Creating Contingency Tables

Now that we know how to get our raw data into R, we are ready to do the fun stuff - investigating our data!

We discussed the main steps of an EDA and covered the most common data validation and basic manipulations for the data. The next few sets of notes dive into how to find summarize our data. Recall, how we summarize our data depends on the type of data we have!

• Categorical (Qualitative) variable - entries are a label or attribute
  
• Numeric (Quantitative) variable - entries are a numerical value where math can be performed

In either situation, we want to describe each variable’s distribution, perhaps comparing across different subgroups!

Let’s start with summaries of strictly categorical data (or numeric variables with only a few values).

• Categorical data is usually stored as a character or factor type

Categorical Data Summaries

To summarize categorical variables numerically, we use contingency tables.

To do so visually, we use bar plots.

First, let’s read in the appendicitis data from the previous lecture.

library(tidyverse)
library(readxl)
app_data <- read_excel("data/app_data.xlsx", sheet = 1)
app_data <- app_data |>
  mutate(BMI = as.numeric(BMI),
         US_Number = as.character(US_Number),
         SexF = factor(Sex, levels = c("female", "male"), labels = c("Female", "Male")),
         DiagnosisF = as.factor(Diagnosis),
         SeverityF = as.factor(Severity))
app_data

# A tibble: 782 × 61
     Age   BMI Sex    Height Weight Length_of_Stay Management   Severity     
   <dbl> <dbl> <chr>   <dbl>  <dbl>          <dbl> <chr>        <chr>        
 1 12.7   16.9 female    148   37                3 conservative uncomplicated
 2 14.1   31.9 male      147   69.5              2 conservative uncomplicated
 3 14.1   23.3 female    163   62                4 conservative uncomplicated
 4 16.4   20.6 female    165   56                3 conservative uncomplicated
 5 11.1   16.9 female    163   45                3 conservative uncomplicated
 6 11.0   30.7 male      121   45                3 conservative uncomplicated
 7  8.98  19.4 female    140   38.5              3 conservative uncomplicated
 8  7.06  NA   female     NA   21.5              2 conservative uncomplicated
 9  7.9   15.7 male      131   26.7              3 conservative uncomplicated
10 14.3   14.9 male      174   45.5              3 conservative uncomplicated
# ℹ 772 more rows
# ℹ 53 more variables: Diagnosis_Presumptive <chr>, Diagnosis <chr>,
#   Alvarado_Score <dbl>, Paedriatic_Appendicitis_Score <dbl>,
#   Appendix_on_US <chr>, Appendix_Diameter <dbl>, Migratory_Pain <chr>,
#   Lower_Right_Abd_Pain <chr>, Contralateral_Rebound_Tenderness <chr>,
#   Coughing_Pain <chr>, Nausea <chr>, Loss_of_Appetite <chr>,
#   Body_Temperature <dbl>, WBC_Count <dbl>, Neutrophil_Percentage <dbl>, …

Let’s go!

Contingency Tables

We can use Base R or the tidyverse.

Via Base R

Honestly, the easiest way to make contingency tables is through BaseR’s table() function.

From the help

table(...,
      exclude = if (useNA == "no") c(NA, NaN),
      useNA = c("no", "ifany", "always"),
      dnn = list.names(...), deparse.level = 1)

where ... is

one or more objects which can be interpreted as factors (including numbers or character strings), or a list (such as a data frame) whose components can be so interpreted.

Ok, so we can just pass it the vectors we want or we could pass it a data frame (which remember, is just a list of equal length vectors!).

