Measurement

A major difference between a “well-developed” science such as physics and some of the less “well-developed” sciences such as psychology or sociology is the degree to which things are measured. In this volume, we develop a theory of measurement that can act as a foundation for measurement in the social and behavioral sciences. Starting with such classical measurement concepts of the physical sciences as temperature and mass, we extend a theory of measurement to the social sciences. We discuss the measurement of preference, loudness, brightness, intelligence, and so on. We also apply measurement to such societal problems as air and noise pollution, weather forecasting, and public health, and comment on the development of pollution indices and consumer price indices.

Throughout, we apply the results to decisionmaking. The decisionmaking applications deal with transportation, consumer behavior, environmental problems, energy use, and medicine, as well as with laboratory situations involving human and animal subjects.

In this introduction, we try to give the reader a quick preview of the contents and organization of the book, and of the problems we shall address. The reader might prefer to read the introduction rather quickly the first time, and to return to it later.

A large body of mathematics consists of facts that can be presented and described much like any other natural phenomenon. These facts, at times explicitly brought out as theorems, at other times concealed within a proof, make up most of the applications of mathematics, and are the most likely to survive changes of style and of interest.

This ENCYCLOPEDIA will attempt to present the factual body of all mathematics. Clarity of exposition, accessibility to the non-specialist, and a thorough bibliography are required of each author. Volumes will appear in no particular order, but will be organized into sections, each one comprising a recognizable branch of present-day mathematics. Numbers of volumes and sections will be reconsidered as times and needs change.

It is hoped that this enterprise will make mathematics more widely used where it is needed, and more accessible in fields in which it can be applied but where it has not yet penetrated because of insufficient information.

The Psychophysical Problem

Loudness

A sound has a variety of physical characteristics. For example, a pure tone can be described by its physical intensity (energy transported), its frequency (in cycles per second), its duration, and so on. The same sound has various psychological characteristics. For example, how loud does it seem? What emotional meaning does it portray? What images does it suggest? Since the middle of the nineteenth century, scientists have tried to study the relationships between the physical characteristics of stimuli like sounds and their psychological characteristics. Some psychological characteristics might have little relationship to physical ones. For example, emotional meaning probably has little relation to the physical intensity of a sound, but rather it may be related to past experiences, as, for example, with the sound of a siren. Other psychological characteristics seem to be related in fairly regular ways to physical characteristics. Such sensations as loudness are an example. Psychophysics is the discipline that studies various psychological sensations such as loudness, brightness, apparent length, and apparent duration, and their relations to physical stimuli. It attempts to scale or measure psychological sensations on the basis of corresponding physical stimuli. In this chapter, we shall describe some of the history of psychophysical scaling and its applications or potential applications to measurement of noise pollution, of attitudes, of utility, etc., and we shall discuss ways to put psychophysical scaling on a firm measurement-theoretic foundation. We shall concentrate on loudness.