Jun 11, 2025·Understanding IQ ScoresMeasurement and IQ Score Properties
Understanding IQ measurement: Why intelligence scores are interval-level data, what mathematical functions apply, and the limits of psychological testing.
Dr. Russell T. WarneChief Scientist
Psychological testing is part of a larger scholarly field called “measurement.” In its broadest sense, measurement includes the science of defining and identifying how to measure everything from physical measurements to psychological traits to opinions to societal characteristics. Most measurement occurs within a scientific discipline, though; the physicists interested in measurement rarely consult with the measurement psychologists (and vice-versa), for example.
An exception to this rule occurred in the 1930s when the British Association for the Advancement of Science convened a committee of physical scientists and psychologists to define how to measure human sensation--one of the few areas where the measurement physicists’ and psychologists’ interests intersect. After 8 years of meetings and correspondence, the committee members could find no common ground on how to measure psychological experience with the precision of physical measurements -- or even whether psychological measurement was possible.
This troubled one member of the committee, S. S. Stevens. As a psychophysicist, Stevens was uniquely situated at the intersection of these two groups of scientists. His specialty was studying how physical properties of stimuli (like volume -- measured in decibels) related to the psychological experience of loudness (measured with subjective rating scales). He knew that this work produced useful, valid results (e.g., Stevens, 1936). There must be a way to reconcile measurement in physics and psychology.
Stevens published this reconciliation in 1946. In a landmark article, he explained that both the physicists and the psychologists were doing measurement, but their data were at different levels of measurement (Stevens, 1946). Stevens also created a framework for understanding different levels of measurement that is still widely used today.
There are four levels of measurement: nominal, ordinal, interval, and ratio, listed in increasing order of complexity (Stevens, 1946). Nominal measurement consists of assigning a consistent number to categories--such as “1” for males and “2” for females. In ordinal measurement, the numbers indicate ascending or descending rank order. For example, when education levels are assigned a series of numbers with an order indicating ascending or descending levels of education (e.g., “1” for high school graduates, “2” for college graduates, and “3” for people with an advanced degree), this is ordinal data.
Interval data preserve the rank order of numbers, but the distance between numbers is equal across the entire scale. The Celsius and Fahrenheit temperature scales are both interval data. Finally, data at a ratio level of measurement have all of the properties of interval data, but with the value of “0” corresponding to a true absence of the thing being measured (Stevens, 1946).
The level of measurement matters because the level determines what mathematical functions can be performed on the data. This is shown in the table below. Nominal data can only be counted, classified, and expressed as proportions and percentages, while ratio data are the most flexible.
| Mathematical function | Nominal data | Ordinal data | Interval data | Ratio data |
| Classification | ✅ | ✅ | ✅ | ✅ |
| Counting | ✅ | ✅ | ✅ | ✅ |
| Proportions and Percentages | ✅ | ✅ | ✅ | ✅ |
| Rank ordering | ❌ | ✅ | ✅ | ✅ |
| Addition | ❌ | ❌ | ✅ | ✅ |
| Subtraction | ❌ | ❌ | ✅ | ✅ |
| Dividing to form averages | ❌ | ❌ | ✅ | ✅ |
| Dividing to form ratios | ❌ | ❌ | ❌ | ✅ |
| Source: Warne, 2021, p. 25 |
Where do IQ scores fit into this? All experts agree that test scores are either ordinal or interval levels of data (Reynolds, 2010; Warne, 2021). IQ scores, specifically, function as interval-level data (Jensen, 1998). That means that it makes sense to rank-order people on the basis of their IQs, meaningfully add and subtract scores (for example, by stating that the 10-point difference in intelligence between an IQ of 80 and 90 is the same as the 10-point difference in intelligence between an IQ of 110 and 120). IQ scores can also be averaged.
However, because IQ scores cannot be used to form ratios, it does not make sense to say that a person with an IQ of 125 is 25% smarter than 100 (a ratio of 1.25:1) or that a person with an IQ of 140 is twice as smart as someone with an IQ of 70 (a ratio of 2:1). That is because--unlike measurements of speed, weight, or many other scales in the physical sciences--the 0 on an IQ scale does not indicate the total absence of intelligence. Instead, IQs are arbitrarily set so that 100 corresponds to the population mean and 15 is the population average.
Intelligence testing is a form of measurement. Indeed, it is one of the most sophisticated measurement methods in the social sciences. It does not have a physical standard to define it (like the speed of light is used to define a second, for example), which is IQ is not ratio-level data. But, as the table shows, interval-level scores, like IQs, are extremely flexible and can be used in a variety of ways.
Almost 80 years after Stevens’s insights, psychologists know the strengths and limits of their measurements, whether that is for intelligence, personality, creativity, or many other traits. While these psychological measurements are not at the same level of measurement as most of the data from physics, psychological scores like IQs are extremely useful and versatile.
References
Jensen, A. R. (1998). The g factor: The science of mental ability. Praeger.
Reynolds, C. R. (2010). Measurement and assessment: An editorial view. Psychological Assessment, 22(1), 1-4. https://doi.org/10.1037/a0018811
Stevens, S. S. (1936). A scale for the measurement of a psychological magnitude: Loudness. Psychological Review, 43(5), 405-416. https://doi.org/10.1037/h0058773
Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677-680. https://doi.org/10.1126/science.103.2684.677
Warne, R. T. (2021). Statistics for the social sciences: A general linear model approach (2nd ed.). Cambridge University Press.
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AuthorDr. Russell T. WarneChief Scientist
