Probability and Statistics Index > Statistics Definitions > Nominal Variable

## Definition of Nominal Variable

A nominal variable is another name for a categorical variable. Nominal variables have two or more categories without having any kind of natural order. they are variables with no numeric value, such as occupation or political party affiliation. Another way of thinking about nominal variables is that they are **named **(nominal is from Latin *nominalis*, meaning *pertaining to names*).

**Nominal variables:**

- Cannot be quantified. In other words, you can’t perform arithmetic operations on them, like addition or subtraction, or logical operations like “equal to” or “greater than” on them.
- Cannot be assigned any order.

## Examples of Nominal Variables

- Gender (Male, Female, Transgender).
- Eye color (Blue, Green, Brown, Hazel).
- Type of house (Bungalow, Duplex, Ranch).
- Type of pet (Dog, Cat, Rodent, Fish, Bird).
- Genotype ( AA, Aa, or aa).

Nominal variables are related to the nominal scale, where data is categorized without any order.

## The Nominal Scale

The nominal scale, sometimes called the* qualitative type*, places non-numerical data into **categories or classifications**. For example:

- Placing cats into breed type. Example: a Persian is a breed of cat.
- Putting cities into states. Example: Jacksonville is a city in Florida.
- Surveying people to find out if men or women have higher self-esteem.
- Finding out if introverts or extroverts are more likely to be philanthropic.

These pieces of information aren’t numerical. They are assigned a **category** (breeds of cat, cities in Florida, men and women, introvert and extrovert). Qualitative variables are measured on the nominal scale.

## Mean Mode and Median for the Nominal Scale

The nominal scale uses categories, so **finding the mean or the median makes no sense**. You *could* put the items in alphabetical order but even then, the middle item would have no meaning as a median. However, a mode (the most frequent item in the set) is possible. For example, if you were to survey a group of random people and ask them what the most romantic city in the World is, Venice or Paris might be the most common response (the mode).

The nominal scale is one of **four scales of measurement** in statistics. The other three are:

- The Ordinal Scale: Rank order (1st, 2nd 3rd), dichotomous data that has two choices like true/false or guilty/innocent and non-dichotomous data with choices like “completely agree” “somewhat agree” “neutral” and “disagree.”
- The Interval Scale, sometimes called
*Scaled Variable*: data with degrees of difference like time B.C. or Celsius.. Interval scales have arbitrary zeros (for example, when B.C. began and ended has no real mathematical basis). - The Ratio Scale: encompasses most measurements in physics and engineering like mass and energy. Ratio scales have meaningful zeros (zero energy means that energy does not exist).

The four scales were suggested by Stanley Smith Stevens in a 1946 Science article titled “On the Theory of Scales of Measurement.”

## When can Quantitative Variables be treated as Nominal Variables?

If you have a tiny amount of discrete, quantitative variables, you may want to treat them as nominal variables for data analysis. For example, let’s say you were studying the average number of children in a certain small town and want to know if the number of children vary between poor and middle class households. The number of children could be 0,1,2,3,4,5,6+. However, when you actually perform the study you find out the families in this particular town either have two children or none. You could analyze your results using a two-sample Student’s t–test or a one-way ANOVA. However, you’ll get better results if you treat number of children as a nominal variable, with the values “0” and “1,” and compare the results using Fisher’s exact test of independence (used when you have two nominal variables and you want to compare proportions); if you have a very large sample size you could also use chi-square or a G test of independence.

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WABWIRE Paul Francis