Exploratory data analysis II

Lecture 6

Dr. Mine Çetinkaya-Rundel and Josh Lim

Duke University
STA 199 - Fall 2026

September 14, 2026

Warm up

While you wait: Get your application exercise

If you haven’t done so at the end of last class:

  • Go to your ae project in Positron.

  • Make sure all of your changes up to this point are committed and pushed, i.e., there’s nothing left in your source control pane.

  • Click sync to get today’s application exercise file. You can also click on the three dots next to CHANGES and click Pull.

Wait a minute, this ain’t Mine

  • Hi, I’m Josh
  • 3rd Year PhD in Statistical Science
  • From the Bay Area, California
  • Graduated from UCLA in 2024
  • Fun Fact: I actually got to teach this course in the summer (like just over a month ago!)

My lovely class

Photo of Josh's STA 199 class from Summer 2026.

Hmm, Josh have I seen you somewhere before?

Josh at a Duke Chinese dance event.
Josh with Duke Gymnastics.

Josh playing volleyball at Duke.

Announcements

HW 2 is due Wednesday, Sep 16 at 11:59 pm:

  • Push all work to GitHub.

  • Submit a PDF of your hw-2.pdf file to Gradescope and mark your pages.

From last time: Application exercise

AE 02

Work through the application exercise ae-02. Periodically, and at the end, preview, commit, and push your edits.

Multivariate analysis

Analyzing the relationship between multiple variables:

  • In general, one variable is identified as the outcome of interest

  • The remaining variables are predictors or explanatory variables

  • Plots for exploring multivariate relationships are the same as those for bivariate relationships, but conditional on one or more variables

    • Conditioning can be done via faceting or aesthetic mappings (e.g., scatterplot of y vs. x1, colored by x2, faceted by x3)

  • Summary statistics for exploring multivariate relationships are the same as those for bivariate relationships, but conditional on one or more variables

    • Conditioning can be done via grouping (e.g., correlation between y and x1, grouped by levels of x2 and x3)

From the application exercise: flip_22_24

gerrymander_24 <- gerrymander_24 |>
  mutate(
    flip_22_24 = case_when(
      house_party_22 == "Republican" &
        house_party_24 == "Democrat" ~ "Flip R to D",
      house_party_22 == "Democrat" &
        house_party_24 == "Republican" ~ "Flip D to R",
      .default = "No Flip"
    )
  ) |>
  relocate(house_party_22, house_party_24, flip_22_24, gerry_26, .after = state)

mutate()

From grades to categories

How can we combine the 2026 gerrymandering grades into low, medium, and high prevalence of gerrymandering?

  • A or B → Low
  • C → Medium
  • D or F → High

We’ll create a new variable called gerry_26_cat from gerry_26.

mutate()

  • The mutate() function transforms (mutates) a data frame by creating a new column or updating an existing one

  • We choose a name for the column on the left of = and describe how to calculate it on the right

  • To create gerry_26_cat, we need different values for different grades

gerrymander_24 |>
  mutate(gerry_26_cat = ...)

mutate() and case_when()

Use case_when() to recode with multiple conditions:

gerrymander_24 |>
  mutate(
    gerry_26_cat = case_when(
      gerry_26 %in% c("A", "B") ~ "Low",
      gerry_26 == "C" ~ "Medium",
      gerry_26 %in% c("D", "F") ~ "High"
    )
  ) |>
  select(district, gerry_26, gerry_26_cat)
# A tibble: 435 × 3
   district gerry_26 gerry_26_cat
   <chr>    <chr>    <chr>       
 1 AK-00    <NA>     <NA>        
 2 AL-01    B        Low         
 3 AL-02    B        Low         
 4 AL-03    B        Low         
 5 AL-04    B        Low         
 6 AL-05    B        Low         
 7 AL-06    B        Low         
 8 AL-07    B        Low         
 9 AR-01    C        Medium      
10 AR-02    C        Medium      
# ℹ 425 more rows
  • Each condition goes on the left of ~, and its new value goes on the right
  • The first matching condition determines the value
  • Grades that don’t match any condition, including missing grades, get NA

mutate() and store

Creating a column in a pipeline doesn’t change the original data frame:

gerrymander_24 |>
  select(district, gerry_26, gerry_26_cat)
Error in `select()`:
! Can't select columns that don't exist.
✖ Column `gerry_26_cat` doesn't exist.

