Ordinal Scale

Chapter 1. Descriptive Statistics: Types of Data and Measurements

Ordinal Scale

The second scale of measurement is the ordinal scale.

Ordinal scale

Definition

Similar to the nominal scale, the categories of an ordinal scale are identified by names or labels. However, whereas nominal categories are completely unrelated to each other, the categories of an ordinal scale are organized in a fixed order according to their size or quality.

Examples

Olympic medals
T-shirt sizes
Likert scales
Socioeconomic class

Because the categories of an ordinal scale can be ordered in a meaningful way, it is possible to detect differences as well as the direction of the difference between two individuals. However, since the distance between categories is free to vary, no conclusive statements can be made about the size of the difference.

\[\begin{array}{r|cccc}\begin{array}{r|cccc}
&\text{Detect differences}?&\text{Direction of the difference?}&\text{Size of the difference?}&\text{Calculate ratios?}\\
&(=, \neq)&(>,<)&(+,-)&(\times , \div)\\
\hline
\text{Nominal}&\green{\text{Yes}}&\red{\text{No}}&\red{\text{No}}&\red{\text{No}}\\
\text{Ordinal}&\green{\text{Yes}}&\green{\text{Yes}}&\red{\text{No}}&\red{\text{No}}\\
\end{array}\\ \phantom{x}\end{array}\]

Olympic medals as an ordinal scale measurement

An example of an ordinal measurement would be to categorize individuals on the basis of their Olympic medal. This type of measurement makes it possible to distinguish between someone who won a gold medal and someone who won a silver medal. Thus, an ordinal scale allows the researcher to detect differences between two individuals.

Additionally, because Olympic medals have a natural ordering to them, it would be a valid statement to say that the gold medalist performed better than the silver medalist. In other words, an ordinal measurement can identify the direction of the difference between two individuals.

However, solely on the basis of their Olympic medals, it is not possible to determine how much better the gold medalist performed than the silver medalist. That is to say, no statements can be made about the size of the difference between the two medalists.