case1202: Sex discrimination in Employment
In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"
Description
Usage
Format
Source
References
See Also
Examples
Description
Data on employees from one job category (skilled, entry–level
clerical) of a bank that was sued for sex discrimination. The data
are on 32 male and 61 female employees, hired between 1965 and 1975.
Usage
1
Format
A data frame with 93 observations on the following 7 variables.
- Bsal
Annual salary at time of hire
- Sal77
Salary as of March 1975
- Sex
Sex of employee
- Senior
Seniority (months since first hired)
- Age
Age of employee (in months)
- Educ
Education (in years)
- Exper
Work experience prior to employment with the bank (months)
Source
Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A
Course in Methods of Data Analysis (3rd ed), Cengage Learning.
References
Roberts, H.V. (1979). Harris Trust and Savings Bank: An Analysis of
Employee Compensation, Report 7946, Center for Mathematical
Studies in Business and Economics, University of Chicago Graduate
School of Business.
See Also
Examples
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str(case1202)
attach(case1202)
## EXPLORATION
logSal <- log(Bsal)
myMatrix <- cbind (logSal, Senior,Age, Educ, Exper)
if(require(car)){ # Use the car library
scatterplotMatrix(myMatrix, smooth=FALSE, diagonal="histogram",
groups=Sex, col=c("red","blue") )
}
myLm1 <- lm(logSal ~ Senior + Age + Educ + Exper + Sex)
plot(myLm1, which=1)
plot(myLm1, which=4) # Cook's Distance
if(require(car)){ # Use the car library
crPlots(myLm1) # Partial residual plots
}
ageSquared <- Age^2
ageCubed <- Age^3
experSquared <- Exper^2
experCubed <- Exper^3
myLm2 <- lm(logSal ~ Senior + Age + ageSquared + ageCubed +
Educ + Exper + experSquared + experCubed + Sex)
plot(myLm2, which=1) # Residual plot
plot(myLm1, which=4) # Cook's distance
if(require(leaps)){ # Use the leaps library
mySubsets <- regsubsets(logSal ~ (Senior + Age + Educ + Exper +
ageSquared + experSquared)^2, nvmax=25, data=case1202)
mySummary <- summary(mySubsets)
p <- apply(mySummary$which, 1, sum)
plot(mySummary$bic ~ p, ylab = "BIC")
cbind(p,mySummary$bic)
mySummary$which[8,] # Note that Age:ageSquared = ageCubed
}
myLm3 <- lm(logSal ~ Age + Educ + ageSquared + Senior:Educ +
Age:Exper + ageCubed + Educ:Exper + Exper:ageSquared)
summary(myLm3)
myLm4 <- update(myLm3, ~ . + Sex)
summary(myLm4)
myLm5 <- update(myLm4, ~ . + Sex:Age + Sex:Educ + Sex:Senior +
Sex:Exper + Sex:ageSquared)
anova(myLm4, myLm5)
## INFERENCE AND INTERPRETATION
summary(myLm4)
beta <- myLm4$coef
exp(beta[6])
exp(confint(myLm4,6))
# Conclusion: The median beginning salary for males was estimated to be 12%
# higher than the median salary for females with similar values of the available
# qualification variables (95% confidence interval: 7% to 17% higher).
## DISPLAY FOR PRESENTATION
years <- Exper/12 # Change months to years
plot(Bsal ~ years, log="y", xlab="Previous Work Experience (Years)",
ylab="Beginning Salary (Dollars); Log Scale",
main="Beginning Salaries and Experience for 61 Female and 32 Male Employees",
pch= ifelse(Sex=="Male",24,21), bg = "gray",
col= ifelse(Sex=="Male","blue","red"), lwd=2, cex=1.8 )
myLm6 <- lm(logSal ~ Exper + experSquared + experCubed + Sex)
beta <- myLm6$coef
dummyExper <- seq(min(Exper),max(Exper),length=50)
curveF <- beta[1] + beta[2]*dummyExper + beta[3]*dummyExper^2 +
beta[4]*dummyExper^3
curveM <- curveF + beta[5]
dummyYears <- dummyExper/12
lines(exp(curveF) ~ dummyYears, lty=1, lwd=2,col="red")
lines(exp(curveM) ~ dummyYears, lty = 2, lwd=2, col="blue")
legend(28,8150, c("Male","Female"),pch=c(24,21), pt.cex=1.8, pt.lwd=2,
pt.bg=c("gray","gray"), col=c("blue","red"), lty=c(2,1), lwd=2)
detach(case1202)
Example output
'data.frame': 93 obs. of 7 variables:
$ Bsal : int 5040 6300 6000 6000 6000 6840 8100 6000 6000 6900 ...
