Representational Measurement Theory

Representational measurement is, on the one hand, an attempt to understand the nature of empirical observations that can be usefully recoded, in some reasonably unique fashion, in terms of familiar mathematical structures. The most common of these representing structures are the ordinary real numbers ordered in the usual way and with the operations of addition, +, and/or multiplication, ·. Intuitively, such representations seems a possibility when dealing with variables for which people have a clear sense of “greater than.” When data can be summarized numerically, our knowledge of how to calculate and to relate numbers can usefully come into play. However, as we will see, caution must be exerted not to go beyond the information actually coded numerically. In addition, more complex mathematical structures such as geometries are often used, for example, in multidimensional scaling. On the other hand, representational measurement goes well beyond the mere construction of numerical representations to a careful examination of how such representations relate to one another in substantive scientific