case1402 {Sleuth3}

Effect of Ozone, SO2 and Drought on Soybean Yield

Description

In a completely randomized design with a 2x3x5 factorial treatment structure, researchers randomly assigned one of 30 treatment combinations to open-topped growing chambers, in which two soybean cultivars were planted. The responses for each chamber were the yields of the two types of soybean.

Usage

case1402

Format

A data frame with 30 observations on the following 5 variables.

Stress

a factor indicating treatment, with two levels "Well-watered" and "Stressed"

SO2

a quantitative treatment with three levels 0, 0.02 and 0.06

O3

a quantitative treatment with five levels 0.02, 0.05, 0.07, 0.08 and 0.10

Forrest

the yield of the Forrest cultivar of soybean (in kg/ha)

William

the yield of the Williams cultivar of soybean (in kg/ha)

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Heggestad, H.E. and Lesser, V.M. (1990). Effects of Chronic Doses of Sulfur Dioxide, Ozone, and Drought on Yields and Growth of Soybeans Under Field Conditions, Journal of Environmental Quality 19: 488–495.

Examples

str(case1402)
attach(case1402)

## EXPLORATION AND MODEL DEVELOPMENT; FORREST CULTIVAR
logForrest <- log(Forrest) 
# Fit model without interactions first--to examine partial residual plots.             
myLm1 <- lm(logForrest ~ Stress + SO2 + O3) 
if(require(car)){  # Use the car library
  crPlots(myLm1)   # Partial res plots => linear effects of SO2 and O3 look ok.
}  
myLm2 <- lm(logForrest ~ (Stress + SO2  + O3)^2) # all 2-factor interactions.
plot(myLm1, which=1)   # Residual plot looks ok.
anova(myLm1,myLm2) # Test for interactive effects.

## INFERENCE AND INTERPRETATION; FORREST CULTIVAR
summary(myLm1)   
betaF  <- myLm1$coef
# Effect of 0.01 increase in SO2 (note coeff is negative):
100*(1 - exp(0.01*betaF[3]))                
#1.655701;   a 1.65% decrease in median yield 
100*(1-exp(0.01*confint(myLm1,"SO2")))  
#3.772277 -0.5074294: 95% onfidence interval for effect of 0.01 increase in SO2
# Effect of 0.01 increase in O3 (note coeff is negative):
100*(1 - exp(0.01*betaF[4]))             
# 5.585979   I.e. a 5.6% decrease in median yield  
100*(1-exp(0.01*confint(myLm1,"O3")))   
#7.445966 3.688613: 95% confidence interval for effect of 0.01 increase in O3
# Effect of water stress (note coeff is positive for effect of well-watered):
100*(1 - exp(-betaF[2]))  # Get estimate for negative of this beta                
#3.220556:  a 3.2% decrease in median yield due to water stress
100*(1-exp(-confint(myLm1,2)))          
#-7.875521 13.17529: 95% confidence interval

## DISPLAY FOR PRESENTATION; FORREST CULTIVAR 
jO3     <- jitter(O3,factor=.25) # Jitter for plotting; jittering factor 0.25.
jS      <- jitter(SO2,factor=.25)  # Jitter SO2 for plotting.
cexfac  <- 1.75  # Use character expansion factor of 1.75 for plotting symbols.
opar <- par(no.readonly=TRUE)  # Store current graphics parameters settings
par(mfrow=c(1,2))  # Make a panel of 2 plots in 1 row.
myPointCode  <- ifelse(Stress=="Well-watered",21,24)
myPointColor <- ifelse(Stress=="Well-watered","green","orange")
par(mar=c(4.1,4.1,2.1,0.1))
plot(Forrest ~ jO3, log="y", ylab="Yield of Forrest Cultivar (kg/ha)",
	xlab=expression(paste(italic("Ozone ("),mu,"L/L), jittered")),
  pch=myPointCode, lwd=2, bg=myPointColor, cex=cexfac)
legend(.02,2400, c("Well-watered","Water Stressed"), pch=c(21,24),
  pt.cex=cexfac, pt.bg=c("green","orange"), pt.lwd=2, lty=c(3,1), lwd=c(2,2))
dummyO    <- seq(min(O3), max(O3), length=2)
curve1    <- exp(betaF[1] + betaF[3]*mean(SO2) + betaF[4]*dummyO)
curve2    <- exp(betaF[1] + betaF[2] + betaF[3]*mean(SO2)+ betaF[4]*dummyO)
lines(curve1 ~ dummyO,lwd=2)
lines(curve2 ~ dummyO,lwd=2,lty=3)

# PLOT FORREST VS SO2
par(mar=c(4.1,2.1,2.1,2.1)) # Change margins
plot(Forrest ~ jS, log="y", ylab="",
	xlab=expression(paste(italic("Sulfur Dioxide ("),mu,"L/L), jittered")),
  yaxt="n", pch=myPointCode, lwd=2, bg=myPointColor, cex=cexfac)
dummyS    <- seq(min(SO2),max(SO2),length=2)
curve1    <- exp(betaF[1] + betaF[3]*dummyS + betaF[4]*mean(O3))
curve2    <- exp(betaF[1] + betaF[2] + betaF[3]*dummyS + betaF[4]*mean(O3))
lines(curve1 ~ dummyS,lwd=2)
lines(curve2 ~ dummyS,lwd=2,lty=3)
par(opar) # Restore previous graphics parameter settings

detach(case1402)