Ordinal Measure

A measure is a data point. In many research applications, a measure is a number assigned to an individual, organism, or research participant that reflects his or her or its standing on some construct. A measure is taken at a given time, on a given individual, in a given setting, using a given type of recording device. A set of measures refers to multiple data points. For example, a measure of height on each of 10 individuals represents a set of 10 measures.

Ordinal measures can be described from different vantage points. Ordinality as applied to a set of measures describes a property of the function that relates observed measures of a construct to the true values of that construct. A set of measures of a construct has the property of ordinality if the values of the measure are a strictly monotonic function of the true values of the construct, that is, if the relative ordering of individuals on the true construct is preserved when one uses the observed measure to order individuals. For example, 10 individuals may differ in their height, and they can be ordered from shortest to tallest. A researcher may develop a strategy for measuring height such that higher scores on the index imply greater height. The set of measures taken on the 10 individuals is said to have ordinal properties if the ordering of individuals on the index is the same as the ordering of individuals on the underlying dimension of height.

Strictly speaking, ordinal measures do not convey information about the magnitude of differences between individuals or organisms on the underlying dimension. They only permit us to state that one individual has more or less of the dimension than another individual.