In This Article
Introduction
Understanding scales of measurement is fundamental to proper data analysis. The scale determines what statistical operations are meaningful and which statistical tests can be applied. Using the wrong analysis for a given scale leads to incorrect conclusions.
Stanley Stevens introduced four levels of measurement in 1946: Nominal, Ordinal, Interval, and Ratio (often remembered as NOIR). Each successive level has all the properties of the previous levels plus additional properties.
Nominal Scale
The simplest scale—used for categorization only.
Properties
- Categories are mutually exclusive
- No inherent order or ranking
- Numbers are labels only (arbitrary)
Examples
- Gender (Male/Female)
- Colors (Red/Blue/Green)
- Country of origin
- Product categories
- Jersey numbers in sports
Permissible Statistics
- Frequency counts
- Mode
- Chi-square tests
Ordinal Scale
Categories with a meaningful order, but unequal intervals.
Properties
- Categories have rank order
- Intervals between ranks are not equal
- Can say "greater than" but not "how much greater"
Examples
- Education level (High School < Bachelor's < Master's < PhD)
- Satisfaction ratings (Very Dissatisfied < Dissatisfied < Neutral < Satisfied < Very Satisfied)
- Class rank (1st, 2nd, 3rd...)
- Likert scales (often treated as ordinal)
Permissible Statistics
- Frequency, mode
- Median, percentiles
- Non-parametric tests (Mann-Whitney, Spearman correlation)
Interval Scale
Ordered categories with equal intervals, but no true zero.
Properties
- Meaningful equal intervals
- No true zero point (zero is arbitrary)
- Can add and subtract meaningfully
- Cannot form meaningful ratios
Examples
- Temperature (Celsius/Fahrenheit): 0°C doesn't mean "no temperature"
- Calendar years: Year 0 is arbitrary
- IQ scores: 0 doesn't mean "no intelligence"
- SAT/GRE scores
Permissible Statistics
- All ordinal statistics
- Mean, standard deviation
- Parametric tests (t-tests, ANOVA, Pearson correlation)
Ratio Scale
The highest level—has all properties including a true zero.
Properties
- Equal intervals
- True zero point (zero means absence)
- Can form meaningful ratios
- All mathematical operations permitted
Examples
- Height, weight, distance
- Money, sales revenue
- Age (from birth)
- Temperature in Kelvin
- Units sold, time duration
Permissible Statistics
- All statistics
- Geometric mean, coefficient of variation
- Meaningful ratio statements
Example
₹200 is twice as much as ₹100 (meaningful ratio). Zero rupees means no money (true zero).
Comparison of Scales
| Property | Nominal | Ordinal | Interval | Ratio |
|---|---|---|---|---|
| Categories | ✓ | ✓ | ✓ | ✓ |
| Order | ✗ | ✓ | ✓ | ✓ |
| Equal Intervals | ✗ | ✗ | ✓ | ✓ |
| True Zero | ✗ | ✗ | ✗ | ✓ |
| Central Tendency | Mode | Median | Mean | Mean |
Conclusion
Key Takeaways
- Four scales: Nominal, Ordinal, Interval, Ratio (NOIR)
- Nominal: Categories only, no order (use mode)
- Ordinal: Ordered categories, unequal intervals (use median)
- Interval: Equal intervals, no true zero (use mean)
- Ratio: Equal intervals plus true zero (all statistics valid)
- Scale determines appropriate statistical tests
- Higher scales have all properties of lower scales