Types of Data
Before you can analyze a variable, you have to know what kind of variable it is. The type determines which chart makes sense, which average is meaningful and which tests you can use. A "mean eye color" is nonsense, and this section explains why.
The big split: categorical vs. quantitative
Categorical (qualitative) variables put things into groups, recording labels rather than amounts. Quantitative variables record amounts, numbers you can do arithmetic on. Each splits again into two finer levels, giving four in total:
- Nominal (categorical): named categories with no order. Eye color, country, blood type.
- Ordinal (categorical): ordered categories, but the gaps aren't equal or measurable. Survey "agree/neutral/disagree," movie star-ratings, education level.
- Interval (quantitative): equal gaps, but no true zero, so ratios are meaningless. Temperature in °C, calendar years. (20 °C isn't "twice as hot" as 10 °C.)
- Ratio (quantitative): equal gaps and a true zero, so ratios work. Height, weight, reaction time, income. (10 kg is twice 5 kg.)
🎮 Name That Data Type
Classify each variable. You'll get instant feedback and a one-line reason.
The litmus tests: Can you put the categories in a meaningful order? If no → nominal; if yes, keep going. Are the gaps between values equal and numeric? If no → ordinal; if yes, keep going. Is "zero" a true absence of the thing (making "twice as much" meaningful)? No → interval; yes → ratio.
Why the label matters
The data type limits which summaries are meaningful:
- You can count and find the mode of nominal data, but not its mean or median.
- Ordinal data has a median, but its "mean" is shaky (the gaps aren't equal).
- Only interval and ratio data support means, standard deviations, and most of the tests in this course.
The same applies to charts: the Which Chart Should I Use? chooser starts from these data types.
Why it matters: nearly every "which test do I use?" question starts with "what type is your outcome variable?" It is the first question the test chooser asks, and the top-left cell of the printable test-chooser poster. If you get the type wrong, the analysis still produces numbers, but they mean nothing. The guide Choosing Statistics for Your Dissertation opens with a longer explanation of that first question.
Problem 1 of the practice problems sorts eight library columns, from membership number to age to postcode, into nominal, ordinal, interval, and ratio, then asks which ones it even makes sense to average.
Common questions
Is age nominal, ordinal, interval, or ratio data?
Age in years is ratio data: zero means no age at all, so "twice as old" is meaningful. But the level of measurement depends on how you record a variable, not on the thing itself. Age groups (18–25, 26–40, 41+) are ordinal. Birth year is interval, because year 0 is an arbitrary calendar convention, so 1990 isn't "twice" 995. Recording age as coarse groups throws information away permanently, so collect the exact value and bin later if you must.
Is a Likert scale ordinal or interval data?
Strictly, a single Likert item ("strongly disagree … strongly agree") is ordinal — the gaps between labels aren't guaranteed equal. In practice, researchers often treat the sum or average of several items as approximately interval, which is usually defensible. For a single item, ordinal-friendly methods (medians, rank-based tests) are the safer choice.
Why can't you calculate a mean for nominal data?
Because nominal categories are labels, not amounts, so there is no quantity to average. If you code eye colors as 1, 2, 3 and compute a "mean of 2.1," the number depends entirely on your arbitrary coding and describes nothing real. For nominal data, report counts, percentages, and the mode.