The Theory of Scale Types
Stevens (1946, 1951) proposed that measurements can be classified into four different types of scales. These are shown in the table below as: nominal, ordinal, interval, and ratio.
| Scale Type | Mathematical structure | Permissible Statistics | Admissible Scale Transformation |
|---|---|---|---|
| nominal categorical |
standard set structure (unordered) | mode, Chi-squared | One to One (equality (=)) |
| ordinal | totally ordered set | Median and mode, percentile, rank order correlation, non-parametric analysis of variance, | Monotonic increasing (order (<)) |
| interval | affine line | mean, standard deviation, correlation-r, regression, analysis of variance, Factor analysis | Positive linear (affine) |
| ratio | one-dimensional vector space | All statistics permitted for interval scales plus the following: geometric mean, harmonic mean, coefficient of variation, logarithms | Positive similarities (multiplication) |
Read more about this topic: Level Of Measurement
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