# Nominal scale

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The **nominal scale** is a type of measurement scale used in statistics and research. It is used to categorize data into distinct, non-numeric groups or categories. Nominal data cannot be quantitatively measured or ordered, and the categories are simply used to label or identify the data, rather than to indicate a specific value or rank. Examples of nominal data include gender, hair color, and religion. Nominal scales are not able to be used for mathematical operations such as addition, subtraction, multiplication or division.

## Nominal scale examples

Examples of nominal scale data include:

- Gender (male, female, non-binary, etc.)
- Hair color (brown, blonde, black, red, etc.)
- Eye color (blue, green, brown, etc.)
- Religion (Christianity, Islam, Buddhism, etc.)
- Political affiliation (Democrat, Republican, Independent, etc.)
- Marital status (single, married, divorced, etc.)
- Occupation (teacher, doctor, lawyer, etc.)
- Brand of car (Toyota, Ford, Honda, etc.)
- Type of music (pop, rock, classical, etc.)
- Color of a product (red, blue, green, etc)
- City or Country of origin (New York, Paris, Beijing, etc)
- Size of a clothing item (small, medium, large, etc)
- Name of a person

These are just a few examples, but nominal data can be any categorical data that cannot be quantitatively measured or ordered.

## Nominal scale vs. ordinal and other scales

Nominal scale is one of several types of measurement scales used in statistics and research. Some other types of scales include:

**Ordinal scale**: This type of scale is similar to nominal, in that it is used to categorize data into distinct groups or categories. However, ordinal data can be ordered or ranked. For example, a survey question that asks respondents to rank their satisfaction with a product on a scale of 1 to 5 would use ordinal data.**Interval scale**: This type of scale is used to measure data that has equal intervals between values, but does not have a true zero point. For example, temperature measured in degrees Celsius is an interval scale, because the difference between 10 degrees and 20 degrees is the same as the difference between 20 degrees and 30 degrees, but there is no true zero point for temperature, as temperatures below absolute zero do not exist.**Ratio scale**: This type of scale is similar to interval, but it also has a true zero point, meaning it is possible to meaningfully compare the ratio of two or more values. For example, weight or height are measured on a ratio scale, as there is a true zero point for weight and height (zero weight or zero height).

In summary, nominal data cannot be quantitatively measured or ordered, ordinal data can be ordered or ranked, interval data has equal intervals between values but no true zero point, and ratio data has a true zero point and equal intervals between values.

## Typical statistical measures to be used with nominal scale

Statistical measures that can be used with nominal scale data include:

**Frequency and percentage**: This measure indicates how often a particular category or group appears in a dataset. For example, if a survey asked respondents their gender, the frequency and percentage of males and females in the sample could be calculated.**Cross-tabulation**: This measure is used to examine the relationship between two nominal variables. For example, a cross-tabulation of gender and hair color would show the number or percentage of males and females with different hair colors.**Chi-square test**: This test is used to determine if there is a significant association between two nominal variables. For example, a chi-square test could be used to determine if there is a significant association between gender and hair color in a sample.**Mode**: The mode is the value that appears most frequently in a dataset. For nominal variable, it is the category that appears most frequently in a dataset.

It is important to note that most of the mathematical operation such as mean, median or standard deviation cannot be used with nominal scale data as it does not have numerical values.

## References

- Hubert, L. (1977).
*Nominal scale response agreement as a generalized correlation*. British Journal of Mathematical and Statistical Psychology, 30(1), 98-103. - Schouten, H. J. (1986).
*Nominal scale agreement among observers*. Psychometrika, 51(3), 453-466. - Gwet, K. L. (2008).
*Variance estimation of nominal-scale inter-rater reliability with random selection of raters*. Psychometrika, 73(3), 407-430.