$ Sal77 : int 12420 12060 15120 16320 12300 10380 13980 10140 12360 10920 ...
$ Sex : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
$ Senior: int 96 82 67 97 66 92 66 82 88 75 ...
$ Age : int 329 357 315 354 351 374 369 363 555 416 ...
$ Educ : int 15 15 15 12 12 15 16 12 12 15 ...
$ Exper : num 14 72 35.5 24 56 41.5 54.5 32 252 132 ...
Loading required package: car
Loading required package: carData
Warning message:
In applyDefaults(diagonal, defaults = list(method = "adaptiveDensity"), :
unnamed diag arguments, will be ignored
Loading required package: leaps
(Intercept) Senior Age
TRUE FALSE TRUE
Educ Exper ageSquared
TRUE FALSE TRUE
experSquared Senior:Age Senior:Educ
FALSE FALSE TRUE
Senior:Exper Senior:ageSquared Senior:experSquared
FALSE FALSE FALSE
Age:Educ Age:Exper Age:ageSquared
FALSE TRUE TRUE
Age:experSquared Educ:Exper Educ:ageSquared
FALSE TRUE FALSE
Educ:experSquared Exper:ageSquared Exper:experSquared
FALSE TRUE FALSE
ageSquared:experSquared
FALSE
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + Senior:Educ +
Age:Exper + ageCubed + Educ:Exper + Exper:ageSquared)
Residuals:
Min 1Q Median 3Q Max
-0.230710 -0.050695 0.004412 0.051503 0.195887
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.478e+00 5.798e-01 9.448 7.45e-15 ***
Age 1.767e-02 3.633e-03 4.864 5.31e-06 ***
Educ 5.875e-02 9.296e-03 6.320 1.20e-08 ***
ageSquared -3.799e-05 7.299e-06 -5.204 1.36e-06 ***
ageCubed 2.614e-08 4.826e-09 5.416 5.68e-07 ***
Educ:Senior -3.110e-04 7.697e-05 -4.040 0.000118 ***
Age:Exper 1.358e-05 2.880e-06 4.716 9.46e-06 ***
Educ:Exper -1.086e-04 4.617e-05 -2.352 0.020996 *
ageSquared:Exper -1.697e-08 3.658e-09 -4.639 1.27e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09101 on 84 degrees of freedom
Multiple R-squared: 0.547, Adjusted R-squared: 0.5039
F-statistic: 12.68 on 8 and 84 DF, p-value: 8.856e-12
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + ageCubed + Sex +
Educ:Senior + Age:Exper + Educ:Exper + ageSquared:Exper)
Residuals:
Min 1Q Median 3Q Max
-0.173459 -0.037584 0.004244 0.047305 0.192259
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.929e+00 5.105e-01 11.614 < 2e-16 ***
Age 1.480e-02 3.200e-03 4.626 1.36e-05 ***
Educ 4.957e-02 8.253e-03 6.006 4.83e-08 ***
ageSquared -3.097e-05 6.473e-06 -4.784 7.36e-06 ***
ageCubed 2.108e-08 4.296e-09 4.907 4.56e-06 ***
SexMale 1.115e-01 2.092e-02 5.330 8.29e-07 ***
Educ:Senior -3.206e-04 6.686e-05 -4.795 7.06e-06 ***
Age:Exper 9.231e-06 2.631e-06 3.509 0.000729 ***
Educ:Exper -6.919e-05 4.077e-05 -1.697 0.093388 .
