case1702: Love and Marriage

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

Love and Marriage

Description

Thirty couples participated in a study of love and marriage. Wives and husbands responded separately to four questions:

1. What is the level of passionate love you feel for your spouse?

2. What is the level of passionate love your spouse feels for you?

3. What is the level of compassionate love you feel for your spouse?

4. What is the level of compassionate love your spouse feels for you?

Each response was recorded on a five-point scale: 1=None, 2=Very Little, 3=Some, 4=A Great Deal and 5=A Tremendous Amount.

Usage

case1702

Format

A data frame with 30 observations on the following 9 variables.

Couple

couple identification number

HP

level of passionate love husband feels for spouse

WP

level of passionate love wife feels for spouse

HC

level of compassionate love husband feels for spouse

WC

level of compassionate love wife feels for spouse

PW

level of passionate love husband perceives spouse to have for him

PH

level of passionate love wife perceives spouse to have for her

CW

level of compassionate love husband perceives spouse to have for him

CH

level of compassionate love husband perceives spouse to have for her

Source

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

References

Johnson, R.A. and Wichern, D.W. (1988). Applied Multivariate Statistical Analysis (2nd ed), Prentice-Hall.

Examples

str(case1702)
attach(case1702)
      
## EXPLORATION   
x <- cbind(HP,WP,HC,WC) # 4 components of level of love you feel for spouse
y <- cbind(PW,PH,CW,CH) # 4 components of level of love you perceive from spouse 

if(require(CCA)){     # Use the CCA library         
  myCCA   <- cc(x,y)  # Store canonical correlation computations 
  canCor   <- myCCA$cor  # Extract the canonical correlations
  canCor  #[1] 0.9506990 0.8665601 0.5571876 0.1106555

# Make a function to test the number of canonical correlations (advanced).
# Bartlett modification of likelihood ratio test
# Reference: Mardia, Kent, and Bibby, 1980, Multivariate Analysis, 
myTest  <- function(xMatrix,yMatrix) { 
  if(require(CCA)){     # Use the CCA library    
    myCCA       <- cc(xMatrix,yMatrix) # Store CCA computations  
    canCor      <- myCCA$cor   # extract the canonical correlations
    n           <- dim(x)[1] # number of rows of x,= sample size
    p           <- dim(y)[2] # number of component variables in y
    q           <- dim(x)[2] # number of component variables in x
    k           <- min(p,q) # the maximum number of canonical pairs
    testStat    <- rep(0,k) #  store the test statistics; initially set to 0
    degFr       <- rep(0,k)  # store the associated degrees of freedom
    canCor2     <- canCor[k:1] # Reverse order for the following calculations
    productTerm <-  1        
    for (i in 1:k)  {
      productTerm   <-  productTerm*(1 - canCor2[i]^2)
      degFr[i]      <-  (p + 1 - i)*(q + 1 - i)
      testStat[i]   <- -(n -(p+q+3)/2)*log(productTerm)
        } 
    pair <- 1:k
    testStat <- round(testStat[k:1],2)  # Revert to original order; round  
    pValue  <- round(1 - pchisq(testStat,degFr),4) # p-value   to 4 digits
    canCor  <- round(canCor,4)   # Round to 4 digits
    cbind(pair,canCor, testStat,degFr, pValue) # Show the results; 
    }    }
myTest(x,y)

# Explore possible meaningful linear combination suggested by first pair of CCs
round(myCCA$xcoef,1)
round(myCCA$ycoef,1)
# The 1st column of xcoef is almost entirely HC; 1st column of ycoef is CW
ccX1 <- myCCA$scores$xscores[,1]
plot(ccX1 ~ jitter(HC)) # See if HC is a good substitute for 1st X canonical var
cor(ccX1,HC)    #[1] 0.9719947

ccY1 <- myCCA$scores$yscores[,1]
plot(ccY1 ~ jitter(CW)) # See if CW is a good substitute for 1st y canonical var
cor(ccY1, CW)   #[1] 0.9975468

# Analyze the correlation of the meaningful substitute variables 
cor(HC,CW)   # [1]  0.9280323
myLm1 <- lm(HC ~ CW)
summary(myLm1) # p-value < 0.0001 (test for slope= 0 equiv to test that corr = 0)


