Stevens' Levels of Measurement
Everyone learns nominal, ordinal, interval, and ratio as if the taxonomy fell from the sky -- it came from one 1946 paper written to settle an argument about whether psychology could measure anything at all
Traces the nominal/ordinal/interval/ratio taxonomy to S.S. Stevens' 1946 Science paper, written to answer the British Ferguson Committee's 1940 report that psychological measurement wasn't measurement at all. Gives the precise mathematical content behind the four scales -- each is defined by the broadest class of relabeling transformations (arbitrary bijections, monotonic functions, affine, or similarity transformations) that preserve its meaningful structure, reproducing Stevens' own pairing of each scale with permissible statistics. Demonstrates the stakes with a numerically verified worked example: two ordinal-scale groups whose mean-based comparison completely reverses under a valid, order-preserving relabeling of the same categories, while the median-based comparison stays identical. Covers the pushback too -- Lord's 1953 football-numbers satire and Velleman and Wilkinson's 1993 critique -- and closes by mapping each scale to the specific tools in this site's own test library that are actually appropriate for it.
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