An (Incomprehensive) Analysis of the College Scorecard Data

Introduction

This is an analysis of the relationship between the median earnings of a college’s graduates and other characteristics of the college. The data was obtained from the College Scorecard dataset produced by the U.S. Department of Education and can be found here. The U.S. Department of Education obtains the data through several sources including “federal reporting from institutions, data on federal financial aid, and tax information.”

In this analysis, I wish to use the R programming language to visually and quantitatively determine the effect several numerical and categorical variables have on the post-graduation median earnings of college students. The reason for inquiry lies in my interest in determining trends regarding the quality of universities in relationship to a variety of economic and academic factors. In determining the effect of certain variables on eventual economic outcome, I seek to better understand the tradeoffs of different college characteristics.

Data Import and Processing

Library imports:

library(dplyr)
library(ggplot2)
library(scales)
library(readr)
library(knitr)

Data import:

df <- read_csv("Most-Recent-Cohorts-All-Data-Elements.csv")

There are 7593 colleges in this dataset with 1777 variables. For this analysis, we are only interested in several defining characteristics (e.g. institution name), categorical factors (e.g. operational status), and quantitative variables (e.g. admission rate).

The following code selects only the variables relevant to our analysis and only retains colleges that:

1. are currently operating
2. are in the 50 states (i.e. excluding territories)
3. are not for-profit institutions
4. predominantly award bachelor’s degrees

college <- df %>%
  filter(CURROPER == 1,
         ST_FIPS <= 56,
         CONTROL != 3,
         PREDDEG == 3) %>%
  select(name = INSTNM, funding = CONTROL, admit = ADM_RATE, med_earnings = MD_EARN_WNE_P10,
         med_fam_inc = MD_FAMINC, NPT4_PUB, NPT4_PRIV)

In order to create visualizations of the data, we need to convert the variables admit, med_earnings, med_fam_inc, NPT4_PUB, and NPT4_PRIV from the character type to the double type. The following code also merges the NPT4_PUB column and NPT4_PRIV column into a single price column.

college$admit <- as.double(college$admit)
college$med_earnings <- as.double(college$med_earnings)
college$med_fam_inc <- as.double(college$med_fam_inc)
college$NPT4_PUB <- as.double(college$NPT4_PUB)
college$NPT4_PRIV <- as.double(college$NPT4_PRIV)

college <- college %>%
  rowwise %>%
  mutate(price = sum(NPT4_PUB, NPT4_PRIV, na.rm = TRUE)) %>%
  select(-c(NPT4_PUB, NPT4_PRIV))

college["price"][college["price"] == 0] <- NA

Here is a small view of what the data now looks like:

kable(head(college))

The variables selected are:

names(college)

## [1] "name"         "funding"      "admit"        "med_earnings"
## [5] "med_fam_inc"  "price"

• funding refers to the source of funding for the institution, 1 coding for a public university and 2 coding for a private university
• admit is the admission rate of the institution on a scale of 0 to 1
• med_earnings represents the median earnings of the institution’s students who are employed 10 years after enrollment in 2015 USD
• med_fam_inc is the median family income of the institution’s current students in 2015 USD
• price indicates the average net price of attendance in USD accounting for the full costs of attendance and awarded financial aid

The following code stores certain purely cosmetic alterations of the visualizations as the variables xdollar, ydollar, and titling to allow for cleaner looking code.

xdollar <- c(scale_x_continuous(labels = dollar,
                              breaks = seq(0, 130000, 25000),
                              limits = c(0, NA)))

ydollar <- c(scale_y_continuous(labels = dollar,
                                        breaks = seq(0, 130000, 25000),
                                        limits = c(0, NA)))

titling <- theme(plot.title = element_text(hjust = 0.5,
                                           face = "bold"),
                 axis.title.x = element_text(face = "bold"),
                 axis.title.y = element_text(face = "bold"))

Distribution of Median Earnings

To analyze the relationship between median earnings and other factors, we would first like to get a preliminary understanding of the distribution of the median earnings of colleges’ graduates. We will create a boxplot of med_earnings below:

ggplot(data = college) +
  geom_boxplot(mapping = aes(x = "", y = med_earnings)) +
  labs(title = "Median Earnings of \na College's Graduates",
       x = NULL,
       y = "Median Earnings in USD") +
  ydollar +
  titling

Due to the inclusion of outliers in our boxplot, we do not receive a good representation of the scale of the distribution of median earnings. Let’s take a look at a histogram instead:

ggplot(data = college) +
  geom_histogram(mapping = aes(x = med_earnings)) +
  labs(title = "Median Earnings of a College's Graduates",
       x = "Median Earnings in USD",
       y = "Frequency of Colleges") +
  xdollar +
  titling

Differences between the Median Earnings of Public Universities versus Private Universities

A histogram of med_earnings gives us a better visualization of the distribution of the median earnings of colleges’ graduates. However, to better understand the effect of different characteristics on economic outcomes, we would like to separate and compare the distributions of med_earnings between public and private institutions.