ageSquared:Exper -1.213e-08 3.304e-09 -3.670 0.000427 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07903 on 83 degrees of freedom
Multiple R-squared: 0.6625, Adjusted R-squared: 0.6259
F-statistic: 18.1 on 9 and 83 DF, p-value: 3.109e-16
Analysis of Variance Table
Model 1: logSal ~ Age + Educ + ageSquared + ageCubed + Sex + Educ:Senior +
Age:Exper + Educ:Exper + ageSquared:Exper
Model 2: logSal ~ Age + Educ + ageSquared + ageCubed + Sex + Educ:Senior +
Age:Exper + Educ:Exper + ageSquared:Exper + Age:Sex + Educ:Sex +
Sex:Senior + Sex:Exper + ageSquared:Sex
Res.Df RSS Df Sum of Sq F Pr(>F)
1 83 0.51839
2 78 0.51429 5 0.0041066 0.1246 0.9865
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + ageCubed + Sex +
Educ:Senior + Age:Exper + Educ:Exper + ageSquared:Exper)
Residuals:
Min 1Q Median 3Q Max
-0.173459 -0.037584 0.004244 0.047305 0.192259
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.929e+00 5.105e-01 11.614 < 2e-16 ***
Age 1.480e-02 3.200e-03 4.626 1.36e-05 ***
Educ 4.957e-02 8.253e-03 6.006 4.83e-08 ***
ageSquared -3.097e-05 6.473e-06 -4.784 7.36e-06 ***
ageCubed 2.108e-08 4.296e-09 4.907 4.56e-06 ***
SexMale 1.115e-01 2.092e-02 5.330 8.29e-07 ***
Educ:Senior -3.206e-04 6.686e-05 -4.795 7.06e-06 ***
Age:Exper 9.231e-06 2.631e-06 3.509 0.000729 ***
Educ:Exper -6.919e-05 4.077e-05 -1.697 0.093388 .
ageSquared:Exper -1.213e-08 3.304e-09 -3.670 0.000427 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07903 on 83 degrees of freedom
Multiple R-squared: 0.6625, Adjusted R-squared: 0.6259
F-statistic: 18.1 on 9 and 83 DF, p-value: 3.109e-16
SexMale
1.117974
2.5 % 97.5 %
SexMale 1.072404 1.165481
Sleuth3 documentation built on May 2, 2019, 6:41 a.m.
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Description Usage Format Source References See Also Examples
Description
Data on employees from one job category (skilled, entry–level clerical) of a bank that was sued for sex discrimination. The data are on 32 male and 61 female employees, hired between 1965 and 1975.
Usage
1 |
Format
A data frame with 93 observations on the following 7 variables.
- Bsal
Annual salary at time of hire
- Sal77
Salary as of March 1975
- Sex
Sex of employee
- Senior
Seniority (months since first hired)
- Age
Age of employee (in months)
- Educ
Education (in years)
- Exper
Work experience prior to employment with the bank (months)
Source
Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.
References
Roberts, H.V. (1979). Harris Trust and Savings Bank: An Analysis of Employee Compensation, Report 7946, Center for Mathematical Studies in Business and Economics, University of Chicago Graduate School of Business.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | str(case1202)
attach(case1202)
## EXPLORATION
logSal <- log(Bsal)
myMatrix <- cbind (logSal, Senior,Age, Educ, Exper)
if(require(car)){ # Use the car library
scatterplotMatrix(myMatrix, smooth=FALSE, diagonal="histogram",
groups=Sex, col=c("red","blue") )
}
myLm1 <- lm(logSal ~ Senior + Age + Educ + Exper + Sex)
plot(myLm1, which=1)
plot(myLm1, which=4) # Cook's Distance
if(require(car)){ # Use the car library
crPlots(myLm1) # Partial residual plots
}
ageSquared <- Age^2
ageCubed <- Age^3
experSquared <- Exper^2
experCubed <- Exper^3
myLm2 <- lm(logSal ~ Senior + Age + ageSquared + ageCubed +
Educ + Exper + experSquared + experCubed + Sex)
plot(myLm2, which=1) # Residual plot
plot(myLm1, which=4) # Cook's distance
if(require(leaps)){ # Use the leaps library
mySubsets <- regsubsets(logSal ~ (Senior + Age + Educ + Exper +
ageSquared + experSquared)^2, nvmax=25, data=case1202)
mySummary <- summary(mySubsets)
p <- apply(mySummary$which, 1, sum)
plot(mySummary$bic ~ p, ylab = "BIC")
cbind(p,mySummary$bic)
mySummary$which[8,] # Note that Age:ageSquared = ageCubed
}
myLm3 <- lm(logSal ~ Age + Educ + ageSquared + Senior:Educ +
Age:Exper + ageCubed + Educ:Exper + Exper:ageSquared)
summary(myLm3)
myLm4 <- update(myLm3, ~ . + Sex)
summary(myLm4)
myLm5 <- update(myLm4, ~ . + Sex:Age + Sex:Educ + Sex:Senior +
Sex:Exper + Sex:ageSquared)
anova(myLm4, myLm5)
## INFERENCE AND INTERPRETATION
summary(myLm4)
beta <- myLm4$coef
exp(beta[6])
exp(confint(myLm4,6))
