Over-measurement

Abstract

Measurement is a special type of evaluation that is more exact than either opinion or estimation. In the social sciences, in particular, most evaluations are not measures, but rather mixtures of opinion and estimation. Over-measurement represents anchoring to evaluations which are not measures. For an over-measured characteristic, single measures are used when instead a portfolio of possible measures should be used. There are three implications. First, measurements of characteristics which depend on the over-measured characteristic are biased. Secondly, decisions which depend on the over-measured characteristic are biased. Thirdly, over-measurement biases the measurement of uncertainty.

Introduction

In his Epistemology of Measurement, Mari [1] asserts that measurement is a specific form of evaluation. While the term measurement is often used synonymously with other types of evaluation, measurement is a process with more precision. The purpose of measurement is to construct a measure function to determine measurement values from a sample of observations; just as the purpose of estimation is to construct an estimator to determine estimates from a sample of observations. A measure function has more exactitude than an estimator, and more structure than an opinion. Measure functions and measurement values have invariance properties not shared by other forms of evaluation. A measure function should be invariant across observers, continuous across time and continuous across small perturbations of characteristics, conditions summarized in Sawyer et al. [2]. These invariance and continuity conditions distinguish measurement from other types of evaluation.

Measurement is a process designed to measure characteristics of objects.¹ Finkelstein [3, p. 41] defined measurement as the process which assigns symbols to attributes of real objects and events, with the purpose of quantification. Rossi [4, p. 558] defined the process in terms of the empirical properties of the characteristics, a reference measurement scale and a measuring system. And Urbanski and Samsonowicz [5, p. 36] distinguished two stages; a mapping of states of real objects into states of measuring instruments and a mapping of states of measuring instruments into real numbers. But the measurement process is more involved than just a mapping from a state space of characteristics onto the real number line. As discussed by Sawyer et al. [2, p. 95], measurement typically involves a process of convergence from an initial measure function to an existing measure function.² The process is an iterative process with the initial measure as its starting point. The measurement process depends on the initial measure³; and often the process is anchored by that measure. For example, Mohs scale of hardness (Cordua [6]) was the first measure of mineralogical hardness and subsequent measures of hardness correlate highly with it. Similarly, measures of the national accounts have been anchored by the system of national accounts first proposed by Meade and Stone [7]. Regarding measurement as an iterative process necessarily leads to questions as to whether the process is convergent and whether one measure or a portfolio of measures is required.

The questions posed in this paper relate to the convergence of the measurement process; in particular whether for every characteristic the measurement process necessarily converges to a measure function which satisfies invariance and continuity properties; and the implications of measuring characteristics for which the measurement process is not convergent. In sum, we posit the question is it possible to over-measure and if so, what are the consequences of over-measurement?

Section 2 begins with an exposition of measurement and how it differs from other evaluations such as opinion and estimation. In Section 3 the concept of over-measurement is defined and the consequences of over-measurement explored. Section 4 presents an illustration of over-measurement by examining a measure of the economy the gross domestic product GDP.