case1002: The Energy Costs of Echolocation by Bats

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

The Energy Costs of Echolocation by Bats

Description

The data are on in–flight energy expenditure and body mass from 20 energy studies on three types of flying vertebrates: echolocating bats, non–echolocating bats and non–echolocating birds.

Usage

case1002

Format

A data frame with 20 observations on the following 3 variables.

Mass

mass (in grams)

Type

a factor with 3 levels indicating the type of flying vertebrate: non-echolocating bats, non-echolocating birds, echolocating bats

Energy

in–flight energy expenditure (in W)

Source

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

References

Speakman, J.R. and Racey, P.A. (1991). No cost of Echolocation for Bats in Flight, Nature 350: 421–423.

Examples

str(case1002)
attach(case1002)
    
## EXPLORATION
plot(Energy~Mass, case1002, log="xy", xlab = "Body Mass (g) (log scale)",
  ylab = "Energy Expenditure (W) (log scale)", 
  pch = ifelse(Type=="echolocating bats", 19,
     ifelse(Type=="non-echolocating birds", 21, 24)))
legend(7, 50, pch=c(24, 21, 19),
     c("Non-echolocating bats", "Non-echolocating birds","Echolocating bats"))

logEnergy  <- log(Energy)
logMass <- log(Mass)
myLm2 <- lm(logEnergy ~ logMass + Type + logMass:Type)
plot(myLm2, which=1)                
myLm3 <- update(myLm2, ~ . - logMass:Type)  
anova(myLm3, myLm2)   # Test for interaction with extra ss F-test

## INFERENCE AND INTERPRETATION
myLm4 <- update(myLm3, ~ . - Type)  # Reduced model...with no effect of Type
anova(myLm4, myLm3)   # Test for Type effect
myType <- factor(Type,
 levels=c("non-echolocating bats","echolocating bats","non-echolocating birds"))
myLm3a <- lm(logEnergy ~ logMass + myType) 
summary(myLm3a)
100*(exp(myLm3a$coef[3]) - 1) 
100*(exp(confint(myLm3a,3))-1)  
# Conclusion: Adjusted for body mass, the median energy expenditure for 
# echo-locating bats exceeds that for echo-locating bats by an estimated 
# 8.2% (95% confidence interval: 29.6% LESS to 66.3% MORE) 

# DISPLAY FOR PRESENTATION 
myPlotCode    <- ifelse(Type=="non-echolocating birds",24,21)        
myPointColor  <- ifelse(Type=="echolocating bats","green","white")  
plot(Energy ~ Mass, log="xy", xlab="Body Mass (g); Log Scale ",
  ylab="In-Flight Energy Expenditure (W); Log Scale",
  main="In-Flight Energy Expenditure Study",
  pch=myPlotCode,bg=myPointColor,lwd=2, cex=1.5) 
dummyMass  <- seq(5,800,length=50)
beta       <- myLm3$coef
curve1     <- exp(beta[1] + beta[2]*log(dummyMass))
curve2     <- exp(beta[1] + beta[2]*log(dummyMass) + beta[3])
curve3     <- exp(beta[1] + beta[2]*log(dummyMass) + beta[4])
lines(curve1 ~ dummyMass)
lines(curve2 ~ dummyMass, lty=2)
lines(curve3 ~ dummyMass, lty=3)
legend(100,3,
  c("Echolocating Bats","Non-Echolocating Bats","Non-Echolocating Birds"),
  pch=c(21,21,24),lwd=2,pt.cex=c(1.5,1.5,1.5),pt.lwd=c(2,2,2),
  pt.bg=c("green","white","white"),lty=c(1,2,3))
  
detach(case1002)

Sleuth3 documentation built on May 29, 2024, 2:56 a.m.