# Conclusion: The median beginning salary for males was estimated to be 12%
# higher than the median salary for females with similar values of the available
# qualification variables (95% confidence interval: 7% to 17% higher).
## DISPLAY FOR PRESENTATION
years <- Exper/12 # Change months to years
plot(Bsal ~ years, log="y", xlab="Previous Work Experience (Years)",
ylab="Beginning Salary (Dollars); Log Scale",
main="Beginning Salaries and Experience for 61 Female and 32 Male Employees",
pch= ifelse(Sex=="Male",24,21), bg = "gray",
col= ifelse(Sex=="Male","blue","red"), lwd=2, cex=1.8 )
myLm6 <- lm(logSal ~ Exper + experSquared + experCubed + Sex)
beta <- myLm6$coef
dummyExper <- seq(min(Exper),max(Exper),length=50)
curveF <- beta[1] + beta[2]*dummyExper + beta[3]*dummyExper^2 +
beta[4]*dummyExper^3
curveM <- curveF + beta[5]
dummyYears <- dummyExper/12
lines(exp(curveF) ~ dummyYears, lty=1, lwd=2,col="red")
lines(exp(curveM) ~ dummyYears, lty = 2, lwd=2, col="blue")
legend(28,8150, c("Male","Female"),pch=c(24,21), pt.cex=1.8, pt.lwd=2,
pt.bg=c("gray","gray"), col=c("blue","red"), lty=c(2,1), lwd=2)
detach(case1202)
|
Example output
'data.frame': 93 obs. of 7 variables:
$ Bsal : int 5040 6300 6000 6000 6000 6840 8100 6000 6000 6900 ...
$ Sal77 : int 12420 12060 15120 16320 12300 10380 13980 10140 12360 10920 ...
$ Sex : Factor w/ 2 levels "Female","Male": 2 2 2 2 2 2 2 2 2 2 ...
$ Senior: int 96 82 67 97 66 92 66 82 88 75 ...
$ Age : int 329 357 315 354 351 374 369 363 555 416 ...
$ Educ : int 15 15 15 12 12 15 16 12 12 15 ...
$ Exper : num 14 72 35.5 24 56 41.5 54.5 32 252 132 ...
