Ordinal Level of Measurement

The ordinal level of measurement refers to measurement in which the distances between observed values are irrelevant and only the order relations of <, >, and = should be considered.

Consider the Likert-type item common in the social sciences. Typically, such an item consists of a statement that captures the essence of the construct being measured (e.g., depression), followed by adjectives or adjectival response phrases indicating degree of endorsement of the statement. Very often, the adjectival phrases are coded by increasing integer values, an example being 0 = not at all,1= a little bit,2= moderately,3= a lot,4= quite a bit. It is important to realize that considered in isolation (e.g., not in the context of a scaling model), the statements are inexact to the extent that they do not imply distances between them. Equidistant interpretations such as quite a bit − a lot = moderately − a little bit, characteristic of interval-level measurement, are not justified. On the other hand, ordinal interpretations such as not at all < quite a bit are justified. Suppose there is no response error for an item and Respondent A selects not at all and Respondent B selects quite a bit. Then the empirical ordering with respect to endorsement is Respondent A < Respondent B, which is represented by0<4. The empirical ordering of the respondents is accurately represented by the order relations of the observed values. The representation is limited to the relations

[Page 717]

of <, >, and =, because 4 − 3=2 − 1, for example, is not a valid representation for ordinal level of measurement.

An interesting characteristic of the ordinal level of measurement is invariance under any order-preserving transformation such as the natural log transformation. Suppose we obtain the following observed values from five people using our Likert-type item: 1, 2, 2, 3, 4. Ordinal level of measurement dictates that the values of the number are irrelevant and only their order is important. Thus, any other set of numbers with the same order will be an equally valid ordinal representation. For example, taking the natural log of the original values, we obtain 0, .6932, .6932, 1.0986, 1.3863. The logtransformed values look quite different from the original numbers but retain the same ordinal information.

Depending on an analyst's epistemology, the monotonic invariance property may proscribe certain statistical methods for ordinal-level data. Methods such as the Spearman rank correlation coefficient yield invariant results under any monotonic transformation whereas methods such as Pearson's correlation coefficient do not. When one is analyzing ordinal data, it may be desirable to use a statistical method that considers only ordinal relations so that test statistics and p values do not change under order-preserving transformations.