Finding the Modal School District

Inspired by NPR Planet Money's Modal American Analysis

11 minute read

My good friend Ryan Estrellado recommended an NPR Planet Money podcast episode on the “Modal American.” Working with Ben Casselman, Planet Money explored the most ‘typical’ American. It was a fantastic, engaging episode about a common statistical technique that I’ve never seen applied in this way before. They ran the numbers on a variety of demographic variables to see what group is the most common in the U.S. (I highly recommend the episode - it’s pretty surprising!).

Ben Casselman shared the code he ran for the analysis. Ryan suggested running a similar analysis to find the modal school district, which I thought was brilliant! The analysis is below, but if you are desperate for the answer, the modal school district in the U.S. is [drum roll please]: (1) Majority (>=50%) White, (2) Small, (3) Rural, and (4) Medium-Low FRPL (between 25% and 50% FRPL).

Downloading and Parsing Data

I used NCES Common Core of Data (CCD) to pull Local Educational Agency (LEA) (a.k.a. school districts) demographic data. I wanted to try Urban Institute’s {educationdata} R package. They have enrollment and racial demographic data available to download through their package. For Free/Reduced Price Lunch data, I had to pull the data directly from the CCD as it’s not available via the Urban API.

What buckets do you choose for analysis? This is a bit tricky. I chose buckets I typically refer to for work. I also looked at some NCES reports to see how they typically think about districts. Ultimately, I decided on four buckets: urban-centric locale bucket, race/ethnicity bucket, size bucket, and FRPL bucket.


knitr::opts_chunk$set(out.width = '100%') 

Urban-Centric Locale Bucket

First, we download the directory data using the Urban Institute’s API. These data include the districts and their urban-centric_locale.

ccd_dir <- get_education_data(level = 'school-districts',
                              source = 'ccd', 
                              topic = 'directory', 
                              filters = list(year = 2016),
                              add_labels = TRUE)

Because there are so many options for urban-centric locale, let’s collapse them to just the biggest buckets: City, Town, Rural, and Suburb.

ccd_urbanicity <-
  ccd_dir %>% 
  select(leaid, urban_centric_locale) %>% 
  mutate(leaid = as.numeric(leaid), # the enrollment file loads these as numeric
         geography = case_when(str_detect(urban_centric_locale, "City|city") ~ "City",
                               str_detect(urban_centric_locale, "Town|town") ~ "Town",
                               str_detect(urban_centric_locale, "Rural|rural") ~ "Rural",
                               str_detect(urban_centric_locale, "Suburb|suburb") ~ "Suburb")) %>% 

Size & Race/Ethnicity Buckets

Then, we download the enrollment data from the Urban Institute.

ccd_enroll <- get_education_data(level = 'school-districts',
                                 source = 'ccd', 
                                 topic = 'enrollment', 
                                 filters = list(year = 2016,
                                             grade = 99),
                                 by = list('race'),
                                 add_labels = TRUE) 

We want to create two buckets here:

  • Size: Bucket districts by enrollment size, Small (less than 2500 students), Medium (between 2500 and 10,000 students), or Large (10,000 students or more). I used MDR’s definition for this.
  • Race/Ethnicity: Bucket districts by Majority Non-White (50% or fewer of students are White) or Majority White (more than 50% of students are White).
ccd_enroll_buckets <-
  ccd_enroll %>% 
  select(leaid, race, enrollment) %>% 
  spread(race, enrollment, -1) %>%
  mutate(white_na = case_when(White == 0 ~ NA_real_, # districts with missing data loaded as 0 instead of NA for some reason
                              TRUE ~ White),
         pct_white = white_na/Total,
         enroll_na = case_when(Total < 0 ~ NA_real_, # districts with missing data loaded as 0 instead of NA for some reason
                               TRUE ~ Total)) %>% 
  mutate(demographics = case_when(pct_white >= .5 ~ "Majority White",
                                  pct_white < .5 ~ "Majority Non-White",
                                  TRUE ~ NA_character_),
         size = case_when(enroll_na >= 10000 ~ "Large",
                          enroll_na < 10000 & enroll_na >= 2500 ~ "Medium",
                          enroll_na < 2500 ~ "Small"))