Loading required package: car
Loading required package: carData
Warning message:
In applyDefaults(diagonal, defaults = list(method = "adaptiveDensity"), :
unnamed diag arguments, will be ignored
Loading required package: leaps
(Intercept) Senior Age
TRUE FALSE TRUE
Educ Exper ageSquared
TRUE FALSE TRUE
experSquared Senior:Age Senior:Educ
FALSE FALSE TRUE
Senior:Exper Senior:ageSquared Senior:experSquared
FALSE FALSE FALSE
Age:Educ Age:Exper Age:ageSquared
FALSE TRUE TRUE
Age:experSquared Educ:Exper Educ:ageSquared
FALSE TRUE FALSE
Educ:experSquared Exper:ageSquared Exper:experSquared
FALSE TRUE FALSE
ageSquared:experSquared
FALSE
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + Senior:Educ +
Age:Exper + ageCubed + Educ:Exper + Exper:ageSquared)
Residuals:
Min 1Q Median 3Q Max
-0.230710 -0.050695 0.004412 0.051503 0.195887
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.478e+00 5.798e-01 9.448 7.45e-15 ***
Age 1.767e-02 3.633e-03 4.864 5.31e-06 ***
Educ 5.875e-02 9.296e-03 6.320 1.20e-08 ***
ageSquared -3.799e-05 7.299e-06 -5.204 1.36e-06 ***
ageCubed 2.614e-08 4.826e-09 5.416 5.68e-07 ***
Educ:Senior -3.110e-04 7.697e-05 -4.040 0.000118 ***
Age:Exper 1.358e-05 2.880e-06 4.716 9.46e-06 ***
Educ:Exper -1.086e-04 4.617e-05 -2.352 0.020996 *
ageSquared:Exper -1.697e-08 3.658e-09 -4.639 1.27e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09101 on 84 degrees of freedom
Multiple R-squared: 0.547, Adjusted R-squared: 0.5039
F-statistic: 12.68 on 8 and 84 DF, p-value: 8.856e-12
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + ageCubed + Sex +
Educ:Senior + Age:Exper + Educ:Exper + ageSquared:Exper)
Residuals:
Min 1Q Median 3Q Max
-0.173459 -0.037584 0.004244 0.047305 0.192259
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.929e+00 5.105e-01 11.614 < 2e-16 ***
Age 1.480e-02 3.200e-03 4.626 1.36e-05 ***
Educ 4.957e-02 8.253e-03 6.006 4.83e-08 ***
ageSquared -3.097e-05 6.473e-06 -4.784 7.36e-06 ***
ageCubed 2.108e-08 4.296e-09 4.907 4.56e-06 ***
SexMale 1.115e-01 2.092e-02 5.330 8.29e-07 ***
Educ:Senior -3.206e-04 6.686e-05 -4.795 7.06e-06 ***
Age:Exper 9.231e-06 2.631e-06 3.509 0.000729 ***
Educ:Exper -6.919e-05 4.077e-05 -1.697 0.093388 .
ageSquared:Exper -1.213e-08 3.304e-09 -3.670 0.000427 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07903 on 83 degrees of freedom
Multiple R-squared: 0.6625, Adjusted R-squared: 0.6259
F-statistic: 18.1 on 9 and 83 DF, p-value: 3.109e-16
Analysis of Variance Table
Model 1: logSal ~ Age + Educ + ageSquared + ageCubed + Sex + Educ:Senior +
Age:Exper + Educ:Exper + ageSquared:Exper
Model 2: logSal ~ Age + Educ + ageSquared + ageCubed + Sex + Educ:Senior +
Age:Exper + Educ:Exper + ageSquared:Exper + Age:Sex + Educ:Sex +
Sex:Senior + Sex:Exper + ageSquared:Sex
Res.Df RSS Df Sum of Sq F Pr(>F)
1 83 0.51839
2 78 0.51429 5 0.0041066 0.1246 0.9865
Call:
lm(formula = logSal ~ Age + Educ + ageSquared + ageCubed + Sex +
Educ:Senior + Age:Exper + Educ:Exper + ageSquared:Exper)
Residuals:
Min 1Q Median 3Q Max
-0.173459 -0.037584 0.004244 0.047305 0.192259
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.929e+00 5.105e-01 11.614 < 2e-16 ***
Age 1.480e-02 3.200e-03 4.626 1.36e-05 ***
Educ 4.957e-02 8.253e-03 6.006 4.83e-08 ***
ageSquared -3.097e-05 6.473e-06 -4.784 7.36e-06 ***
ageCubed 2.108e-08 4.296e-09 4.907 4.56e-06 ***
SexMale 1.115e-01 2.092e-02 5.330 8.29e-07 ***
Educ:Senior -3.206e-04 6.686e-05 -4.795 7.06e-06 ***
Age:Exper 9.231e-06 2.631e-06 3.509 0.000729 ***
Educ:Exper -6.919e-05 4.077e-05 -1.697 0.093388 .
ageSquared:Exper -1.213e-08 3.304e-09 -3.670 0.000427 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07903 on 83 degrees of freedom
Multiple R-squared: 0.6625, Adjusted R-squared: 0.6259
F-statistic: 18.1 on 9 and 83 DF, p-value: 3.109e-16
SexMale
1.117974
2.5 % 97.5 %
SexMale 1.072404 1.165481
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