types of variables

A folding ruler, a glass thermometer, a kitchen scale and a sheet with a tally list on a black surface

a ruler, a thermometer, a scale and a tally sheet all measure, but what you may do with their numbers is not the same.

image: ai-generated (gpt-image-2.5-flare)

one row per game, one column per fact

an observation is one game, and a variable is one fact that can differ from game to game.

after Döring (2023), p. 577, and R for Data Science, chapter "data tidying"

a variable varies

a fact that is the same in every game is a constant, and a constant needs no column.

types of variables

after Döring (2023), chapter 8.4

Three branches first. Categorical variables sort observations into groups, numerical variables measure an amount, and qualitative variables hold free text that has to be read before it can be counted. On the key, the scales of measurement, which Döring calls Skalenniveaus: a categorical variable is nominal if its groups have no order and ordinal if they do; a numerical variable is on an interval scale if only differences are meaningful and on a ratio scale if it has a true zero. On the key, one common example each: eye colour is nominal, shirt size from S to L is ordinal, a temperature in degrees Celsius is on an interval scale, and body height in centimetres is on a ratio scale; a free comment is qualitative. Other interval variables are calendar dates and years, the time of day, and IQ scores: differences between them mean something, but their zero was set by someone. Döring also calls interval and ratio together metric. Some books split numerical variables into continuous ones and counts instead; that matters for R and comes back in part 3.

what each scale allows

each scale keeps everything the one above it allows and adds one more question you may ask.

door 3 is not three times door 1

a number used as a name is still a name, so count it instead of averaging it.

On the left the five games of the room, and in each game the door with the car. The doors carry numbers, but the numbers are names: we could just as well call them left, middle and right. R does not know that and computes the mean of the prize doors without complaint, here 2, as if the average car stood behind door 2. In fact door 2 had the car least often. The meaningful question is how often each door had the car, and table() answers it. Döring warns of exactly this: statistics software computes meaningless means whenever categories are coded as numbers. A coding plan, which writes down what each number stands for, is the defence, and in R so is the type of the column, as part 3 shows. Whether the doors in our own table stay numbers or become a factor is worth a short debate: as numbers they can be compared, as in prize_door == contestant_choice, as a factor they are more honest. Either is fine as long as nobody reports the mean door.

ten degrees are not twice as warm as five

ratios need a true zero, which a price has and a temperature in Celsius does not.

is a rating scale ordinal or interval?

if in doubt, compute both, and say which one you report.

every scale has its type in R

a factor is how R remembers that a column is categorical.

telling R what a column is

library(dplyr)

monty_hall <- monty_hall |>
  mutate(decision = factor(decision, levels = c("stay", "switch")))

survey <- survey |>
  mutate(organic_share = factor(organic_share, levels = 1:5, ordered = TRUE))

factor() marks a column as nominal, ordered = TRUE as ordinal, and numbers stay double or integer.

what you may compute

the scale tells you which function makes sense, while R will run all of them anyway.

the scale of a variable decides what you may compute with it, and R's type should say so.

to read on: Döring (2023), Forschungsmethoden und Evaluation, chapter 8.4, and R for Data Science, chapter "factors"