All the variables in this dataset were compiled from a sample of the National Survey of College Graduates through the IPUMS-HigherEd site.
For this assignment, I will focus on salary as my outcome variable. I examine the relationship between gender, level of education at the bachelor’s level and higher to determine the impact on salary. Other variables included are the number of children living in the household and race that are also included in the sample but excluded for this particular analysis and assignment.
I predict that salary will be higher for males than for females at all levels of education.
The data used for this analysis consists of a sample from the National Survey of College Graduates gathered through IPUMS-Higher Ed.
library(haven)
library(car)
library(stargazer)##
## Please cite as:## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.1. https://CRAN.R-project.org/package=stargazerlibrary(survey)## Loading required package: grid## Loading required package: Matrix## Loading required package: survival##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchartlibrary(questionr)cpsipums<-read_dta("highered_00005.dta")
names(cpsipums) #print the column names## [1] "personid" "year" "weight" "sample" "surid" "gender"
## [7] "raceth" "chtot" "dgrdg" "salary"In this sample, there are 38,626 females and 45,830 males.
#gender
cpsipums$female<-recode(cpsipums$gender, recodes=1)
cpsipums$male<-recode(cpsipums$gender, recodes=2)
cpsipums$gender<-recode(cpsipums$gender, recodes="1='female'; 2='male'", as.factor.result=T)
table(cpsipums$gender)##
## female male
## 38626 45830#race/ethnicity
#There are no entries in this data set under "other"
cpsipums$asian<-recode(cpsipums$raceth, recodes=1)
cpsipums$white<-recode(cpsipums$raceth, recodes=2)
cpsipums$minorities<-recode(cpsipums$raceth, recodes=3)
cpsipums$other<-recode(cpsipums$raceth, recodes=4)
cpsipums$raceth<-recode(cpsipums$raceth, recodes="1='asian'; 2='white'; 3='minorities'", as.factor.result=T)
table(cpsipums$raceth)##
## asian minorities white
## 13868 18742 51846#education level
cpsipums$dgrdg<-recode(cpsipums$dgrdg, recodes="1='0bachelors'; 2='1masters'; 3='2doctorate'; 4='3professional'", as.factor.result=T)
table(cpsipums$dgrdg, cpsipums$gender)##
## female male
## 0bachelors 18930 25269
## 1masters 16756 16585
## 2doctorate 1103 1611
## 3professional 1837 2365#income grouping
cpsipums$salary<-ifelse(cpsipums$salary==9999998:9999999, NA, cpsipums$salary)
summary (cpsipums$salary)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0 44000 71000 906935 108000 9999998 6519#number of children living in the household
cpsipums$chtot<-recode(cpsipums$chtot, recodes="00='no children'; 01='one child'; 02='one to three children'; 03='two or more children'; 04='more than 3 children'; 98=NA", as.factor.result=T)
table (cpsipums$chtot)##
## one child two or more children
## 14472 20517The percentage of the sample with a bachelors, doctorate and professional degrees is higher for males than it is for females. However, the percentage of females is higher as the masters level. The chi square test for independence is significant which tells us that these variables are independent of each other.
#column percentages of level of education by gender
prop.table(table(cpsipums$dgrdg, cpsipums$gender), margin=2)##
## female male
## 0bachelors 0.49008440 0.55136374
## 1masters 0.43380107 0.36188086
## 2doctorate 0.02855589 0.03515165
## 3professional 0.04755864 0.05160375#basic chi square test of independence of level of education and salary
chisq.test(table(cpsipums$dgrdg, cpsipums$gender))##
## Pearson's Chi-squared test
##
## data: table(cpsipums$dgrdg, cpsipums$gender)
## X-squared = 460.3, df = 3, p-value < 2.2e-16options(survey.lonely.psu = "adjust")
des<-svydesign(ids=~1, strata=~sample, weights=~weight, data = cpsipums[is.na(cpsipums$weight)==F,] )Column percentages of level of education by gender adjusted for weight
A comparison of the percentages of males and females by level of education follows the same pattern when comparing with weights than without weights. However, it is important to notice that the difference between males and females is much smaller when considering survey design at 1% versus without the weights which showed a difference of 6%.