Let’s create some contingency tables for the SexF, DiagnosisF, and SeverityF variables.

table(app_data$SexF)

Female   Male 
   377    403 

We can include NA if we want to via the useNA argument:

table(app_data$SexF, useNA = "always")

Female   Male   <NA> 
   377    403      2 

We can create a two-way table (two-way for two variables) by adding the second variable in:

table(app_data$SexF, app_data$DiagnosisF)

        
         appendicitis no appendicitis
  Female          200             176
  Male            262             141

What is returned from when we create a table? An array! (homogenous data structure - 1D array is a vector, 2D is a matrix)

That means we can subset them if want to! Let’s return the conditional one-way table of Sex based on only those that had appendicitis:

two_way_sex_diag <- table(app_data$SexF, app_data$DiagnosisF)
two_way_sex_diag[,1]

Female   Male 
   200    262 

Nice! Things do get more complicated if we add in a third variable as it is tough to display that info compactly.

table(app_data$SexF, app_data$DiagnosisF, app_data$SeverityF)

, ,  = complicated

        
         appendicitis no appendicitis
  Female           55               1
  Male             63               0

, ,  = uncomplicated

        
         appendicitis no appendicitis
  Female          145             175
  Male            199             141

If you look at the output you see , , = complicated. This is R hinting at how to access this 3D array!

We can return the conditional two-way table of Sex and Diagnosis for only those with an uncomplicated situation:

three_way <- table(app_data$SexF, app_data$DiagnosisF, app_data$SeverityF)
three_way[, , "uncomplicated"]

        
         appendicitis no appendicitis
  Female          145             175
  Male            199             141

#or
three_way[, , 2]

        
         appendicitis no appendicitis
  Female          145             175
  Male            199             141

We can also get a one-way table conditional on two of the variables. Here is the one-way table for sex for only those with an uncomplicated situation and no appendicitis:

three_way[, 2, 2]

Female   Male 
   175    141 

Lastly, just note that you can supply a data frame instead of the individual vectors.

table(app_data[, c("SexF", "DiagnosisF")])

        DiagnosisF
SexF     appendicitis no appendicitis
  Female          200             176
  Male            262             141

Via the tidyverse

Ok, great. But we might want to stay in the tidyverse. We can use the dplyr::summarize() function to compute summaries on a tibble. This generally outputs a tibble with fewer rows than the original (as we are summarizing the variables to view them in a more compact form). We often use group_by() to set a grouping variable. Any summary done will respect the groupings!

Any of the common summarization functions you can think of are likely permissible in summarize(). The one for counting values is simply n(). Let’s recreate all of our above tables under the tidyverse method.

One-way table:

app_data |>
  group_by(SexF) |>
  summarize(count = n())

# A tibble: 3 × 2
  SexF   count
  <fct>  <int>
1 Female   377
2 Male     403
3 <NA>       2

Notice that NA values are included by default (probably a good thing). We can remove those with tidyr::drop_na().

app_data |>
  drop_na(SexF) |>
  group_by(SexF) |>
  summarize(count = n())

# A tibble: 2 × 2
  SexF   count
  <fct>  <int>
1 Female   377
2 Male     403

Two-way table: Simply add another grouping variable. The summarize() function respects these groups when counting!

app_data |>
  drop_na(SexF, DiagnosisF) |>
  group_by(SexF, DiagnosisF) |>
  summarize(count = n())

`summarise()` has regrouped the output.
ℹ Summaries were computed grouped by SexF and DiagnosisF.
ℹ Output is grouped by SexF.
ℹ Use `summarise(.groups = "drop_last")` to silence this message.
ℹ Use `summarise(.by = c(SexF, DiagnosisF))` for per-operation grouping
  (`?dplyr::dplyr_by`) instead.

# A tibble: 4 × 3
# Groups:   SexF [2]
  SexF   DiagnosisF      count
  <fct>  <fct>           <int>
1 Female appendicitis      200
2 Female no appendicitis   176
3 Male   appendicitis      262
4 Male   no appendicitis   141

Nice. But that isn’t in the best way for viewing (i.e. a wider format would be more compact for displaying). Let’s use tidyr::pivot_wider() to fix that!

app_data |>
  drop_na(SexF, DiagnosisF) |>
  group_by(SexF, DiagnosisF) |>
  summarize(count = n()) |>
  pivot_wider(names_from = DiagnosisF, values_from = count)

`summarise()` has regrouped the output.
ℹ Summaries were computed grouped by SexF and DiagnosisF.
ℹ Output is grouped by SexF.
ℹ Use `summarise(.groups = "drop_last")` to silence this message.
ℹ Use `summarise(.by = c(SexF, DiagnosisF))` for per-operation grouping
  (`?dplyr::dplyr_by`) instead.