Free/Reduced Price Lunch Bucket

Now, we load the FRPL data.

ccd_frpl <-
  read_csv(here::here("content", "blog", "modal_district_files", "ccd_sch_033_1617_l_2a_11212017.csv"))

We want Free + Reduced Price Lunch numbers by district. This file also has Free Lunch and Reduced Lunch numbers, and it is school-level. We aggregate up Free + Reduced Price Lunch by district.

ccd_frpl_wide <-
  ccd_frpl %>% 
  clean_names() %>% 
  mutate(leaid = as.numeric(leaid)) %>% 
  filter(data_group == "Free and Reduced-price Lunch Table",
         lunch_program == "No Category Codes") %>% 
  select(leaid, student_count) %>% 
  group_by(leaid) %>% 
  summarise(frpl_student_count = sum(student_count))

Then, we merge with the enrollment data to calculate percent FRPL by district. Our buckets are Low FRPL (less than 25%), Medium-Low FRPL (between 25% and 50% FRPL), Medium-High FRPL (between 50% and 75% FRPL), and High FRPL (greater than 75% FRPL). I originally did not have Medium-Low and Medium High split out but that bucket was so large that I thought this would bring more nuance.

ccd_enroll_buckets <-
  left_join(ccd_enroll_buckets, ccd_frpl_wide) %>% 
  mutate(pct_frpl = frpl_student_count/enroll_na,
         frpl = case_when(pct_frpl <= .25 ~ "Low FRPL",
                          pct_frpl > .25 & pct_frpl <= .5 ~ "Medium-Low FRPL",
                          pct_frpl > .5 & pct_frpl <= .75 ~ "Medium-High FRPL",
                          pct_frpl > .75 ~ "High FRPL"))

Bringing It All Together

Finally, we put all the datasets together. One question raised was what to do with missing data. Some districts, either because of small n-sizes or policy, do not report their demographic or FRPL numbers. In fact, some districts were missing enrollment data altogether! For the purposes of this analysis, I removed any district that was missing data in the FRPL or Race/Ethnicity Buckets. Any data without enrollment data is also excluded.

ccd_all <-
  full_join(ccd_urbanicity, ccd_enroll_buckets, by = "leaid") %>% 

ccd_all <- # reordering factors
  ccd_all %>% 
  mutate(demographics = factor(demographics, c("Majority White", "Majority Non-White")),
         size = factor(size, c("Small", "Medium", "Large")),
         geography = factor(geography, c("Rural", "Suburb", "Town", "City")),
         frpl = factor(frpl, c("Low FRPL", "Medium-Low FRPL", "Medium-High FRPL", "High FRPL")))

Running the Analysis

We can see what is the modal school district - that is, the combination of our buckets that represents the most districts in the U.S.

Update 2019-09-18: Thanks to the input from Alison Hill on Twitter, instead of the grouper() function in the original analysis I’m using dplyr::count().

The n shows how many districts fit these criteria. Here are the first four but the full table is in the Appendix.

modal <- 
  ccd_all %>% 
  count(demographics, frpl, geography, size, sort = TRUE)

modal %>% 
  top_n(4) %>% 
Majority WhiteMedium-Low FRPLRuralSmall2484
Majority WhiteMedium-High FRPLRuralSmall1572
Majority WhiteLow FRPLRuralSmall888
Majority Non-WhiteHigh FRPLCitySmall689

The modal school district ends up being: Majority White, Rural, Small, Medium-Low FRPL districts. 18% (2484) of the 13,464 districts in our analysis fall within these criteria.


Some districts are all alike; every district is different in its own way

If you run each bucket individually, you get the same results as all of the groups together (as in, when running only based on size, the result is that Rural districts are the modal districts). This is slightly different from the Modal American analysis from NPR - none of these demographics seem to ‘split’ the groups.

