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)

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)

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

There are two ways we can address this problem. One would be to round the unemployment_rate variable in the dataset or we can change the number of digits displayed, without touching the input data.

Below are instructions for how you would do both of these:

• Round unemployment_rate: We create a new variable with the mutate function. In this case, we’re overwriting the existing unemployment_rate variable, by rounding it to 4 decimal places.

college_recent_grads %>%
  arrange(unemployment_rate) %>%
  select(rank, major, unemployment_rate) %>%
  mutate(unemployment_rate = round(unemployment_rate, digits = 4))

• Change displayed number of digits without touching data: We can add an option to our R Markdown document to change the displayed number of digits in the output. To do so, add a new chunk, and set:

options(digits = 4)

Note that the digits in options is scientific digits, and in round they are decimal places. If you’re thinking “Wouldn’t it be nice if they were consistent?”, you’re right…

You don’t need to do both of these, that would be redundant. The next exercise asks you to choose one.

1. Which of these options, changing the input data or altering the number of digits displayed without touching the input data, is the better option? Explain your reasoning. Then, implement the option you chose.

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)

2. 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 head(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.

3. 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()

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 thing 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.

4. 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))

5. 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.

Next, we facet the plot by major category.

ggplot(data = college_recent_grads, mapping = aes(x = median)) +
  geom_histogram() +
  facet_wrap( ~ major_category, ncol = 4)

6. 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.

7. 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(___)

8. 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)

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 vector called stem_categories we created earlier, and as "not stem" otherwise.

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

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
  )

9. Which STEM majors have median salaries less than the median for all majors’s median earnings? Structure your output to only show the major name and median, 25th percentile, and 75th percentile earning for that major and sort it such that the major with the highest median earning is on top.

What types of majors do women tend to major in?

10. 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.

Principles of Data Analysis

11. Rank each of the following principles from the Elements and Principles of Data Analysis article for this data analysis from 1 to 10 along with a one sentence summary (I have done the first one as an example.):

• data matching: 10 The data matched the analysis requested exactly, so there is high data matching.
• exhaustive:
• skeptical:
• second order:
• transparency:
• reproducible:

Extra Credit (5 points)

Discover how to change the scale of the x-axis labels of the plot created in Exercise 10 to dollars. Re-plot with this new scale.

Grading

Lab adapted from datasciencebox.org by Dr. Lucy D’Agostino McGowan