On the application of measurement theory in software engineering

Elements of measurement theory have recently been introduced into the software engineering discipline. It has been suggested that these elements should serve as the basis for developing, reasoning about, and applying measures. For example, it has been suggested that software complexity measures should be additive, that measures fall into a number of distinct types (i.e., levels of measurement: nominal, ordinal, interval, and ratio), that certain statistical techniques are not appropriate for certain types of measures (e.g., parametric statistics for less-than-interval measures), and that certain transformations are not permissible for certain types of measures (e.g., non-linear transformations for interval measures). In this paper we argue that, inspite of the importance of measurement theory, and in the context of software engineering, many of these prescriptions and proscriptions are either premature or, if strictly applied, would represent a substantial hindrance to the progress of empirical research in software engineering. This argument is based partially on studies that have been conducted by behavioral scientists and by statisticians over the last five decades. We also present a pragmatic approach to the application of measurement theory in software engineering. While following our approach may lead to violations of the strict prescriptions and proscriptions of measurement theory, we demonstrate that in practical terms these violations would have diminished consequences, especially when compared to the advantages afforded to the practicing researcher.