HW 03 - What should I major in?

Photo by Marleena Garris on Unsplash Photo by Marleena Garris on Unsplash

The first step in the process of turning information into knowledge process is to summarize and describe the raw information - the data. In this assignment we explore data on college majors and earnings, specifically the data begind the FiveThirtyEight story “The Economic Guide To Picking A College Major”.

These data originally come from the American Community Survey (ACS) 2010-2012 Public Use Microdata Series. While this is outside the scope of this assignment, if you are curious about howraw data from the ACS were cleaned and prepared, see the code FiveThirtyEight authors used.

We should also note that there are many considerations that go into picking a major. Earnings potential and employment prospects are two of them, and they are important, but they don’t tell the whole story. Keep this in mind as you analyze the data.

Packages

In this assignment we will work with the tidyverse as usual. In addition, we’ll use the scales package for formatting numerical values, and the fivethirtyeight package for data. tidyverse and scales packages are already installed for you, so you can load them with the following:

library(tidyverse)
library(scales)

You’ll first need to install the fivethirtyeight package by running the following in the console once:

install.packages("fivethirtyeight")

and then you can load it as usual with:

library(fivethirtyeight)

Note that these packages are also loaded in your R Markdown document.

The data

The data frame we will be working with today is called college_recent_grads and it’s in the fivethirtyeight package.

To find out more about the dataset, type the following in your Console: ?college_recent_grads. A question mark before the name of an object will always bring up its help file. This command must be ran in the Console.

college_recent_grads is a tidy data frame, with each row representing an observation and each column representing a variable.

To view the data, click on the name of the data frame in the Environment tab.

You can also take a quick peek at your data frame and view its dimensions with the glimpse function.

glimpse(college_recent_grads)
## Rows: 173
## Columns: 21
## $ rank                        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …
## $ major_code                  <int> 2419, 2416, 2415, 2417, 2405, 2418, 6202, 5001, 241…
## $ major                       <chr> "Petroleum Engineering", "Mining And Mineral Engine…
## $ major_category              <chr> "Engineering", "Engineering", "Engineering", "Engin…
## $ total                       <int> 2339, 756, 856, 1258, 32260, 2573, 3777, 1792, 9122…
## $ sample_size                 <int> 36, 7, 3, 16, 289, 17, 51, 10, 1029, 631, 399, 147,…
## $ men                         <int> 2057, 679, 725, 1123, 21239, 2200, 2110, 832, 80320…
## $ women                       <int> 282, 77, 131, 135, 11021, 373, 1667, 960, 10907, 16…
## $ sharewomen                  <dbl> 0.12056434, 0.10185185, 0.15303738, 0.10731320, 0.3…
## $ employed                    <int> 1976, 640, 648, 758, 25694, 1857, 2912, 1526, 76442…
## $ employed_fulltime           <int> 1849, 556, 558, 1069, 23170, 2038, 2924, 1085, 7129…
## $ employed_parttime           <int> 270, 170, 133, 150, 5180, 264, 296, 553, 13101, 126…
## $ employed_fulltime_yearround <int> 1207, 388, 340, 692, 16697, 1449, 2482, 827, 54639,…
## $ unemployed                  <int> 37, 85, 16, 40, 1672, 400, 308, 33, 4650, 3895, 227…
## $ unemployment_rate           <dbl> 0.018380527, 0.117241379, 0.024096386, 0.050125313,…
## $ p25th                       <dbl> 95000, 55000, 50000, 43000, 50000, 50000, 53000, 31…
## $ median                      <dbl> 110000, 75000, 73000, 70000, 65000, 65000, 62000, 6…
## $ p75th                       <dbl> 125000, 90000, 105000, 80000, 75000, 102000, 72000,…
## $ college_jobs                <int> 1534, 350, 456, 529, 18314, 1142, 1768, 972, 52844,…
## $ non_college_jobs            <int> 364, 257, 176, 102, 4440, 657, 314, 500, 16384, 108…
## $ low_wage_jobs               <int> 193, 50, 0, 0, 972, 244, 259, 220, 3253, 3170, 980,…

The description of the variables, i.e. the codebook, is given below.