A violin plot should combine the compactness of a boxplot with the visualization of the distribution of a histogram. Additionally, I have overlaid a plot of the data points to further aid with visualizing the distribution. Here is a violin plot of med_earnings separated by the two values of funding:

ggplot(data = college,
       mapping = aes(x = factor(funding),
                     y = med_earnings)) +
  geom_violin() +
  geom_jitter(alpha = 0.15) +
  scale_x_discrete(labels = c("Public", "Private")) +
  labs(title = "Median Earnings of a College's Graduates \nby Source of Funding",
       x = "Funding Source",
       y = "Median Earnings in USD") +
  ydollar +
  titling

Constructing a violin plot does well in illustrating the visible difference in the distributions of med_earnings between different kinds of universities. However, we should also verify the difference in distribution computationally. We will conduct a Kolmogorov-Smirnov test to determine if the difference in the distribution of the median earnings of colleges’ graduates between public and private institutions is statistically significant. For this analysis, we will consider any p-value less than 0.05 to be statistically significant.

public <- (college %>% filter(funding == 1))$med_earnings
private <- (college %>% filter(funding == 2))$med_earnings
ks.test(public, private, "two.sided")

## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  public and private
## D = 0.085491, p-value = 0.009165
## alternative hypothesis: two-sided

With an incredibly small p-value of 0.009165, we reject the null hypothesis that public and private colleges share the same distribution of the median earnings of their graduates in favor of our alternative hypothesis that the two different types of institutions have statistically significant differences between their distributions of med_earnings.

Determining a Relationship between Median Earnings and Other Factors

In order to further examine the effect various factors have on the economic outcome of a college’s graduates, it would serve us well to fit a linear model to the data. Constructing a least squares regression line using med_earnings and another variable will allow us to quantitatively observe the two variables’ relationship and determine the strength of the relationship, which might allow us to establish which variables are better predictors of good economic incomes than others.

We will utilize scatterplots to visibly observe the relationships between variables. The code below stores certain functions as variables to allow for neater code.

• point_theme affects nothing more than some simple cosmetics of the created plots
• scatter stores the bulk of the coding that declares the variables of interest to be plotted and the type of plot to be constructed, as well as some cosmetic alterations

point_theme <- c(scale_x_continuous(labels = percent),
                 ydollar,
                 scale_color_manual(labels = c("Public","Private"),
                                    values = c("#F8766D", "#00BFC4")))

scatter <- ggplot(data = college,
                  mapping = aes(x = admit,
                                y = med_earnings)) +
  geom_point(mapping = aes(color = factor(funding)),
             size = 2) +
  point_theme +
  titling

scatter +
  labs(title = "Median Earnings of Graduates against Admission Rate of Colleges",
       x = "Admission Rate",
       y = "Median Earnings in USD",
       color = "Source of Funding")

scatter +
  geom_smooth(method = "lm",
              color = "black") +
  labs(title = "Median Earnings of Graduates against Admission Rate of Colleges",
       x = "Admission Rate",
       y = "Median Earnings in USD",
       color = "Source of Funding")

fit1 <- lm(data = college,
           med_earnings ~ admit)
summary(fit1)

## 
## Call:
## lm(formula = med_earnings ~ admit, data = college)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -27624  -6376   -755   5106  79688 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  53340.8      952.8   55.98   <2e-16 ***
## admit       -15831.6     1396.5  -11.34   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10390 on 1455 degrees of freedom
##   (339 observations deleted due to missingness)
## Multiple R-squared:  0.08116,    Adjusted R-squared:  0.08053 
## F-statistic: 128.5 on 1 and 1455 DF,  p-value: < 2.2e-16

scatter +
  labs(title = "Median Earnings of Graduates against Admission Rate of Colleges \nSeparated by Source of Funding",
       x = "Admission Rate",
       y = "Median Earnings in USD",
       color = "Source of Funding") +
  facet_wrap(~ funding)

ggplot(data = college,
       mapping = aes(x = med_fam_inc,
                     y = med_earnings)) +
  geom_point(size = 2,
             color = "skyblue2") +
  geom_smooth(method = "lm",
              color = "black") +
  labs(title = "Median Earnings of Graduates against Median Family Income of Current Students",
       x = "Median Family Income in USD",
       y = "Median Earnings in USD") +
  xdollar +
  ydollar +
  titling

fit2 <- lm(data = college,
           med_earnings ~ med_fam_inc)
summary(fit2)

## 
## Call:
## lm(formula = med_earnings ~ med_fam_inc, data = college)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -32127  -6140  -2113   3923  88726 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.134e+04  6.767e+02   46.31   <2e-16 ***
## med_fam_inc 2.344e-01  1.257e-02   18.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10780 on 1620 degrees of freedom
##   (174 observations deleted due to missingness)
## Multiple R-squared:  0.1768, Adjusted R-squared:  0.1763 
## F-statistic:   348 on 1 and 1620 DF,  p-value: < 2.2e-16

ggplot(data = college,
       mapping = aes(x = price,
                     y = med_earnings)) +
  geom_point(size = 2,
             color = "thistle3") +
  geom_smooth(method = "lm",
              color = "black") +
  labs(title = "Median Earnings of Graduates against Net Price of Attendance",
       x = "Net Price in USD",
       y = "Median Earnings in USD") +
  xdollar +
  ydollar +
  titling

fit3 <- lm(data = college,
           med_earnings ~ price)
summary(fit3)

## 
## Call:
## lm(formula = med_earnings ~ price, data = college)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -30182  -5703   -947   4629  74205 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.203e+04  7.599e+02   42.15   <2e-16 ***
## price       5.269e-01  3.634e-02   14.50   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10330 on 1550 degrees of freedom
##   (244 observations deleted due to missingness)
## Multiple R-squared:  0.1194, Adjusted R-squared:  0.1189 
## F-statistic: 210.2 on 1 and 1550 DF,  p-value: < 2.2e-16

Conclusion

I began this analysis introducing the goals I wanted to achieve through the use of the R programming language. Through the construction of several visualizations, we have examined the effect of several numerical and categorical variables on the economic outcome of college graduates: the median earnings 10 years after enrollment.

Since the R² value of the relationship between the median earnings of a college’s graduates and the median family income of the college’s students is the highest among the three variables examined (i.e. admit, med_fam_inc, and price), it is the better predictor of the potential economic outcome of an institution’s students.

I look forward to conducting a further analysis of the effect of more variables on the ultimate economic outcome of students in post-secondary education.