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Stevens's four levels of measurement — nominal, ordinal, interval, and ratio — determine which statistical operations are meaningful for a given variable. Nominal data consist of unordered categories (e.g., diagnosis type). Ordinal data have rank order but unequal intervals (e.g., Likert ratings). Interval data have equal intervals but no true zero (e.g., temperature in Celsius). Ratio data have a true zero and all arithmetic operations apply (e.g., reaction time). The level of measurement constrains which statistics can be legitimately computed.
Classify common psychology measures by level and explain what operations are permitted. For example: Why can you compute a mean for IQ scores but not for diagnostic categories?
Stevens's four levels of measurement — nominal, ordinal, interval, and ratio — form a hierarchy of informativeness, with each level permitting all the operations of the level below it plus additional ones. Understanding which level a variable belongs to determines which statistics are legitimate and, more practically, protects you from drawing conclusions that the data cannot support.
Nominal variables are the most restricted: they are labels with no inherent order. Whether you code biological sex as M/F or 1/2 is arbitrary — the numbers carry no mathematical meaning. The only operations that make sense are counting (how many in each category?) and identifying the mode. Ordinal variables add rank order: finishing 1st, 2nd, and 3rd tells you who was faster, but not by how much. The gap between 1st and 2nd place might be a tenth of a second while the gap between 2nd and 3rd is three minutes. Because intervals are unequal and unknown, computing a mean on ordinal data requires an assumption — often unjustified — that the intervals are approximately equal.
Interval variables have equal, known intervals between all values, which makes subtraction meaningful. The difference between 70°F and 60°F is the same as the difference between 90°F and 80°F. But interval scales lack a true zero, so ratios are meaningless: 80°F is not "twice as hot" as 40°F in any physical sense. Ratio variables add the true zero, unlocking all arithmetic operations. Reaction time, height, and weight are ratio variables because zero means the genuine absence of the quantity, making it valid to say someone ran twice as fast or weighed half as much.
In psychology, the level of measurement is rarely clear-cut. Likert scales (Strongly Disagree to Strongly Agree, scored 1–5) are formally ordinal — we don't know whether the psychological distance from 1 to 2 equals the distance from 4 to 5. Yet computing means on Likert items is standard practice, defended on practical and simulation-based grounds. This is not sloppy — it is a recognized and debated pragmatic choice. Understanding the formal classification helps you reason about when these shortcuts are likely to mislead you.