### Chapter 1. Descriptive Statistics: Types of Data and Measurements

### Nominal Scale

The first and weakest scale of measurement is the *nominal* scale.

Nominal scale

**Definition**

The sole purpose of a **nominal** scale is to classify individuals into categories with different names or labels.

A nominal scale is made up of *completely unrelated* categories that cannot be arranged or ordered in any meaningful way.

**Examples:**

- Eye color
- Religion
- Academic major
- Emotions

#\phantom{0}#

Using a nominal measurement, it is possible to *detect differences* between two individuals, but no conclusions can be drawn about the *direction* or *size* of the difference. As such, no mathematical operations should be applied to data measured on a nominal level. This severely limits the number of statistical techniques that can be used to describe and analyze nominal data.

\[\begin{array}{r|cccc}\begin{array}{r|cccc}

&\text{Detect differences}?&\text{Direction of the difference?}&\text{Size of the difference?}&\text{Calculate ratios?}\\

&(=, \neq)&(>,<)&(+,-)&(\times , \div)\\

\hline

\text{Nominal}&\green{\text{Yes}}&\red{\text{No}}&\red{\text{No}}&\red{\text{No}}\\

\end{array}\\ \phantom{x}\end{array}\]

Eye color as nominal scale measurement

An example of a nominal measurement would be to categorize individuals on the basis of their eye color. This type of measurement makes it possible to distinguish between someone with blue eyes and someone with brown eyes. Thus, a nominal scale allows the researcher to *detect differences *between two individuals.

It would be inappropriate, however, to claim that someone with blue eyes has more or less eye color than someone with brown eyes. In other words, a nominal measurement cannot identify the *direction *of the difference between two individuals.

Along those same lines, because nominal categories are non-numeric in nature, one cannot subtract blue eyes from brown eyes in order to calculate the *size *of the difference between two individuals.

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