Header Description
rank Rank by median earnings
major_code Major code, FO1DP in ACS PUMS
major Major description
major_category Category of major from Carnevale et al
total Total number of people with major
sample_size Sample size (unweighted) of full-time, year-round ONLY (used for earnings)
men Male graduates
women Female graduates
sharewomen Women as share of total
employed Number employed (ESR == 1 or 2)
employed_full_time Employed 35 hours or more
employed_part_time Employed less than 35 hours
employed_full_time_yearround Employed at least 50 weeks (WKW == 1) and at least 35 hours (WKHP >= 35)
unemployed Number unemployed (ESR == 3)
unemployment_rate Unemployed / (Unemployed + Employed)
median Median earnings of full-time, year-round workers
p25th 25th percentile of earnigns
p75th 75th percentile of earnings
college_jobs Number with job requiring a college degree
non_college_jobs Number with job not requiring a college degree
low_wage_jobs Number in low-wage service jobs

The college_recent_grads data frame is a trove of information. Let’s think about some questions we might want to answer with these data:

In the next section we aim to answer these questions.

Data wrangling and visualization

Which major has the lowest unemployment rate?

In order to answer this question all we need to do is sort the data. We use the arrange function to do this, and sort it by the unemployment_rate variable. By default arrange sorts in ascending order, which is what we want here – we’re interested in the major with the lowest unemployment rate.

college_recent_grads %>%
  arrange(unemployment_rate)
## # A tibble: 173 x 21
##     rank major_code major major_category total sample_size   men women sharewomen employed
##    <int>      <int> <chr> <chr>          <int>       <int> <int> <int>      <dbl>    <int>
##  1    53       4005 Math… Computers & M…   609           7   500   109      0.179      559
##  2    74       3801 Mili… Industrial Ar…   124           4   124     0      0            0
##  3    84       3602 Bota… Biology & Lif…  1329           9   626   703      0.529     1010
##  4   113       1106 Soil… Agriculture &…   685           4   476   209      0.305      613
##  5   121       2301 Educ… Education        804           5   280   524      0.652      703
##  6    15       2409 Engi… Engineering     4321          30  3526   795      0.184     3608
##  7    20       3201 Cour… Law & Public …  1148          14   877   271      0.236      930
##  8   120       2305 Math… Education      14237         123  3872 10365      0.728    13115
##  9     1       2419 Petr… Engineering     2339          36  2057   282      0.121     1976
## 10    65       1100 Gene… Agriculture &… 10399         158  6053  4346      0.418     8884
## # … with 163 more rows, and 11 more variables: employed_fulltime <int>,
## #   employed_parttime <int>, employed_fulltime_yearround <int>, unemployed <int>,
## #   unemployment_rate <dbl>, p25th <dbl>, median <dbl>, p75th <dbl>, college_jobs <int>,
## #   non_college_jobs <int>, low_wage_jobs <int>

This gives us what we wanted, but not in an ideal form. First, the name of the major barely fits on the page. Second, some of the variables are not that useful (e.g. major_code, major_category) and some we might want front and center are not easily viewed (e.g. unemployment_rate).

We can use the select function to choose which variables to display, and in which order:

Note how easily we expanded our code with adding another step to our pipeline, with the pipe operator: %>%.

college_recent_grads %>%
  arrange(unemployment_rate) %>%
  select(rank, major, unemployment_rate)
## # A tibble: 173 x 3
##     rank major                                      unemployment_rate
##    <int> <chr>                                                  <dbl>
##  1    53 Mathematics And Computer Science                     0      
##  2    74 Military Technologies                                0      
##  3    84 Botany                                               0      
##  4   113 Soil Science                                         0      
##  5   121 Educational Administration And Supervision           0      
##  6    15 Engineering Mechanics Physics And Science            0.00633
##  7    20 Court Reporting                                      0.0117 
##  8   120 Mathematics Teacher Education                        0.0162 
##  9     1 Petroleum Engineering                                0.0184 
## 10    65 General Agriculture                                  0.0196 
## # … with 163 more rows

Ok, this is looking better, but do we really need to display all those decimal places in the unemployment variable? Not really!

