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:

**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**Likert or “Summative” Scale**: respondents are asked to rate items according to a level of agreement.**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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