Variable Types and Levels of Measurement#

The type of variable largely determines which statistical test is appropriate. In statistics, we distinguish four levels of measurement that form a hierarchy: from nominal (least informative) to ratio (most informative).

The Four Levels of Measurement#

Nominal Scale#

Nominal variables describe categories without a natural order. The values are merely labels.

Examples of nominal variables

Gender (male, female, non-binary)
Blood type (A, B, AB, O)
Marital status (single, married, divorced)
Favorite color (red, blue, green)

Possible operations: Count frequencies, determine mode. Typical tests: Chi-square test, Fisher's exact test.

Ordinal Scale#

Ordinal variables have a meaningful rank order, but the distances between levels are not equal or not interpretable.

Examples of ordinal variables

Pain rating (none, mild, moderate, severe) — the difference between "none" and "mild" is not necessarily the same as between "moderate" and "severe"
Satisfaction (very dissatisfied, dissatisfied, neutral, satisfied, very satisfied)
Education level (high school, bachelor's, master's, doctorate)

Possible operations: Rank ordering, determine median. Typical tests: Mann-Whitney U test, Kruskal-Wallis test, Spearman correlation.

Interval Scale#

Interval variables have equal distances between values but no true zero point.

Examples of interval variables

Temperature in Celsius (0°C does not mean "no temperature")
IQ scores (an IQ of 0 is not meaningfully interpretable)
Calendar year (year 0 is arbitrarily set)

Possible operations: Addition, subtraction, mean. Typical tests: t-test, ANOVA, Pearson correlation.

Ratio Scale#

Ratio variables have equal distances and a true zero point. This allows ratio statements (e.g., "twice as much").

Examples of ratio variables

Weight in kg (0 kg = no weight)
Reaction time in milliseconds
Income in dollars
Age in years

Possible operations: All arithmetic operations, including multiplication and division. Typical tests: t-test, ANOVA, Pearson correlation.

The Practical Distinction: Categorical vs. Metric#

For choosing a statistical test, the simplified distinction is often more relevant:

Property	Categorical	Metric
Level of measurement	Nominal, Ordinal	Interval, Ratio
Typical tests	Chi-square, Mann-Whitney	t-test, ANOVA
Central tendency	Mode, Median	Mean
Spread	—	Standard deviation, Variance

Practical Implications for Test Choice#

The most important question is: Is my dependent variable metric or categorical?

Metric DV → parametric tests (t-test, ANOVA) or their non-parametric alternatives
Categorical DV → Chi-square test, logistic regression

The independent variable defines the groups:

Categorical with 2 groups → t-test or Mann-Whitney
Categorical with 3+ groups → ANOVA or Kruskal-Wallis
Metric → Correlation or regression

Common Misconceptions#

"Likert scales are always ordinal." This is debated. Individual Likert items (e.g., 1–5) are strictly ordinal. However, sum scores from multiple items are often treated as quasi-metric in practice, especially when the scale has at least 5 levels and is approximately normally distributed.

"Ordinal data must never be analyzed with parametric tests." In practice, parametric tests often produce robust results with ordinal data that has many levels (≥ 5). The decision depends on the actual data distribution.

"Numbers automatically mean metric level." Zip codes, phone numbers, or coded categories (1 = male, 2 = female) are numbers but nominally scaled. The level of measurement depends on the meaning, not the representation.

Variable Types