In statistics, not all numbers are created equal. A temperature of 10°C is different from a rank of #10 in a race. Understanding these differences is key to interpreting research correctly, especially in psychology. The meaning of our data hinges on four fundamental properties of measurement.

These four properties are not independent. They form a hierarchy, where each successive property builds on the one before it. This hierarchy is the foundation for the different levels of measurement used in research.

The four properties combine to create four levels of measurement, often remembered by the acronym NOIR. Each level, or scale, has more statistical power than the one before it because it possesses more of the fundamental properties.

Let's break down what this means for psychological constructs.

Nominal scales are about categorization. Think of diagnostic categories in the DSM-5, like 'Major Depressive Disorder' or 'Generalized Anxiety Disorder'. The numbers assigned to these categories are just labels. We can count how many people fall into each category (frequency), but we can't rank them or calculate an average diagnosis.

Ordinal scales introduce ranking. A common tool in psychology is the Likert scale, where a person might rate their agreement from 'Strongly Disagree' to 'Strongly Agree'. We know that 'Agree' is more than 'Disagree' (magnitude), but we don't know if the psychological distance between 'Disagree' and 'Neutral' is the same as between 'Neutral' and 'Agree'. The intervals are not necessarily equal.

Interval scales are where things get more mathematical. These scales have equal intervals, allowing us to perform addition and subtraction. Temperature in Celsius or Fahrenheit is a classic example: the difference between 10° and 20° is the same as between 70° and 80°.

In psychology, IQ scores are designed to be an interval scale. The difference between an IQ of 100 and 110 is intended to represent the same jump in cognitive ability as the difference between 110 and 120. This allows us to calculate means and standard deviations meaningfully. However, an IQ score of 0 does not mean a person has zero intelligence. It's a score, not a complete absence of the trait. This is the key distinction between interval and ratio scales.

Ratio scales have all four properties, including a true zero. A true zero means the complete absence of the thing being measured. In psychology, this is common for behavioral measures. Reaction time, the number of words recalled in a memory test, or the duration of eye contact are all ratio variables.

A score of 0 on a word recall test means zero words were recalled. This true zero allows for the most powerful statistical analyses. We can say that recalling 20 words is twice as many as recalling 10 words. We can't make this kind of ratio comparison with interval data. You can't say someone with an IQ of 120 is twice as smart as someone with an IQ of 60.

Knowing these properties helps you critically evaluate research and design better studies yourself. The scale dictates the statistics you can use and the conclusions you can draw.