Scales of measurement

Why can't you calculate an 'average religion'? Because religion is a nominal variable — the numbers are just name tags. Understanding the four scales of measurement tells you which statistics are even legal on your data, and examiners lean on the mnemonic NOIR (like the French for 'black,' or the film genre) to lock the order: Nominal, Ordinal, Interval, Ratio.

Nominal scales name or categorize with no order — diagnostic categories, gender, ethnicity, marital status, a client ID number. You can count frequencies and find the mode, nothing more. Ordinal scales rank in order, but the intervals between ranks are unequal — a Likert satisfaction rating (1=very dissatisfied to 5=very satisfied), class rank, or the order clients finish a task. You know the sequence but not the distance between steps; the median works here. Interval scales have equal intervals between points but no true (absolute) zero — the classic examples are temperature in Fahrenheit/Celsius and, importantly for counselors, standardized test scores like IQ and most personality-inventory scores. Equal distances are meaningful, but you can't say a score of 100 is 'twice' a score of 50. Ratio scales have equal intervals and a true zero, so ratios are meaningful — number of therapy sessions attended, reaction time, age, weight, number of panic attacks per week. Zero really means 'none.'

The progression matters: each level up permits more mathematical operations. The single most tested distinction is interval vs. ratio — both have equal intervals, but only ratio has a true zero that makes 'twice as much' meaningful.

Clinical Pearl: Remember NOIR for the order, and the trap examiners set: IQ and most test scores are interval (no true zero), while counts like number of sessions attended are ratio (zero means none).