Statistics in Psychology

An Historical Perspective

Michael Cowles

• Publisher: Psychology Press
• Year: 2005
• ISBN:
  9781135660888
• Edition: 2
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

This book presents an historical overview of the field--from its development to the present--at an accessible mathematical level. This edition features two new chapters--one on factor analysis and the other on the rise of ANOVA usage in psychological research. Written for psychology, as well as other social science students, this book introduces the major personalities and their roles in the development of the field. It provides insight into the disciplines of statistics and experimental design through the examination of the character of its founders and the nature of their views, which were sometimes personal and ideological, rather than objective and scientific. It motivates further study by illustrating the human component of this field, adding dimension to an area that is typically very technical. Intended for advanced undergraduate and/or graduate students in psychology and other social sciences, this book will also be of interest to instructors and/or researchers interested in the origins of this omnipresent discipline.

1
The Development of Statistics

Evolution, Biometrics, and Eugenics

The central concern of the life sciences is the study of variation. To what extent does this individual or group of individuals differ from another? What are the reasons for the variability? Can the variability be controlled or manipulated? Do the similarities that exist spring from a common root? What are the effects of the variation on the life of the organisms? These are questions asked by biologists and psychologists alike.

The life-science disciplines are defined by the different emphases placed on observed variation, by the nature of the particular variables of interest, and by the ways in which the different variables contribute to the life and behavior of the subject matter. Change and diversity in nature rest on an organizing principle, the formulation of which has been said to be the single most influential scientific achievement of the 19th century: the theory of evolution by means of natural selection. The explication of the theory is attributed, rightly, to Charles Darwin (1809–1882). His book The Origin of Species was published in 1859, but a number of other scientists had written on the principle, in whole or in part, and these men were acknowledged by Darwin in later editions of his work.

Natural selection is possible because there is variation in living matter. The struggle for survival within and across species then ruthlessly favors the individuals that possess a combination of traits and characters, behavioral and physical, that allows them to cope with the total environment, exist, survive, and reproduce.

Not all sources of variability are biological. Many organisms to a greater or lesser extent reshape their environment, their experience, and therefore their behavior through learning. In human beings this reshaping of the environment has reached its most sophisticated form in what has come to be called cultural evolution. A fundamental feature of the human condition, of human nature, is our ability to process a very great deal of information. Human beings have originality and creative powers that continually expand the boundaries of knowledge. And, perhaps most important of all, our language skills, verbal and written, allow for the accumulation of knowledge and its transmission from generation to generation. The rich diversity of human civilization stems from cultural, as well as genetic, diversity.

Curiosity about diversity and variability leads to attempts to classify and to measure. The ordering of diversity and the assessment of variation have spurred the development of measurement in the biological and social sciences, and the application of statistics is one strategy for handling the numerical data obtained.

As science has progressed, it has become increasingly concerned with quantification as a means of describing events. It is felt that precise and economical descriptions of events and the relationships among them are best achieved by measurement. Measurement is the link between mathematics and science, and the apparent (at any rate to mathematicians!) clarity and order of mathematics foster the scientist’s urge to measure. The central importance of measurement was vigorously expounded by Francis Galton (1822–1911): “Until the phenomena of any branch of knowledge have been submitted to measurement and number it cannot assume the status and dignity of a Science.”

These words formed part of the letterhead of the Department of Applied Statistics of University College, London, an institution that received much intellectual and financial support from Galton. And it is with Galton, who first formulated the method of correlation, that the common statistical procedures of modern social science began.

The nature of variation and the nature of inheritance in organisms were much-discussed and much-confused topics in the second half of the 19th century. Galton was concerned to make the study of heredity mathematical and to bring order into the chaos.

Francis Galton was Charles Darwin’s cousin. Galton’s mother was the daughter of Erasmus Darwin (1731–1802) by his second wife, and Darwin’s father was Erasmus’s son by his first. Darwin, who was 13 years Galton’s senior, had returned home from a 5-year voyage as the naturalist on board H.M.S. Beagle (an Admiralty expeditionary ship) in 1836 and by 1838 had conceived of the principle of natural selection to account for some of the observations he had made on the expedition. The careers and personalities of Galton and Darwin were quite different. Darwin painstakingly marshaled evidence and single-mindedly buttressed his theory, but remained diffident about it, apparently uncertain of its acceptance. In fact, it was only the inevitability of the announcement of the independent discovery of the principle by Alfred Russell Wallace (1823–1913) that forced Darwin to publish, some 20 years after he had formed the idea. Gallon, on the other hand, though a staid and formal Victorian, was not without vanity, enjoying the fame and recognition brought to him by his many publications on a bewildering variety of topics. The steady stream of lectures, papers and books continued unabated from 1850 until shortly before his death.

The notion of correlated variation was discussed by the new biologists. Darwin observes in The Origin of Species:

Many laws regulate variation, some few of which can be dimly seen,… I will here only allude to what may be called correlated variation. Important changes in the embryo or larva will probably entail changes in the mature animal… Breeders believe that long limbs are almost always accompanied by an elongated head …cats which are entirely white and have blue eyes are generally deaf… it appears that white sheep and pigs are injured by certain plants whilst dark-coloured individuals escape … (Darwin, 1859/1958, p. 34)

Of course, at this time, the hereditary mechanism was unknown, and, partly in an attempt to elucidate it, Galton began, in the mid-1870s, to breed sweet peas.¹ The results of his study of the size of sweet pea seeds over two generations were published in 1877. When a fixed size of parent seed was compared with the mean size of the offspring seeds, Galton observed the tendency that he called then reversion and later regression to the mean. The mean offspring size is not as extreme as the parental size. Large parent seeds of a particular size produce seeds that have a mean size that is larger than average, but not as large as the parent size. The offspring of small parent seeds of a fixed size have a mean size that is smaller than average but now this mean size is not as small as that of the fixed parent size. This phenomenon is discussed later in more detail. For the moment, suffice it to say that it is an arithmetical artifact arising from the fact that offspring sizes do not match parental sizes absolutely uniformly. In other words, the correlation is imperfect.