# Explore possible meaningful linear combination suggested by 2nd pair of CCs
# Suggested substitutes from 2nd columns above are WC and CH
ccX2  <- myCCA$scores$xscores[,2]
WCres  <- lm(WC ~ HC)$res  # WC with effect of HC removed
plot(ccX2 ~ WCres)
cor(ccX2,WCres)   #[1] 0.9045225

ccY2  <- myCCA$scores$yscores[,2]
CHres  <- lm(CH ~ CW)$res  # CH with effect of CW removed
plot(ccY2 ~ CHres)
cor(ccY2,CHres)   # [1] 0.9280248

cor(WC,CH)           #[1] 0.8134213
myLm2 <- lm(WC ~ CH)
summary(myLm2)       # p-value < 0.0001 for test that correlation = 0

# Explore cannonical correlations from other groupings of variables
x <- cbind(HP, HC, PW, CW)  # husband's responses
y <- cbind(WP, WC, PH, CH)  # wife's responses
myTest(x,y)    # No evidence that husbands' responses are correlated with wifes'  
x <- cbind(HP,PW,WP,PH)    # passionate responses 
y <- cbind(HC,CW,WC,CH)    # compassionate responses
myTest(x,y) #No evidence that passionate anc compassionate responses are correlated 


##  GRAPHICAL DISPLAYS FOR PRESENTATION
jFactor <- 0.3   # Jittering factor (try different values to see what works)
jHC <- jitter(HC,factor=jFactor)
jCW <- jitter(CW,factor=jFactor)
jCH <- jitter(CH,factor=jFactor)
jWC <- jitter(WC,factor=jFactor)
opar <- par(no.readonly=TRUE)  # Store current graphical parameter settings
par(mfrow=c(2,2)) # Prepare to make a 2x2 panel of graphs
par(mar=c(1.1,4.1,1.1,1.1) )  # Adjust margins
plot(jHC ~ jCW, ylab="Husband's Compassionate Love For His Wife (Jittered)",
  xlab="", ylim=c(3,5.1), xlim=c(3,5.1), col="black", pch=21, lwd=2,  
  bg="green", cex=2 )  
text(3,5.1,"correlation = 0.93",adj=0)
text(3,5.0,"p-value < 0.0001",adj=0)
abline(myLm1)
 
par(mar=c(1.1,1.1,1.1,4.1)) 
plot(jHC ~ jCH, xlab="", ylab="", ylim=c(3,5.1), xlim=c(3,5.1), 
  col="black", pch=21, lwd=2, bg="green",  cex=2 )  
cor(HC,CH)      #[1] 0.274204
myLm3 <- lm(HC ~ CH)
summary(myLm3)# p-value = 0.143
text(3,5.1,"correlation = 0.27",adj=0)
text(3,5.0,"p-value = 0.14",adj=0)
abline(myLm3)
 
par(mar=c(4.1,4.1,1.1,1.1)) 
plot(jWC ~ jCW,
  xlab="Husband's Perceived Compassionate Love From His Wife (Jittered)",
  ylab="Wife's Compassionate Love For Her Husband (Jittered)",
  ylim=c(3,5.1), xlim=c(3,5.1), col="black", pch=21, lwd=2, bg="green", cex=2 ) 
cor(WC,CW)           #[1] 0.04171195
myLm4 <- lm(WC ~ CW)
summary(myLm4)       # p-value = 0.827
text(3,3.1,"correlation = 0.04",adj=0)
text(3,3,"p-value = 0.8",adj=0)
abline(myLm4)
 
par(mar=c(4.1,1.1,1.1,4.1))   
plot(jWC ~ jCH, ylab="",  
  xlab="Wife's Perceived Compassionate Love From Her Husband (Jittered)",
  ylim=c(3,5.1), xlim=c(3,5.1), col="black", pch=21,  lwd=2, bg="green", cex=2 )  
text(3,3.1,"correlation = 0.81",adj=0)
text(3,3,"p-value < 0.0001",adj=0)
abline(myLm2)

par(opar) # Restore previous graphics parameter settings
}
detach(case1702)

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