# Unidimensionality: Definition, Examples

Statistics Definitions > Unidimensionality

## What is Unidimensionality?

“Unidimensionality” is used to describe a specific type of measurement scale. A unidimensional measurement scale has only one (“uni”) dimension. In other words, it can be represented by a single number line. Some examples of simple, unidimensional scales:

• Height of people.
• Weight of cars.
• IQ.
• Volume of liquid.

Unidimensionality can also refer to measuring a single ability, attribute, construct, or skill. For example, a unidimensional mathematical test would be designed to measure only mathematical ability (and not, say, grasp of English grammar, knowledge of sports, or other non-mathematical subjects or concepts).

Some concepts (like height or weight) are obviously unidimensional. Others can be forced into a unidimensional status by narrowing the idea into a single, measurable construct. For example, self-worth is a psychological concept that has many layers of complexity and can be different for different situations (at home, at a party, at work, at your wedding). However, you can narrow the concept by making a simple line that has “low self worth” on the left and “high self worth” on the right. The three major types of unidimensional scales are:

1. Thurstone or “Equal-Appearing Interval” Scale: has a number of agree/disagree statements with numerical values attached. It is designed to be similar to an interval scale
2. Likert or “Summative” Scale: respondents are asked to rate items according to a level of agreement.
3. Guttman or “Cumulative” Scale: a scale with binary YES/NO answers.

## Unidimensionality vs. Multidimensionality

Sometimes, a unidimensional scale can over-simplify the concept you are studying. For example, scholarly ability can differ according to whether a student is stressed (e.g. exam mode) or non-stressed (e.g homework mode). A multidimensional scale has, as the name implies, multiple scales (which you can think of as multiple number lines). Unidimensionality is a key concept that affects outcomes of many statistical tests and analyses. For example, unidimensional data will maximize Cronbach’s Alpha.

## References

Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. SAGE.

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Stephanie Glen. "Unidimensionality: Definition, Examples" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/unidimensionality/