We can use the percent() function to clean up the display a bit.

college_recent_grads %>%
  arrange(unemployment_rate) %>%
  select(rank, major, unemployment_rate) %>%
  mutate(unemployment_rate = percent(unemployment_rate))
## # A tibble: 173 x 3
##     rank major                                      unemployment_rate
##    <int> <chr>                                      <chr>            
##  1    53 Mathematics And Computer Science           0.00000%         
##  2    74 Military Technologies                      0.00000%         
##  3    84 Botany                                     0.00000%         
##  4   113 Soil Science                               0.00000%         
##  5   121 Educational Administration And Supervision 0.00000%         
##  6    15 Engineering Mechanics Physics And Science  0.63343%         
##  7    20 Court Reporting                            1.16897%         
##  8   120 Mathematics Teacher Education              1.62028%         
##  9     1 Petroleum Engineering                      1.83805%         
## 10    65 General Agriculture                        1.96425%         
## # … with 163 more rows

Which major has the highest percentage of women?

To answer such a question we need to arrange the data in descending order. For example, if earlier we were interested in the major with the highest unemployment rate, we would use the following:

The desc function specifies that we want unemployment_rate in descending order.

college_recent_grads %>%
  arrange(desc(unemployment_rate)) %>%
  select(rank, major, unemployment_rate)
## # A tibble: 173 x 3
##     rank major                                      unemployment_rate
##    <int> <chr>                                                  <dbl>
##  1     6 Nuclear Engineering                                    0.177
##  2    90 Public Administration                                  0.159
##  3    85 Computer Networking And Telecommunications             0.152
##  4   171 Clinical Psychology                                    0.149
##  5    30 Public Policy                                          0.128
##  6   106 Communication Technologies                             0.120
##  7     2 Mining And Mineral Engineering                         0.117
##  8    54 Computer Programming And Data Processing               0.114
##  9    80 Geography                                              0.113
## 10    59 Architecture                                           0.113
## # … with 163 more rows
  1. Using what you’ve learned so far, arrange the data in descending order with respect to proportion of women in a major, and display only the major, the total number of people with major, and proportion of women. Show only the top 3 majors by adding top_n(3) at the end of the pipeline.

How do the distributions of median income compare across major categories?

A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th percentile is the value below which 20% of the observations may be found. (Source: Wikipedia

There are three types of incomes reported in this data frame: p25th, median, and p75th. These correspond to the 25th, 50th, and 75th percentiles of the income distribution of sampled individuals for a given major.

  1. Why do we often choose the median, rather than the mean, to describe the typical income of a group of people?

The question we want to answer “How do the distributions of median income compare across major categories?”. We need to do a few things to answer this question: First, we need to group the data by major_category. Then, we need a way to summarize the distributions of median income within these groups. This decision will depend on the shapes of these distributions. So first, we need to visualize the data.

We use the ggplot() function to do this. The first argument is the data frame, and the next argument gives the mapping of the variables of the data to the aesthetic elements of the plot.

Let’s start simple and take a look at the distribution of all median incomes, without considering the major categories.

ggplot(data = college_recent_grads, mapping = aes(x = median)) +
  geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Along with the plot, we get a message:

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

This is telling us that we might want to reconsider the binwidth we chose for our histogram – or more accurately, the binwidth we didn’t specify. It’s good practice to always think in the context of the data and try out a few binwidths before settling on a binwidth. You might ask yourself: “What would be a meaningful difference in median incomes?” $1 is obviously too little, $10000 might be too high.

  1. Try binwidths of $1000 and $5000 and choose one. Explain your reasoning for your choice. Note that the binwidth is an argument for the geom_histogram function. So to specify a binwidth of $1000, you would use geom_histogram(binwidth = 1000).

We can also calculate summary statistics for this distribution using the summarise function:

college_recent_grads %>%
  summarise(min = min(median), max = max(median),
            mean = mean(median), med = median(median),
            sd = sd(median), 
            q1 = quantile(median, probs = 0.25),
            q3 = quantile(median, probs = 0.75))
## # A tibble: 1 x 7
##     min    max   mean   med     sd    q1    q3
##   <dbl>  <dbl>  <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1 22000 110000 40151. 36000 11470. 33000 45000
  1. Based on the shape of the histogram you created in the previous exercise, determine which of these summary statistics is useful for describing the distribution. Write up your description (remember shape, center, spread, any unusual observations) and include the summary statistic output as well.

  2. Plot the distribution of median income using a histogram, faceted by major_category. Use the binwidth you chose in the earlier exercise.

Now that we’ve seen the shapes of the distributions of median incomes for each major category, we should have a better idea for which summary statistic to use to quantify the typical median income.

