines A and B with a hybrid combination H. The plants were grown at field stations at three latitudes, 25, 35, 45, and a number of measurements were taken. Unfortunately, the records were burned and the scientist only has the mean values from each station. The data suggest that genotype and latitude are not additive. All three lines appear to perform equally well at latitude 25. Line A grows shorter while line B and the hybrid H Grow taller as latitude increases. The hybrid shows evidence of ‘hybrid vigor’, doing much better than either parent line at higher latitudes.

Usage

data(Tukey)

Format

Tukey data frame with 9 observations on 3 variables.

[,1]	geno	factor	genotype
[,2]	lat	factor	latitude
[,3]	y	numeric	response

References

Milliken GA and Johnson DE (1989) Analysis of Messy Data vol. 2: Non-replicated Experiments. Chapman & Hall, London.

See Also

tukey.plot, margin.plot.

Examples

###NOTE: These data differ somewhat from the book figures.
data( Tukey )
Tukey$geno <- ordered( Tukey$geno, c("A","H","B") )
Tukey$lat <- ordered( Tukey$lat )

# Figure C:9.3  Interaction Plots for Tukey Data

trellis.par.set(theme=col.whitebg())
print(xyplot(y ~ lat, Tukey, groups = geno, cex = 2,
               pch = levels( Tukey$geno ), type = "b",
   xlab = "(a) latitude by geno", ylab = "height",
   main = "Figure C:9.3" ),
   more = TRUE, split = c(1,1,2,1) )
print(xyplot(y ~ geno, Tukey, groups = lat, cex = 2,
               pch = levels( Tukey$lat ), type = "b",
   xlab = "(b) geno by latitude", ylab = "height",
   main = "Tukey Interaction Plot" ),
   split = c(2,1,2,1) )

# Figure C:9.4 Tukey raw margin plots

tmpar <- par( mfrow = c(1,2) )

attach( Tukey )
margin.plot( lat, y, geno, xlim = c(95,105), error = "red",
   xlab = "(a) lat marginals by geno", ylab = "height",
   xpos = 103.5, ypos = 100, mod = "",
   main = "Figure C:9.4",
   more = TRUE, split = c(1,1,2,1) )
margin.plot( lat, y, geno, orient = "switch", error = "red",
   xlab = "(b) geno marginals by lat", ylab = "height",
   xpos = 115, ypos = 100, mod = "",
   main = "Raw Margin Plot",
   split = c(2,1,2,1) )
detach()

# Figure C:9.5 Tukey fitted margin plots

attach( Tukey )
Tukey.fit <- tukey.plot( lat, y, geno,
   xlab = "(a) lat marginals by geno", ylab = "height",
   main = "Figure C:9.5",
   more = TRUE, split = c(1,1,2,1) )
tukey.plot( geno, y, lat,
   xlab = "(b) geno marginals by lat", ylab = "height",
   main = "Fitted Margin Plot",
   split = c(2,1,2,1) )
detach()

Tukey.fit$lsm
summary.aov( Tukey.fit$reduced )
summary.aov( Tukey.fit$full )

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