This makes sense

  • The U.S. is majority White and areas tend to be segregated.
  • Majority of districts fall in the Medium FRPL buckets. Majority Non-White districts tend to have higher levels of FRPL, but there are so few of them compared to Majority White Districts, that they do not change the modal district much.
  • The U.S. is very large and districts cannot get too geographically big in order to serve their students. In places with little population density, which is most of the U.S., these districts must remain small.
  • Similarly, there are not that many Cities/Towns compared to Rural districts, probably because you need many districts in Rural areas to serve the spread-out population of students.

It’s really hard to visualize this

It was interesting trying to visualize these data, especially since there ended up being 87 (!) combinations. I tried a Sankey chart but it is a bit bananas.

       aes(y = n,
           axis1 = demographics, 
           axis2 = geography, 
           axis3 = frpl,
           axis4 = size)) +
  stat_alluvium(aes(fill = n),
                width = 1/6, 
            alpha = 2/3,
            aes.bind = FALSE) +
  guides(fill = FALSE) +
  geom_stratum(width = 1/12, fill = "black", color = "grey") +
  geom_label(stat = "stratum", label.strata = TRUE, size = 2, hjust = "inward") +
  scale_x_continuous(breaks = 1:4, labels = c("Demographics", "Geography", "FRPL", "Size")) +
  ggtitle("Modal District Sankey Chart") +

I tried to visualize the data another way - using bar plots. Again, this gets a bit unruly with all the variables. This leads me to think it’s better to just look at the table.

ccd_all %>% 
  select(leaid, demographics, geography, size, frpl) %>% 
  mutate(count = 1) %>% 
  ggplot(aes(count)) +
  geom_bar() +
  facet_grid(demographics + frpl ~ size + geography)

Next steps

In addition to analyzing more variables (perhaps data that are less likely to correlate), it would be interesting to cut the data using smaller grain size for the buckets. There are probably very interesting nuances between Majority White districts for example - we just need the data (and bandwidth!) to find out.

I am in awe of social media, which allows us to learn and share in so many ways. My friend retweeted a news article, which prompted the person who wrote the code to share, and then we crafted an idea based on that. I think that’s pretty great!

Update 2019-09-18: Ben Casselman wrote a reply on how it would be interesting to conduct an analysis on the modal school experience. So exciting! Can’t wait to continue the analysis (and always looking for collaborators!)