To keep the new column, store the result:

gerrymander_24 <- gerrymander_24 |>
  mutate(
    gerry_26_cat = case_when(
      gerry_26 %in% c("A", "B") ~ "Low",
      gerry_26 == "C" ~ "Medium",
      gerry_26 %in% c("D", "F") ~ "High"
    )
  )

Check the new variable

gerrymander_24 |>
  select(district, gerry_26, gerry_26_cat)
# A tibble: 435 × 3
   district gerry_26 gerry_26_cat
   <chr>    <chr>    <chr>       
 1 AK-00    <NA>     <NA>        
 2 AL-01    B        Low         
 3 AL-02    B        Low         
 4 AL-03    B        Low         
 5 AL-04    B        Low         
 6 AL-05    B        Low         
 7 AL-06    B        Low         
 8 AL-07    B        Low         
 9 AR-01    C        Medium      
10 AR-02    C        Medium      
# ℹ 425 more rows

What value does gerry_26_cat have when gerry_26 is missing? Why?

What’s going on?

The gerrymandering categories appear in an unexpected order. What’s going on?

gerrymander_24 |>
  filter(!is.na(gerry_26_cat)) |>
  ggplot(aes(x = flip_22_24, fill = gerry_26_cat)) +
  geom_bar(position = "fill")

mutate() and fct_relevel()

  • flip_22_24 is a character variable, so the plot orders its values alphabetically
  • fct_relevel() creates a factor with levels in the specified order
  • We can use mutate() to overwrite flip_22_24 and store the change
gerrymander_24 <- gerrymander_24 |>
  mutate(
    gerry_26_cat = fct_relevel(gerry_26_cat, "Low", "Medium", "High")
  )

gerrymander_24 |>
  select(district, gerry_26, gerry_26_cat)
# A tibble: 435 × 3
   district gerry_26 gerry_26_cat
   <chr>    <chr>    <fct>       
 1 AK-00    <NA>     <NA>        
 2 AL-01    B        Low         
 3 AL-02    B        Low         
 4 AL-03    B        Low         
 5 AL-04    B        Low         
 6 AL-05    B        Low         
 7 AL-06    B        Low         
 8 AL-07    B        Low         
 9 AR-01    C        Medium      
10 AR-02    C        Medium      
# ℹ 425 more rows

Revisit the plot

How does the distribution of 2022–2024 flip outcomes vary by prevalence of gerrymandering for the 2026 election?

gerrymander_24 |>
  filter(!is.na(gerry_26_cat)) |>
  ggplot(aes(x = flip_22_24, fill = gerry_26_cat)) +
  geom_bar(position = "fill")

group_by(), summarize(), count()

Spot the difference

What does group_by() do?

gerrymander_24 |>
  filter(!is.na(gerry_26_cat)) |>
  count(flip_22_24, gerry_26_cat)
# A tibble: 8 × 3
  flip_22_24  gerry_26_cat     n
  <chr>       <fct>        <int>
1 Flip D to R Low              5
2 Flip D to R High             4
3 Flip R to D Low              6
4 Flip R to D Medium           1
5 Flip R to D High             2
6 No Flip     Low            220
7 No Flip     Medium          18
8 No Flip     High           169
gerrymander_24 |>
  filter(!is.na(gerry_26_cat)) |>
  count(flip_22_24, gerry_26_cat) |>
  group_by(flip_22_24)
# A tibble: 8 × 3
# Groups:   flip_22_24 [3]
  flip_22_24  gerry_26_cat     n
  <chr>       <fct>        <int>
1 Flip D to R Low              5
2 Flip D to R High             4
3 Flip R to D Low              6
4 Flip R to D Medium           1
5 Flip R to D High             2
6 No Flip     Low            220
7 No Flip     Medium          18
8 No Flip     High           169

Let’s simplify!

What does group_by() do in the following pipeline?

gerrymander |>
  summarize(mean_trump_24 = mean(trump_24, na.rm = TRUE))
# A tibble: 1 × 1
  mean_trump_24
          <dbl>
1          49.2
gerrymander |>
  group_by(state) |>
  summarize(mean_trump_24 = mean(trump_24, na.rm = TRUE))
# A tibble: 50 × 2
   state       mean_trump_24
   <chr>               <dbl>
 1 Alabama              64.0
 2 Alaska               54.5
 3 Arizona              50.3
 4 Arkansas             64.6
 5 California           38.2
 6 Colorado             42.9
 7 Connecticut          41.8
 8 Delaware             41.9
 9 Florida              55.2
10 Georgia              49.9
# ℹ 40 more rows

group_by()

  • Group by converts a data frame to a grouped data frame, where subsequent operations are performed once per group

