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## Quantitative Training in Psychology is Deteriorating: Traditional Methodologists, Mathematical Psychologists, and Psychology Face a Challenge

By James T. Townsend, Richard Golden, and Thomas Wallsten

The scientific community of APA, and psychology in general, are growing increasingly concerned about the shortage of quantitatively trained psychologists. For instance, the September issue of the APA Monitor included a convincing documentation of this disheartening trend. Training in statistics and related methodologies such as experimental design has formed a foundation for rigorous experimentation, drawing of inferences, and theory building since the inception of psychology as a science in the nineteenth century. Virtually every department of psychology with a reputation for solid research has retained sufficient staff for the edification of budding psychologists in quantitative methods. Now, this tradition is at risk.

The modal interpretation of "quantitative psychologist" still tends to connote someone with extended training in statistics (at the least, and sometimes advanced degrees in mathematical statistics). This is natural because the roots of quantitative measurement in psychology were intertwined with the very birth of modern statistics in the 19th century, and especially in Great Britain. However, it is important in modern psychology to include the field of mathematical psychology when confronting issues in quantitative training. The bulk of this article focuses on this discipline and its place in instruction of scientific psychologists. Although mathematical psychology plays a vital role in scientific psychology, as we will demonstrate below, many psychologists are less familiar with the field since training programs, and even courses in that subject, are unfortunately quite rare. Hence, we take a little space to outline some of its history and features.

The use of mathematics to represent and interpret psychological theory appeared quite early in psychophysics and only slightly later in learning theory. Nonetheless, it was not until the 1950's that mathematical psychology became a legitimate field of study in its own right. The first regions of major developments were signal detection theory and methodology, and mathematical learning theory. Since its inception, mathematical modeling has arguably entered, or influenced most of the areas of study in psychology.

Mathematical psychology and traditional quantitative psychology differ in their emphasis on statistics (somewhat more in the traditional sector) and emphasis on a substantive theoretical model of the psychological processes or phenomena (somewhat more in mathematical psychology). Nevertheless, they share many tools, mathematical contents, and philosophy. We can't say how many traditional methodologists learn mathematical modeling, but virtually all mathematical psychologists receive training in psychological and mathematical statistics.

We assert that mathematical psychology has advanced not only empirical data analysis but fundamental theory in psychological science as well. Furthermore, the Society for Mathematical Psychology (whose official journal is the Journal of Mathematical Psychology) continues to actively develop and support training programs in the field of quantitative psychology.

Thus, mathematical psychology now plays a vital role in psychological theorizing and fruitfully interacts with psychological statistics and methodology in many, if not all, content areas. Some of the most influential leaders in advancing psychological science through quantitatively deep theoretical approaches over the past several decades were originally trained in or interacted strongly with the field of mathematical psychology. For example, the National Medal of Science has been awarded for mathematical psychology contributions to the Social and Behavioral Sciences to Duncan Luce, William Estes, Patrick Suppes, and Roger Shepard, all of whom have been active members of the Mathematical Psychology Community. The annual $100,000 David E. Rumelhart Prize is awarded annually to an individual or collaborative team making a significant contemporary contribution to the theoretical foundations of human cognition. Many of the past recipients have been awarded the prize based upon their contributions to mathematical models of cognition (e.g., Roger Shepard (2006), John Anderson (2005), Paul Smolensky (2005), and Richard Shiffrin (2002)) of the David E. Rumelhart Prize (as well as David Rumelhart) are or have been active members of the Society for Mathematical Psychology or were strongly influenced by mentors and colleagues who are or were active participants in the Society. These specific examples illustrate that mathematical modeling in psychology has indeed evolved to be a "respectable" profession from its origin in the 1950's.

Paradoxically, even as mathematical modeling has become "respectable" in recent years, there arguably exist fewer formal training programs than was true twenty or thirty years ago. Just as in the case of psychological statistics, this is a frightening development.

The Society for Mathematical Psychology is the main professional body for the profession in the United States. Its counterpart in Europe is the European Mathematical Psychology Group. Both hold annual conferences and support many innovations aimed at encouraging young psychologists to enter the field or to acquire elementary and advanced training in modeling and mathematics. For instance, Indiana University currently offers an NIMH supported training program in cognitive modeling which supports both pre-doctoral and post-doctoral training in mathematical and computational modeling in perception, cognition and sensory-motor processing. The Society for Mathematical Psychology presents an annual New Investigator Award for exceptional published research in the field of mathematical psychology by a recent Ph.D. The new investigator is provided with an honorary plaque, an honorarium, and an invitation to present their research as a plenary talk at the annual meeting of the Society for Mathematical Psychology. The Society for Mathematical Psychology also sponsors Student Travel Awards and special Tutorial Workshops for training mathematical psychologists.