Galton misinterpreted this statistical phenomenon as a real trend toward a reduction in population variability. Paradoxically, however, it led to the formation of the Biometric School of heredity and thus encouraged the development of a great many statistical methods.

Over the next several years Galton collected data on inherited human characteristics by the simple expedient of offering cash prizes for family records. From these data he arrived at the regression lines for hereditary stature. Figures showing these lines are shown in Chapter 10.

A common theme in Galton’s work, and later that of Karl Pearson (1857–1936), was a particular social philosophy. Ronald Fisher (1890–1962) also subscribed to it, although, it must be admitted, it was not, as such, a direct influence on his work. These three men are the founders of what are now called classical statistics and all were eugenists. They believed that the most relevant and important variables in human affairs are inherited. One’s ancestors rather than one’s environmental experiences are the overriding determinants of intellectual capacity and personality as well as physical attributes. Human well-being, human personality, indeed human society, could therefore, they argued, be improved by encouraging the most able to have more children than the least able. MacKenzie (1981) and Cowan (1972,1977) have argued that much of the early work in statistics and the controversies that arose among biologists and statisticians reflect the commitment of the founders of biometry, Pearson being the leader, to the eugenics movement.

In 1884, Galton financed and operated an anthropometric laboratory at the International Health Exhibition. For a charge of threepence, members of the public were measured. Visual and auditory acuity, weight, height, limb span, strength, and a number of other variables were recorded. Over 9,000 data sets were obtained, and, at the close of the exhibition, the equipment was transferred to the South Kensington Museum where data collection continued. Francis Galton was an avid measurer.

Karl Pearson (1930) relates that Galton’s first forays into the problem of correlation involved ranking techniques, although he was aware that ranking methods could be cumbersome. How could one compare different measures of anthropometric variables? In a flash of illumination, Galton realized that characteristics measured on scales based on their own variability (we would now say standard score units) could be directly compared. This inspiration is certainly one of the most important in the early years of statistics. He recalls the occasion in Memories of my Life, published in 1908:

As these lines are being written, the circumstances under which I first clearly grasped the important generalisation that the laws of heredity were solely concerned with deviations expressed in statistical units are vividly recalled to my memory. It was in the grounds of Naworth Castle, where an invitation had been given to ramble freely. A temporary shower drove me to seek refuge in a reddish recess in the rock by the side of the pathway. There the idea flashed across me and I forgot everything else for a moment in my great delight. (Galton, 1908, p. 300)²

This incident apparently took place in 1888, and before the year was out, Co-relations and Their Measurement Chiefly From Anthropometric Data had been presented to the Royal Society. In this paper Galton defines co-relation: “Two variable organs are said to be co-related when the variation of one is accompanied on the average by more or less variation of the other, and in the same direction” (Gallon, 1888, p. 135).

The last five words of the quotation indicate that the notion of negative correlation had not then been conceived, but this brief but important paper shows that Galton fully understood the importance of his statistical approach. Shortly thereafter, mathematicians entered the picture with encouragement from some, but by no means all, biologists.

Much of the basic mathematics of correlation had, in fact, already been developed by the time of Gallon’s paper, but the utility of the procedure itself in this context had apparently eluded everyone. It was Karl Pearson, Gallon’s disciple and biographer, who, in 1896, set the concept on a sound mathematical foundation and presented statistics with the solution to the problem of representing covariation by means of a numerical index, the coefficient of correlation.

From these beginnings spring the whole corpus of present-day statistical techniques. George Udny Yule (1871–1951), an influential statistician who was not a eugenist, and Pearson himself elaborated the concepts of multiple and partial correlation. The general psychology of individual differences and research into the structure of human abilities and intelligence relied heavily on correlational techniques. The first third of the 20th century saw the introduction of factor analysis through the work of Charles Spearman (1863–1945), Sir Godfrey Thomson (1881–1955), Sir Cyril Burt (1883–1971), and Louis L. Thurstone (1887–1955).

A further prolific and fundamentally important stream of development arises from the work of Sir Ronald Fisher. The technique of analysis of variance was developed directly from the method of intra-class correlation – an index of the extent to which measurements in the same category or family are related, relative to other categories or families.

Fisher studied mathematics at Cambridge but also pursued interests in biology and genetics. In 1913 he spent the summer working on a farm in Canada. He worked for a while with a City investment company and then found himself declared unfit for military service because of his extremely poor eyesight. He turned to school-teaching for which he had no talent and which he hated. In 1919 he had the opportunity of a post at University College with Karl Pearson, then head of the Department of Applied Statistics, but chose instead to develop a statistical laboratory at the Rothamsted Experimental Station near Harpenden in England, where he developed experimental methods for agricultural research.

Over the next several years, relations between Pearson and Fisher became increasingly strained. They clashed on a variety of issues. Some of their disagreements helped, and some hindered, the development of statistics. Had they been collaborators and friends, rather than adversaries and enemies, statistics might have had a quite different history. In 1933 Fisher became Galton Professor of Eugenics at University College and in 1943 moved to Cambridge, where he was Professor of Genetics. Analysis of variance, which has had such far-reaching effects on experimentation in the behavioral sciences, was developed through attempts to tackle problems posed at Rothamsted.

It may be fairly said that the majority of texts on methodology and statistics in the social sciences are the offspring (diversity and selection notwithstanding!) of Fisher’s books, Statistical Methods for Research Workers³ first published in 1925(a), and The Design of Experiments ...