  • ungroup() removes grouping

gerrymander_24 |>
  select(state, district, house_party_22, house_party_24) |>
  group_by(state)
# A tibble: 435 × 4
# Groups:   state [50]
   state    district house_party_22 house_party_24
   <chr>    <chr>    <chr>          <chr>         
 1 Alaska   AK-00    Democrat       Republican    
 2 Alabama  AL-01    Republican     Republican    
 3 Alabama  AL-02    Republican     Democrat      
 4 Alabama  AL-03    Republican     Republican    
 5 Alabama  AL-04    Republican     Republican    
 6 Alabama  AL-05    Republican     Republican    
 7 Alabama  AL-06    Republican     Republican    
 8 Alabama  AL-07    Democrat       Democrat      
 9 Arkansas AR-01    Republican     Republican    
10 Arkansas AR-02    Republican     Republican    
# ℹ 425 more rows
gerrymander_24 |>
  select(state, district, house_party_22, house_party_24) |>
  group_by(state) |>
  ungroup()
# A tibble: 435 × 4
   state    district house_party_22 house_party_24
   <chr>    <chr>    <chr>          <chr>         
 1 Alaska   AK-00    Democrat       Republican    
 2 Alabama  AL-01    Republican     Republican    
 3 Alabama  AL-02    Republican     Democrat      
 4 Alabama  AL-03    Republican     Republican    
 5 Alabama  AL-04    Republican     Republican    
 6 Alabama  AL-05    Republican     Republican    
 7 Alabama  AL-06    Republican     Republican    
 8 Alabama  AL-07    Democrat       Democrat      
 9 Arkansas AR-01    Republican     Republican    
10 Arkansas AR-02    Republican     Republican    
# ℹ 425 more rows

group_by() |> summarize()

A common pipeline is group_by() and then summarize() to calculate summary statistics for each group:

gerrymander_24 |>
  group_by(state) |>
  summarize(
    mean_trump_24 = mean(trump_24, na.rm = TRUE),
    median_trump_24 = median(trump_24, na.rm = TRUE)
  )
# A tibble: 50 × 3
   state       mean_trump_24 median_trump_24
   <chr>               <dbl>           <dbl>
 1 Alabama              64.0            68.5
 2 Alaska               54.5            54.5
 3 Arizona              50.3            50.9
 4 Arkansas             64.6            65.1
 5 California           38.2            37.4
 6 Colorado             42.9            45.3
 7 Connecticut          41.8            42.0
 8 Delaware             41.9            41.9
 9 Florida              55.2            57.4
10 Georgia              49.9            58.8
# ℹ 40 more rows

group_by() |> summarize()

This pipeline can also be used to count number of observations for each group:

gerrymander_24 |>
  group_by(state) |>
  summarize(n = n())
# A tibble: 50 × 2
   state           n
   <chr>       <int>
 1 Alabama         7
 2 Alaska          1
 3 Arizona         9
 4 Arkansas        4
 5 California     52
 6 Colorado        8
 7 Connecticut     5
 8 Delaware        1
 9 Florida        28
10 Georgia        14
# ℹ 40 more rows

summarize()

... |>
  summarize(
    name_of_summary_statistic = summary_function(variable)
  )
  • name_of_summary_statistic: Anything you want to call it!
    • Recommendation: Keep it short and evocative
  • summary_function():
    • n(): number of observations
    • mean(): mean
    • median(): median
    • sd(): standard deviation
    • min(): minimum
    • max(): maximum
    • IQR(): inter-quartile range
    • quantile(): quantile (e.g., 0.25, 0.75, etc.)

Spot the difference

What’s the difference between the following two pipelines?

gerrymander_24 |>
  group_by(state) |>
  summarize(n = n())
# A tibble: 50 × 2
   state           n
   <chr>       <int>
 1 Alabama         7
 2 Alaska          1
 3 Arizona         9
 4 Arkansas        4
 5 California     52
 6 Colorado        8
 7 Connecticut     5
 8 Delaware        1
 9 Florida        28
10 Georgia        14
# ℹ 40 more rows
gerrymander_24 |>
  count(state)
# A tibble: 50 × 2
   state           n
   <chr>       <int>
 1 Alabama         7
 2 Alaska          1
 3 Arizona         9
 4 Arkansas        4
 5 California     52
 6 Colorado        8
 7 Connecticut     5
 8 Delaware        1
 9 Florida        28
10 Georgia        14
# ℹ 40 more rows

count()

... |>
  count(variable)
... |>
  count(variable1, variable2)

  • Count the number of observations in each level of variable(s)

  • Place the counts in a variable called n

Review

How would you write the following pipeline with count() instead?

gerrymander_24 |>
  group_by(state) |>
  summarize(n = n()) |>
  arrange(desc(n))
# A tibble: 50 × 2
   state              n
   <chr>          <int>
 1 California        52
 2 Texas             38
 3 Florida           28
 4 New York          26
 5 Illinois          17
 6 Pennsylvania      17
 7 Ohio              15
 8 Georgia           14
 9 North Carolina    14
10 Michigan          13
# ℹ 40 more rows
  • gerrymander_24 |> arrange(state) |> count()
  • gerrymander_24 |> count(state) |> arrange(desc(n))
  • gerrymander_24 |> count(state) |> sort(n)
  • gerrymander_24 |> count(state, sort = TRUE)