**What is an ordinal variable?**

An ordinal variable is one that takes values that can be ordered (or denote an order). For example, the variable height of a person can be classified as: tall, average and short.

An ordinal scale, in addition to identifying, grouping, and differentiating the study units, like a nominal variable, also describes the magnitude and, therefore, is characterized by ordering; that is, the study units can be ordered in increasing or decreasing order in terms of magnitude.

In this scale we speak of first, second, third, or high, medium, low; but no measure is established between the classes. For example: the rating variable in a satisfaction test for a service provided can be measured in four categories: dissatisfied, indifferent, satisfied, and very satisfied.

It can be ordered according to the satisfaction expressed, but it is not known how different is satisfied from very satisfied, nor is it known if the difference between dissatisfied and indifferent is the same as between satisfied and very satisfied.

The ordinal scale refers to measurements that only make “greater”, “less”, or “equal” comparisons between consecutive measurements. It represents a ranking or ordering of a set of observed values.

**Ordinal variable concept and characteristics**

On an ordinal scale, the observations are placed in relative order with respect to the characteristic being evaluated. That is, the data categories are classified or ordered according to the special characteristic they possess.

If we use numbers, their magnitude represents the rank order of the observed attribute. Only the relationships “greater than”, “less than”, and “equal to” have meaning on an ordinal measurement scale.

From a mathematical point of view, and like nominal scales, ordinal scales only admit the calculation of proportions, percentages and ratios.

The measure of central tendency that best explains an ordinal variable is the median, which is the value that is located in the center of the data set ordered from smallest to largest.

When objects are classified by a characteristic, it is possible to establish which object has more or less of the characteristic compared to another; but the difference cannot be quantified.

For example, three objects that have been ordered as ‘first’, ‘second’ and ‘third’, taking into account some characteristic. Second place differs from first by an amount that is not necessarily equal to the amount by which it differs from third place.

**Examples of ordinal variables**

Some examples of ordinal variables:

– Social class (A – High; B – medium high; C – medium; D – low; E – very low).

– Qualitative school grades (I – insufficient; A – acceptable; B – good; S – outstanding; E – excellent).

– Military ranks (General, Colonel, Lieutenant Colonel, Major, Captain, etc.).

– Education level (primary, high school, professional technician, technologist, university, etc.).

– Stage of development of a human being (newborn, baby, child, young, adult, old).

– Film classification (A – All audiences; B – over 12 years; C – over 18 years; D – Over 21 years).

– Ripeness of a fruit (green, bright, ripe, very ripe, rotten).

– Degree of satisfaction with the provision of a public service. (Very satisfied; Satisfied; Indifferent; etc.).

**– Examples explained**

**Evaluation of a teacher by his students**

The students of a certain course have the possibility of filling out a survey to evaluate the pedagogical capacity of their teacher, which is measured with an ordinal variable whose scale is: 5 – Excellent, 4 – Good, 3 – Average, 2 – Bad , 1 – Poor.

The variable values are ordered from highest or best to lowest or worst: excellent is better than good, good is better than average, etc. However, it is not possible to distinguish the magnitude of the differences.

Is the difference between excellent and good the same as between bad and poor? It is not possible to affirm it.

If we use numbers, they do not indicate magnitude. For example, one should not conclude that the rating Good (rating 4) is twice as high as Bad (rating 2). It can only be said that the Good rating is better than the Bad rating, but how much better it cannot be quantified.

**Acceptance level of a meal**

A tasting contest evaluates meals in a cooking contest through the ordinal variable in level of acceptance expressed in: A – Excellent, B – Good, C – Not acceptable. The use of a measurement scale ordered from highest to lowest is evident, but it is not possible to establish the difference between the values of the scale.

Since it’s a contest, how is the winner determined? It seems that the most appropriate is the use of fashion to make the decision about the winner of the contest. Understand the mode as the name given to the highest value (the most frequent) of the counts per level. For example, 5 A, 14 B, 10 C were counted; the mode is B, since it is the level that had the greatest number of opinions.

**Differences with nominal variable**

The following table presents some differences and similarities between the variables measured on a nominal and ordinal scale:

**References**

Freund, R.; Wilson, W.; Mohr, D. (2010). Statistical methods. Third ed. Academic Press-Elsevier Inc.

Glass, G.; Stanley, J. (1996). Statistical methods not applied to the social sciences. Prentice Hall Hispanoamericana SA

Beautiful.; Marchal, W.; Wathen, S. (2012). Statistics applied to business and economy. Fifteenth ed. McGraw-Hill/Interamericana Publishers SA

Orlandoni, G. (2010). Statistical measurement scales. Telos Magazine. Retrieved from ojs.urbe.edu.

Siegel, S.; Castellán, N. (1998). Non-parametric statistics applied to the behavioral sciences. fourth ed. Editorial Trillas SA

Wikipedia. (2019). Level of measurement. Retrieved from en.wikipedia.org.