case1101: Alcohol Metabolism in Men and Women

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

Description

These data were collected on 18 women and 14 men to investigate a certain theory on why women exhibit a lower tolerance for alcohol and develop alcohol–related liver disease more readily than men.

Usage

case1101

Format

A data frame with 32 observations on the following 5 variables.

Subject

subject number in the study

Metabol

first–pass metabolism of alcohol in the stomach (in mmol/liter-hour)

Gastric

gastric alcohol dehydrogenase activity in the stomach (in mumol/min/g of tissue)

Sex

sex of the subject

Alcohol

whether the subject is alcoholic or not

Source

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

Examples

str(case1101)
attach(case1101)
      
## EXPLORATION
library(lattice) 
xyplot(Metabol~Gastric|Sex*Alcohol, case1101)  

myPch <- ifelse(Sex=="Female",24,21)
myBg  <- ifelse(Alcohol=="Alcoholic","gray","white")
plot(Metabol~Gastric, pch=myPch,bg=myBg,cex=1.5)
legend(1,12, pch=c(24,24,21,21), pt.cex=c(1.5,1.5,1.5,1.5),
  pt.bg=c("white","gray", "white", "gray"),
  c("Non-alcoholic Females", "Alcoholic Females",
  "Non-alcoholic Males", "Alcoholic Males"))                               
identify(Metabol ~ Gastric)
# Left click on outliers to show case number; Esc when finished.

myLm1 <- lm(Metabol ~ Gastric + Sex + Gastric:Sex)  
plot(myLm1, which=1)                                
plot(myLm1, which=4) # Show Cook's Distance; note cases 31 and 32.
plot(myLm1, which=5) # Note leverage and studentized residual for cases 31 and 32.
subject  <- 1:32  # Create ID number from 1 to 32

# Refit model without cases 31 and 32:
myLm2 <- update(myLm1, ~ ., subset = (subject !=31 & subject !=32))      
plot(myLm2,which=1)
plot(myLm2,which=4)
plot(myLm2,which=5)
summary(myLm1)                                                                   
summary(myLm2) # Significance of interaction terms hinges on cases 31 and 32.

myLm3 <- update(myLm2, ~ . - Gastric:Sex) #Drop interaction (without 31,32).
summary(myLm3)
if(require(car)){   # Use the car library
crPlots(myLm3) # Show partial residual (component + residual) plots.
}

## INFERENCE AND INTERPRETATION
summary(myLm3)
confint(myLm3,2:3)

## DISPLAY FOR PRESENTATION 
myCol <- ifelse(Sex=="Male","blue","red")
plot(Metabol ~ Gastric,  
  xlab=expression("Gastric Alcohol Dehydrogenase Activity in Stomach ("*mu*"mol/min/g of Tissue)"), 
  ylab="First-pass Metabolism in the Stomach (mmol/liter-hour)",
  main="First-Pass Alcohol Metabolism and Enzyme Activity for 18 Females and 14 Males", 
  pch=myPch, bg=myBg,cex=1.75, col=myCol, lwd=1)
legend(0.8,12.2, c("Females", "Males"), lty=c(1,2),
    pch=c(24,21), pt.cex=c(1.75,1.75), col=c("red", "blue"))
dummyGastric <- seq(min(Gastric),3,length=100)
beta <- myLm3$coef
curveF <- beta[1] + beta[2]*dummyGastric
curveM <- beta[1] + beta[2]*dummyGastric + beta[3]
lines(curveF ~ dummyGastric, col="red")
lines(curveM ~ dummyGastric, col="blue",lty=2)
text(.8,10,"gray indicates alcoholic",cex = .8, adj=0)

detach(case1101)

Example output

'data.frame':	32 obs. of  5 variables:
 $ Subject: int  1 2 3 4 5 6 7 8 9 10 ...
 $ Metabol: num  0.6 0.6 1.5 0.4 0.1 0.2 0.3 0.3 0.4 1 ...
 $ Gastric: num  1 1.6 1.5 2.2 1.1 1.2 0.9 0.8 1.5 0.9 ...
 $ Sex    : Factor w/ 2 levels "Female","Male": 1 1 1 1 1 1 1 1 1 1 ...
 $ Alcohol: Factor w/ 2 levels "Alcoholic","Non-alcoholic": 1 1 1 2 2 2 2 2 2 2 ...
integer(0)

Call:
lm(formula = Metabol ~ Gastric + Sex + Gastric:Sex)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.4427 -0.6111 -0.0326  0.5436  3.8759 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      -0.1973     0.8022  -0.246   0.8075  
Gastric           0.8369     0.4839   1.730   0.0947 .
SexMale          -0.9885     1.0724  -0.922   0.3645  
Gastric:SexMale   1.5069     0.5591   2.695   0.0118 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.207 on 28 degrees of freedom
Multiple R-squared:  0.8137,	Adjusted R-squared:  0.7938 
F-statistic: 40.77 on 3 and 28 DF,  p-value: 2.386e-10


Call:
lm(formula = Metabol ~ Gastric + Sex + Gastric:Sex, subset = (subject != 
    31 & subject != 32))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.59619 -0.60249 -0.04076  0.47590  1.64726 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      -0.1973     0.5860  -0.337   0.7391  
Gastric           0.8369     0.3535   2.368   0.0256 *
SexMale           0.2668     0.9932   0.269   0.7904  
Gastric:SexMale   0.7285     0.5394   1.351   0.1885  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8819 on 26 degrees of freedom
Multiple R-squared:  0.6729,	Adjusted R-squared:  0.6352 
F-statistic: 17.83 on 3 and 26 DF,  p-value: 1.711e-06


Call:
lm(formula = Metabol ~ Gastric + Sex, subset = (subject != 31 & 
    subject != 32))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.81012 -0.49381 -0.05505  0.52307  2.03515 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.6823     0.4701  -1.451 0.158244    
Gastric       1.1498     0.2710   4.242 0.000232 ***
SexMale       1.5276     0.3445   4.434 0.000139 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8953 on 27 degrees of freedom
Multiple R-squared:   0.65,	Adjusted R-squared:  0.6241 
F-statistic: 25.07 on 2 and 27 DF,  p-value: 7e-07

Loading required package: car
Loading required package: carData

Call:
lm(formula = Metabol ~ Gastric + Sex, subset = (subject != 31 & 
    subject != 32))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.81012 -0.49381 -0.05505  0.52307  2.03515 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.6823     0.4701  -1.451 0.158244    
Gastric       1.1498     0.2710   4.242 0.000232 ***
SexMale       1.5276     0.3445   4.434 0.000139 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8953 on 27 degrees of freedom
Multiple R-squared:   0.65,	Adjusted R-squared:  0.6241 
F-statistic: 25.07 on 2 and 27 DF,  p-value: 7e-07

            2.5 %   97.5 %
Gastric 0.5937204 1.705959
SexMale 0.8206476 2.234454

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.