Descriptive Statistics — Part II: Categorical Summaries and Missing Values

Before you begin, take a few minutes to check what you already know and how confident you feel. You will see the same questions again at the end of the module — this helps both you and us measure what you have learned. Click an option for every question and confidence rating, then click Next to continue.

In Part I you summarised a numeric column with the right centre-and-spread pair — mean (SD) for a symmetric variable, median (IQR) for a skewed one. But many of the columns your reader cares about are not numbers at all: sex, treatment arm, smoking status. And every real clinical dataset has holes — a patient skips a blood test and the cell is blank. This part gives you the tools for both: summarising categories, and summarising honestly when values are missing.

This part of the module covers two skills:

• Categorical summaries — counts and proportions for each group with tabyl(), and a cross-tabulation of two categorical variables to ask whether they are related.
• Honest summaries — handling missing values with na.rm = TRUE, and counting and reporting how many patients you dropped so the holes never hide.

By the end of this part you will be able to tabulate a categorical variable as counts and proportions, cross-tabulate two categories and add totals and row percentages, explain why mean() returns NA when a value is missing, fix it with na.rm = TRUE, and count missing values with sum(is.na(column)) so you never silently hide missing data.

Try every snippet in the R Scratchpad on the right. The datasets patients.csv and diabetes_clinic.csv are already loaded — the first for the categorical tables, the second (which contains missing HbA1c values) for the honest-summary examples.

Location and spread describe numbers. A categorical variable — sex, treatment arm, smoking status — has no average. You summarise it with a count (how many patients in each group) and a proportion (what fraction of the total each group is). Counts and proportions are to categories what the mean and SD are to numbers.

The cleanest way to build a count table is tabyl() from the janitor package. Give it a data frame and a column, and it returns the count and the proportion in one tidy table.

library(readr)
library(janitor)
patients <- read_csv("patients.csv")
patients |> tabyl(sex)

The adorn_*() helpers then dress it up — adorn_pct_formatting() turns the raw proportions into readable percentages.

library(readr)
patients <- read_csv("patients.csv")
library(janitor)
patients |>
  tabyl(smoker) |>
  adorn_pct_formatting()

To ask whether two categories are related — does smoking differ by sex? — you build a cross-tabulation: a table with one variable down the rows and the other across the columns, counting patients in each cell. Pass tabyl() two column names to get one.

The adorn_*() helpers add the finishing touches a reader expects: adorn_totals() adds row and column totals, and adorn_percentages() converts the counts to proportions within each row.

library(readr)
patients <- read_csv("patients.csv")
library(janitor)
patients |>
  tabyl(sex, smoker) |>
  adorn_totals(where = "row")

Real clinical data has holes. A patient skips a blood test and that HbA1c cell is NA — R's marker for a missing value, carried over from Module 1. How you treat those holes decides whether your summary is honest.

By default, R is cautious. If even one value in a column is NA, mean() and sd() return NA, not a number. R is telling you: I cannot average values I do not have. This is a feature, not a bug — it stops a silent wrong answer.

To summarise the values you do have, add the argument na.rm = TRUE — read it as "remove the NAs first". Then mean() averages the non-missing values. The same argument works for sd(), median(), IQR(), and friends.

median(c(5, 7, NA, 9), na.rm = TRUE)

The first trap is forgetting na.rm = TRUE, so your summary silently returns NA and you report a blank where a number belonged. If a summary comes back as NA, suspect a missing value and add na.rm = TRUE.

mean(c(7.2, 8.1, NA, 9.4))

The second trap is quieter and worse: dropping incomplete rows without reporting how many you lost. Setting na.rm = TRUE hides the holes; an honest summary states them. Always count the missing values and report n missing alongside your centre and spread.

Count missing values by combining two functions: is.na() marks each value TRUE if it is missing, and sum() adds up those TRUEs (because R treats TRUE as 1). So sum(is.na(column)) is the number of missing values.

library(readr)
library(dplyr)
clinic <- read_csv("diabetes_clinic.csv")
clinic |>
  summarise(
    n_missing = sum(is.na(hba1c)),
    median_hba1c = median(hba1c, na.rm = TRUE),
    iqr_hba1c = IQR(hba1c, na.rm = TRUE)
  )

Let’s try this Parsons problem for practice

This Parsons problem gives you the right lines in the wrong order, plus a few lines that do not belong. Drag the correct lines into order and leave the wrong ones in the bank.

The worked example below fades the support as you go: first you study a full solution, then you fill the gap, then you solve a fresh one on your own. It walks through the whole decision — check for missing values, compare mean and median, and report the right pair.

crp <- c(4, 5, 6, 7, 9, 12, 45, NA)
sum(is.na(crp))
mean(crp, na.rm = TRUE)
median(crp, na.rm = TRUE)

You have reached the end of the module. Try the same questions again — your answers here, paired with your pre-test answers, are how we measure what the module taught you. Answer every question and confidence rating, then click Submit and see results to view your score.

Here is how your post-test answers compare with your pre-test answers. The pre/post pairing is the most reliable way to see what this module actually taught you.