Full Table

ccd_all %>% 
  count(demographics, frpl, geography, size) %>% 
Majority WhiteLow FRPLRuralSmall888
Majority WhiteLow FRPLRuralMedium53
Majority WhiteLow FRPLRuralLarge2
Majority WhiteLow FRPLSuburbSmall520
Majority WhiteLow FRPLSuburbMedium434
Majority WhiteLow FRPLSuburbLarge43
Majority WhiteLow FRPLTownSmall156
Majority WhiteLow FRPLTownMedium39
Majority WhiteLow FRPLCitySmall102
Majority WhiteLow FRPLCityMedium18
Majority WhiteLow FRPLCityLarge18
Majority WhiteMedium-Low FRPLRuralSmall2484
Majority WhiteMedium-Low FRPLRuralMedium115
Majority WhiteMedium-Low FRPLRuralLarge17
Majority WhiteMedium-Low FRPLSuburbSmall343
Majority WhiteMedium-Low FRPLSuburbMedium260
Majority WhiteMedium-Low FRPLSuburbLarge52
Majority WhiteMedium-Low FRPLTownSmall604
Majority WhiteMedium-Low FRPLTownMedium163
Majority WhiteMedium-Low FRPLTownLarge1
Majority WhiteMedium-Low FRPLCitySmall83
Majority WhiteMedium-Low FRPLCityMedium43
Majority WhiteMedium-Low FRPLCityLarge27
Majority WhiteMedium-High FRPLRuralSmall1572
Majority WhiteMedium-High FRPLRuralMedium106
Majority WhiteMedium-High FRPLRuralLarge14
Majority WhiteMedium-High FRPLSuburbSmall151
Majority WhiteMedium-High FRPLSuburbMedium72
Majority WhiteMedium-High FRPLSuburbLarge25
Majority WhiteMedium-High FRPLTownSmall447
Majority WhiteMedium-High FRPLTownMedium154
Majority WhiteMedium-High FRPLTownLarge3
Majority WhiteMedium-High FRPLCitySmall57
Majority WhiteMedium-High FRPLCityMedium40
Majority WhiteMedium-High FRPLCityLarge10
Majority WhiteHigh FRPLRuralSmall340
Majority WhiteHigh FRPLRuralMedium33
Majority WhiteHigh FRPLSuburbSmall47
Majority WhiteHigh FRPLSuburbMedium9
Majority WhiteHigh FRPLTownSmall53
Majority WhiteHigh FRPLTownMedium14
Majority WhiteHigh FRPLCitySmall20
Majority WhiteHigh FRPLCityMedium2
Majority Non-WhiteLow FRPLRuralSmall24
Majority Non-WhiteLow FRPLSuburbSmall43
Majority Non-WhiteLow FRPLSuburbMedium28
Majority Non-WhiteLow FRPLSuburbLarge6
Majority Non-WhiteLow FRPLTownSmall3
Majority Non-WhiteLow FRPLTownMedium2
Majority Non-WhiteLow FRPLCitySmall47
Majority Non-WhiteLow FRPLCityMedium4
Majority Non-WhiteLow FRPLCityLarge10
Majority Non-WhiteMedium-Low FRPLRuralSmall59
Majority Non-WhiteMedium-Low FRPLRuralMedium7
Majority Non-WhiteMedium-Low FRPLRuralLarge2
Majority Non-WhiteMedium-Low FRPLSuburbSmall101
Majority Non-WhiteMedium-Low FRPLSuburbMedium99
Majority Non-WhiteMedium-Low FRPLSuburbLarge48
Majority Non-WhiteMedium-Low FRPLTownSmall23
Majority Non-WhiteMedium-Low FRPLTownMedium18
Majority Non-WhiteMedium-Low FRPLCitySmall111
Majority Non-WhiteMedium-Low FRPLCityMedium23
Majority Non-WhiteMedium-Low FRPLCityLarge26
Majority Non-WhiteMedium-High FRPLRuralSmall275
Majority Non-WhiteMedium-High FRPLRuralMedium25
Majority Non-WhiteMedium-High FRPLRuralLarge8
Majority Non-WhiteMedium-High FRPLSuburbSmall159
Majority Non-WhiteMedium-High FRPLSuburbMedium134
Majority Non-WhiteMedium-High FRPLSuburbLarge54
Majority Non-WhiteMedium-High FRPLTownSmall130
Majority Non-WhiteMedium-High FRPLTownMedium63
Majority Non-WhiteMedium-High FRPLTownLarge1
Majority Non-WhiteMedium-High FRPLCitySmall261
Majority Non-WhiteMedium-High FRPLCityMedium62
Majority Non-WhiteMedium-High FRPLCityLarge102
Majority Non-WhiteHigh FRPLRuralSmall454
Majority Non-WhiteHigh FRPLRuralMedium53
Majority Non-WhiteHigh FRPLRuralLarge6
Majority Non-WhiteHigh FRPLSuburbSmall184
Majority Non-WhiteHigh FRPLSuburbMedium82
Majority Non-WhiteHigh FRPLSuburbLarge33
Majority Non-WhiteHigh FRPLTownSmall167
Majority Non-WhiteHigh FRPLTownMedium90
Majority Non-WhiteHigh FRPLTownLarge7
Majority Non-WhiteHigh FRPLCitySmall689
Majority Non-WhiteHigh FRPLCityMedium44
Majority Non-WhiteHigh FRPLCityLarge63