# A tibble: 2 × 3
# Groups:   SexF [2]
  SexF   appendicitis `no appendicitis`
  <fct>         <int>             <int>
1 Female          200               176
2 Male            262               141

Three-way table: Again, just add more grouping variables!

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n())

`summarise()` has regrouped the output.
ℹ Summaries were computed grouped by SexF, DiagnosisF, and SeverityF.
ℹ Output is grouped by SexF and DiagnosisF.
ℹ Use `summarise(.groups = "drop_last")` to silence this message.
ℹ Use `summarise(.by = c(SexF, DiagnosisF, SeverityF))` for per-operation
  grouping (`?dplyr::dplyr_by`) instead.

# A tibble: 7 × 4
# Groups:   SexF, DiagnosisF [4]
  SexF   DiagnosisF      SeverityF     count
  <fct>  <fct>           <fct>         <int>
1 Female appendicitis    complicated      55
2 Female appendicitis    uncomplicated   145
3 Female no appendicitis complicated       1
4 Female no appendicitis uncomplicated   175
5 Male   appendicitis    complicated      63
6 Male   appendicitis    uncomplicated   199
7 Male   no appendicitis uncomplicated   141

We can also pivot this, although there is no great way to get all the info there. We’ll just move the severity variable across the top.

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n()) |>
  pivot_wider(names_from = SeverityF, values_from = count)

`summarise()` has regrouped the output.
ℹ Summaries were computed grouped by SexF, DiagnosisF, and SeverityF.
ℹ Output is grouped by SexF and DiagnosisF.
ℹ Use `summarise(.groups = "drop_last")` to silence this message.
ℹ Use `summarise(.by = c(SexF, DiagnosisF, SeverityF))` for per-operation
  grouping (`?dplyr::dplyr_by`) instead.

# A tibble: 4 × 4
# Groups:   SexF, DiagnosisF [4]
  SexF   DiagnosisF      complicated uncomplicated
  <fct>  <fct>                 <int>         <int>
1 Female appendicitis             55           145
2 Female no appendicitis           1           175
3 Male   appendicitis             63           199
4 Male   no appendicitis          NA           141

Making it Pretty

When we create these kinds of tables, we often want to include them in some kind of final document. A great way to customize the look of tables is through the gt package!

library(gt)

We can use the gt() and tab_header() functions (among other things) to easily create nicer looking tables!

gt(app_data[1:10,] |>
     select(Age, Sex, Height, Severity, Diagnosis)) |>
  tab_header(
    title = "First 10 rows of Data",
    subtitle = "Data describes attributes of hospitalized patients"
  )

First 10 rows of Data
Data describes attributes of hospitalized patients
Age	Sex	Height	Severity	Diagnosis
12.68	female	148	uncomplicated	appendicitis
14.10	male	147	uncomplicated	no appendicitis
14.14	female	163	uncomplicated	no appendicitis
16.37	female	165	uncomplicated	no appendicitis
11.08	female	163	uncomplicated	appendicitis
11.05	male	121	uncomplicated	no appendicitis
8.98	female	140	uncomplicated	no appendicitis
7.06	female	NA	uncomplicated	no appendicitis
7.90	male	131	uncomplicated	no appendicitis
14.34	male	174	uncomplicated	appendicitis

We can take our contingency table and make it look a bit nicer.