ex1<-wtd.table(cpsipums$dgrdg, cpsipums$gender, weights = cpsipums$weight)
prop.table(wtd.table(cpsipums$dgrdg, cpsipums$gender, weights = cpsipums$weight), margin=2)## female male
## 0bachelors 0.58641280 0.59767939
## 1masters 0.32837989 0.28164509
## 2doctorate 0.01536567 0.02152942
## 3professional 0.06984164 0.09914609Standard Errors of Percentages of Gender and level of education
n<-table(is.na(cpsipums$salary)==F)
n##
## FALSE TRUE
## 6519 77937p<-prop.table(wtd.table(cpsipums$dgrdg, cpsipums$gender, weights = cpsipums$weight), margin=2)
se<-sqrt((p*(1-p))/n[2])
data.frame(proportion=p, se=se)## proportion.Var1 proportion.Var2 proportion.Freq se.Var1 se.Var2
## 1 0bachelors female 0.58641280 0bachelors female
## 2 1masters female 0.32837989 1masters female
## 3 2doctorate female 0.01536567 2doctorate female
## 4 3professional female 0.06984164 3professional female
## 5 0bachelors male 0.59767939 0bachelors male
## 6 1masters male 0.28164509 1masters male
## 7 2doctorate male 0.02152942 2doctorate male
## 8 3professional male 0.09914609 3professional male
## se.Freq
## 1 0.0017640603
## 2 0.0016822025
## 3 0.0004405968
## 4 0.0009129854
## 5 0.0017565011
## 6 0.0016111975
## 7 0.0005198981
## 8 0.0010705160When including appropriate considerations of weight and standard errors a few changes in the proportions of female vs. males are observed. The gap is slighty larger at 5% than when excluding standard errors. The gap is also larger at the doctorate and professional level however, very small changes are observed at the masters level where females exceed males.
ex2<-svytable(~dgrdg+gender, design = des)
prop.table(svytable(~dgrdg+gender, design = des), margin = 2)## gender
## dgrdg female male
## 0bachelors 0.58641280 0.59767939
## 1masters 0.32837989 0.28164509
## 2doctorate 0.01536567 0.02152942
## 3professional 0.06984164 0.09914609sv.table<-svyby(formula = ~gender, by = ~dgrdg, design = des, FUN = svymean, na.rm=T)
sv.table## dgrdg genderfemale gendermale se.genderfemale
## 0bachelors 0bachelors 0.4768768 0.5231232 0.004787068
## 1masters 1masters 0.5199882 0.4800118 0.005636264
## 2doctorate 2doctorate 0.3987172 0.6012828 0.017227002
## 3professional 3professional 0.3955857 0.6044143 0.012031105
## se.gendermale
## 0bachelors 0.004787068
## 1masters 0.005636264
## 2doctorate 0.017227002
## 3professional 0.012031105A regression analysis shows that there is a negative relationship betweeen males and females particularly at the doctoral level. However, the P values shows a stronger effect of the education on the salaries of males than for females as well as stronger effect for a masters degree.
After incorporating the case weights we lose the effect on the masters degree and a stronger effect on the professional degree emerges. The differens in gender continue to favor men.
Finally, the survey design is included showing similar patterns to the previous case of reg2.
reg1<-lm(salary~dgrdg+gender, data=cpsipums)
summary(reg1)##
## Call:
## lm(formula = salary ~ dgrdg + gender, data = cpsipums)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1166105 -911390 -821121 -608405 9394417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1166105 17908 65.116 < 2e-16 ***
## dgrdg1masters -210715 20836 -10.113 < 2e-16 ***
## dgrdg2doctorate -278540 56095 -4.965 6.87e-07 ***
## dgrdg3professional -225845 45911 -4.919 8.71e-07 ***
## gendermale -281985 19873 -14.189 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2752000 on 77932 degrees of freedom
## (6519 observations deleted due to missingness)
## Multiple R-squared: 0.003902, Adjusted R-squared: 0.003851
## F-statistic: 76.32 on 4 and 77932 DF, p-value: < 2.2e-16Regression Analysis With Case Weights
reg2<-lm(salary~dgrdg+gender, data=cpsipums, weights = cpsipums$weight)
summary(reg2)##
## Call:
## lm(formula = salary ~ dgrdg + gender, data = cpsipums, weights = cpsipums$weight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -155445764 -17717071 -10225678 -6082536 768865324
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1280503 18186 70.412 < 2e-16 ***
## dgrdg1masters 9917 24167 0.410 0.682
## dgrdg2doctorate -41121 79872 -0.515 0.607
## dgrdg3professional -307549 39048 -7.876 3.42e-15 ***
## gendermale -304932 21687 -14.060 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 54510000 on 77932 degrees of freedom
## (6519 observations deleted due to missingness)
## Multiple R-squared: 0.003558, Adjusted R-squared: 0.003507
## F-statistic: 69.57 on 4 and 77932 DF, p-value: < 2.2e-16Regression Analysis With Survey Design
reg3<-svyglm(salary~dgrdg+gender,des, family=gaussian)
summary(reg3)##
## Call:
## svyglm(formula = salary ~ dgrdg + gender, des, family = gaussian)
##
## Survey design:
## svydesign(ids = ~1, strata = ~sample, weights = ~weight, data = cpsipums[is.na(cpsipums$weight) ==
## F, ])
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1280503 39215 32.653 < 2e-16 ***
## dgrdg1masters 9917 48986 0.202 0.840
## dgrdg2doctorate -41121 122430 -0.336 0.737
## dgrdg3professional -307549 73498 -4.184 2.86e-05 ***
## gendermale -304932 44083 -6.917 4.64e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 8.926064e+12)
##
## Number of Fisher Scoring iterations: 2We can conclude after completing the analysis that the only statistical significance is found between gender and the professional level of education which often includes law, medicine, dentistry and other health professions degrees.