Ordinal scale

Variables at an ordinal scale of measurement are, typically, those such as satisfaction, subjective perception of temperature, etc. The values of these variables can be ordered hierarchically against each other, and we can use this ranking as a way of quantification. Yet, the differences between values are not actually quantified and, thus, such variability is in rank only.

For example, job satisfaction may be an interesting variable to use to predict worker's turnaround at a company. It is reasonable to ask people how satisfied they are and rank them according to a scale from, for example, "Very dissatisfied" to "Very satisfied" with their work conditions. In so doing, we know that satisfied workers are more so than dissatisfied ones, and that very satisfied workers are more so than satisfied ones. But we cannot be certain of whether the distance among ranks is the same for all values (ie whether the distance between "very dissatisfied" and "moderately dissatisfied" is the same than between "moderately satisfied" and "very satisfied"). We only know they are higher or lower than the next value, but not how much, precisely.

The values of variables at an ordinal scale are normally coded numerically, although the actual number used for this coding may vary depending on the researcher or on social conventions (eg, a satisfaction scale may run from negative values, to rank dissatisfaction, to positive values, to rank satisfaction, but it may also run from a low positive value to a higher value, respectively. Other ranks, like academic grades, use conventions, such as letter grades or GPA values).

For example, a satisfaction scale may be coded as follows:

 Very dissatisfied Moderately dissatisfied Neither dissatisfied nor satisfied Moderately satisfied Very satisfied -2 -1 0 +1 +2 1 2 3 4 5 +2 +1 0 -1 -2

We may use the concept of "ordinal variable" (or "ordinal-level variable") to refer to those variables which use an ordinal scale of measurement. This is "handy" although not fully correct. That is, the quality of being "ordinal" refers to the scale not to the variable. That is, it is possible to transform the values of any "quantitative" variable into an ordinal scale, and, although less likely, to transform the values of an ordinal variable into another quantitative level of measurement.

For example, we may transform an interval variable (degrees of heat) into an ordinal one (cold, mild, hot) to assess, for example, the relationship between perceived temperature and socialization outside the home.
Alternatively, a scale of dissatisfaction may be treated as if it were an interval scale, analyzing the numerical data using statistics more appropriate to the latter than to the former.

# Properties

• Ordinal variables vary quantitatively, but the most that we can assure is that each level is higher or lower than the next but not how much.
• The values of ordinal variables can, thus, be ranked hierarchically.
• If required, the most appropriate "average" for ordinal variables is the median.

# Want to know more?

Wikipedia - Level of measurement
You can learn a bit more about levels of measurement in Wikipedia.