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n(), .groups = "drop") |>
  pivot_wider(names_from = SeverityF, values_from = count) |>
  gt(groupname_col = "SexF") |> 
  tab_header(
    title = "Patient Diagnosis by Severity",
    subtitle = "Stratified by Biological Sex"
  ) 

Patient Diagnosis by Severity
Stratified by Biological Sex
DiagnosisF	complicated	uncomplicated
Female
appendicitis	55	145
no appendicitis	1	175
Male
appendicitis	63	199
no appendicitis	NA	141

It is easy to add lables on the columns via cols_label().

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n(), .groups = "drop") |>
  pivot_wider(names_from = SeverityF, values_from = count) |>
  gt(groupname_col = "SexF") |> 
  tab_header(
    title = "Patient Diagnosis by Severity",
    subtitle = "Stratified by Biological Sex"
  ) |>
  cols_label(
    DiagnosisF = "Diagnosis",
    complicated = "Complicated",
    uncomplicated = "Uncomplicated"
  ) 

Patient Diagnosis by Severity
Stratified by Biological Sex
Diagnosis	Complicated	Uncomplicated
Female
appendicitis	55	145
no appendicitis	1	175
Male
appendicitis	63	199
no appendicitis	NA	141

We can use other functions such as sub_missing() to change the NA values and put a better label above the Complicated/Uncomplicated column headers with tab_spanner().

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n(), .groups = "drop") |>
  pivot_wider(names_from = SeverityF, values_from = count) |>
  gt(groupname_col = "SexF") |> 
  tab_header(
    title = "Patient Diagnosis by Severity",
    subtitle = "Stratified by Biological Sex"
  ) |>
  cols_label(
    DiagnosisF = "Diagnosis",
    complicated = "Complicated",
    uncomplicated = "Uncomplicated"
  ) |>
  sub_missing(
    columns = everything(),
    missing_text = "0"
  ) |>
  tab_spanner(
    label = "Severity Levels",
    columns = c(complicated, uncomplicated)
  ) 

Patient Diagnosis by Severity
Stratified by Biological Sex
Diagnosis	Severity Levels
	Complicated	Uncomplicated
Female
appendicitis	55	145
no appendicitis	1	175
Male
appendicitis	63	199
no appendicitis	0	141

Lastly, there are functions for changing the font, width, etc. (tab_options()) and there are easy ways to change themes for the table (opt_stylize()).

app_data |>
  drop_na(SexF, DiagnosisF, SeverityF) |>
  group_by(SexF, DiagnosisF, SeverityF) |>
  summarize(count = n(), .groups = "drop") |>
  pivot_wider(names_from = SeverityF, values_from = count) |>
  gt(groupname_col = "SexF") |>
  tab_header(
    title = "Patient Diagnosis by Severity",
    subtitle = "Stratified by Biological Sex"
  ) |>
  cols_label(
    DiagnosisF = "Diagnosis",
    complicated = "Complicated",
    uncomplicated = "Uncomplicated"
  ) |>
  fmt_missing(
    columns = everything(),
    missing_text = "0"
  ) |>
  tab_spanner(
    label = "Severity Levels",
    columns = c(complicated, uncomplicated)
  ) |>
  tab_options(
    row_group.font.weight = "bold",
    table.width = pct(80)
  ) |>
  opt_stylize(style = 1, color = "blue")

Warning: Since gt v0.6.0 `fmt_missing()` is deprecated and will soon be removed.
ℹ Use `sub_missing()` instead.
This warning is displayed once every 8 hours.

Patient Diagnosis by Severity
Stratified by Biological Sex
Diagnosis	Severity Levels
	Complicated	Uncomplicated
Female
appendicitis	55	145
no appendicitis	1	175
Male
appendicitis	63	199
no appendicitis	0	141

Cool - I’m not expecting you to know a lot about this package but it is useful to know that it exists when you want to make a table look clearer!

Recap!

Contingency tables summarize the distribution of one or more categorical variables. We can create them using

• table() - returns an array of counts
• group_by() along with summarize() and the n() function

Use the table of contents on the left or the arrows at the bottom of this page to navigate to the next learning material!