  1. Which major category has the highest typical (you’ll need to decide what this means) median income? Use the partial code below, filling it in with the appropriate statistic and function. Also note that we are looking for the highest statistic, so make sure to arrange in the correct direction.
college_recent_grads %>%
  group_by(major_category) %>%
  summarise(___ = ___(median)) %>%
  arrange(___)
  1. Which major category is the least popular in this sample? To answer this question we use a new function called count, which first groups the data and then counts the number of observations in each category (see below). Add to the pipeline appropriately to arrange the results so that the major with the lowest observations is on top.
college_recent_grads %>%
  count(major_category)
## # A tibble: 16 x 2
##    major_category                          n
##    <chr>                               <int>
##  1 Agriculture & Natural Resources        10
##  2 Arts                                    8
##  3 Biology & Life Science                 14
##  4 Business                               13
##  5 Communications & Journalism             4
##  6 Computers & Mathematics                11
##  7 Education                              16
##  8 Engineering                            29
##  9 Health                                 12
## 10 Humanities & Liberal Arts              15
## 11 Industrial Arts & Consumer Services     7
## 12 Interdisciplinary                       1
## 13 Law & Public Policy                     5
## 14 Physical Sciences                      10
## 15 Psychology & Social Work                9
## 16 Social Science                          9

All STEM fields aren’t the same

One of the sections of the FiveThirtyEight story is “All STEM fields aren’t the same”. Let’s see if this is true.

First, let’s create a new vector called stem_categories that lists the major categories that are considered STEM fields.

stem_categories <- c("Biology & Life Science",
                     "Computers & Mathematics",
                     "Engineering",
                     "Physical Sciences")

Then, we can use this to create a new variable in our data frame indicating whether a major is STEM or not.

college_recent_grads <- college_recent_grads %>%
  mutate(major_type = ifelse(major_category %in% stem_categories, "stem", "not stem"))

Let’s unpack this: with mutate we create a new variable called major_type, which is defined as "stem" if the major_category is in the nector called stem_categories we created earlier, and as "not stem" otherwise.

%in% is a logical operator. Other logical operators that are commonly used are

Operator Operation
x < y less than
x > y greater than
x <= y less than or equal to
x >= y greater than or equal to
x != y not equal to
x == y equal to
x %in% y contains
x | y or
x & y and
!x not

We can use the logical operators to also filter our data for STEM majors whose median earnings is less than median for all majors’s median earnings, which we found to be $36,000 earlier.

college_recent_grads %>%
  filter(
    major_type == "stem",
    median < 36000
  )
## # A tibble: 10 x 22
##     rank major_code major major_category  total sample_size    men  women sharewomen
##    <int>      <int> <chr> <chr>           <int>       <int>  <int>  <int>      <dbl>
##  1    93       1301 Envi… Biology & Lif…  25965         225  10787  15178      0.585
##  2    98       5098 Mult… Physical Scie…  62052         427  27015  35037      0.565
##  3   102       3608 Phys… Biology & Lif…  22060          99   8422  13638      0.618
##  4   106       2001 Comm… Computers & M…  18035         208  11431   6604      0.366
##  5   109       3611 Neur… Biology & Lif…  13663          53   4944   8719      0.638
##  6   111       5002 Atmo… Physical Scie…   4043          32   2744   1299      0.321
##  7   123       3699 Misc… Biology & Lif…  10706          63   4747   5959      0.557
##  8   124       3600 Biol… Biology & Lif… 280709        1370 111762 168947      0.602
##  9   133       3604 Ecol… Biology & Lif…   9154          86   3878   5276      0.576
## 10   169       3609 Zool… Biology & Lif…   8409          47   3050   5359      0.637
## # … with 13 more variables: employed <int>, employed_fulltime <int>,
## #   employed_parttime <int>, employed_fulltime_yearround <int>, unemployed <int>,
## #   unemployment_rate <dbl>, p25th <dbl>, median <dbl>, p75th <dbl>, college_jobs <int>,
## #   non_college_jobs <int>, low_wage_jobs <int>, major_type <chr>
  1. Which STEM majors have median salaries equal to or less than the median for all majors’s median earnings? Your output should only show the major name and median, 25th percentile, and 75th percentile earning for that major as and should be sorted such that the major with the highest median earning is on top.

What types of majors do women tend to major in?

  1. Create a scatterplot of median income vs. proportion of women in that major, colored by whether the major is in a STEM field or not. Describe the association between these three variables.

Further exploration

  1. Ask a question of interest to you, and answer it using summary statistic(s) and/or visualization(s).