data with which the economist deals. For our present purpose one salient fact alone needs to be emphasized. Whether we are concerned with births or deaths, with unemployed men or with stock prices, with interest rates or human welfare, our primary interest is not in the individual event. There are many reasons why this is so. Complete knowledge of all the events of a given type is absolutely impossible.2.All the factors affecting the price set in a given sale of wheat cannot be known to us, nor is it conceivable that we should have direct knowledge of all the individual transactions in wheat during a given day, month or year. Moreover, for the purpose of the economist, the individual event is not significant. In a world marked by absolute sameness such knowledge would be important, but such is not the case in the world of economic events. No price bargain, for example, is identical with any other, in all respects. The economist must, perforce, deal with groups, and must ignore the unique event. All the phenomena with which economics deals are complex, incapable of analysis in terms of individual events. Reverting to Maxwell's classification, economic knowledge is statistical, not historical knowledge. It is knowledge of aggregates and groups in terms of averages, and the conclusions of economic reasoning apply only to aggregates of events or things

The fact of variation, which is an essential element in the statistical view, is of particular importance in the economic field. The mechanical view may be applied to the inorganic world with more accuracy and with fewer qualifications than to the social and economic world, because variation, while it exists in the former field, is less pronounced than in the organic and social realms. Inorganic reality approaches more closely the conceptual limit of absolute sameness than do the facts of social life. Accordingly, natural laws as applied to the physical world have been less hedged about by qualifications than have the generalizations of economics. Economists, in their manipulation of prices, interest rates, profits, and standards of living are handling material characterized by a high degree of variation. The application of the mechanical method, which may involve but small errors in the physical sciences, results in wide discrepancies in the economic sphere between laws of the rigid mechanical type and the facts of economic life. This condition tends to bring about that emasculation of generalizations by a continual process of hedging and qualification which has been characteristic of economics. The existence of variation makes certainty less attainable in economics than in the physical sciences. Our knowledge relates to averages, and when we seek to go beyond the average to the unique.

event we pass into a realm of uncertainty. Because of this wider variation, knowledge in the realm of economics is "mingled with doubt" to a greater degree than in the fields where things and events approach a condition of sameness. As we move away from the conceptual limit of sameness, probability and approximation must play a larger part in our reasoning.

It follows necessarily from this view of the nature of our knowledge of economic events, that generalizations with respect to the data of economics-the laws of economics-are statistical and not mechanical laws. The relations between the events which constitute the raw materials of economics are not constant and immutable. They are relations of partial dependence, of contingency; they are relations in which the element of probability bulks large.

This is quite far removed from that view which was implicit in classical doctrines, and which has been stated by more than one writer of that school. "Alike in the case of the physical and of the economic world," writes Cairnes, "the facts we find existing are the results of causes between which and them the connection is constant and invariable. It is, then, the constant relations exhibited in economic phenomena that we have in view when we speak of the laws of the 'phenomena of wealth,' and in the exposition of these laws consists the science of Political Economy." In this Cairnes reflects the general attitude of his time toward economic generalizations. Political economy was conceived to be a universal science "founded on invariable laws of nature.' Governed by this conception, the elder economists gave themselves to the pursuit of general laws of universal validity. They viewed the economic system as they viewed the physical world, seeing both economic and physical phenomena as manifestations of the reign of law. The task of the economist was the discerning and the expounding of these laws. Such an absolutist and animistic conception of law did not conduce to the increase of useful economic knowledge nor to the forging of effective instruments for the control of economic phenomena.

This mechanical view has been generally discarded by modern economists. Most workers in this field have recognized the true nature of economic laws, viewing them as statements of tendencies and average relationships; although, because the approach has not usually been quantitative, the statistical implications of this fact have not generally been realized. Even in an earlier day, the failure of economic laws to work out uniformly and consistently was recognized, but the

1 J. E. Cairnes, Character and Logical Method of Political Economy, 19-20.

subterfuge of caeteris paribus was used to take up the slack-a means of evasion rather widely resorted to in traditional economics. In arguing, therefore, that the laws of economics are statements of average relationships, not of uniform and unvarying rules, no new truth is enunciated. Alfred Marshall long since called economic laws "statements of economic tendencies," and this view prevails among economists today. But a fuller recognition and acknowledgment of the implications of this view of the nature of law, both as regards the body of economic theory and the methods of economic research, would serve to advance economic knowledge and to facilitate the effective utilization of that knowledge.

Economists, in accepting Marshall's definition of economic laws as statements of "tendencies," are accepting the statistical view of nature, in the economic sphere. In Royce's language, ... the term tendency is, in every exact usage which you can give it, an essentially statistical term." But the acceptance of the statistical view has been in most cases unconscious and unavowed. Mechanistic preconceptions, as to the nature of economic data and the character of economic laws, survive to confuse thought and to hamper research. An archaic view of cause and effect run through much of our thinking on economic subjects, even though, in the formulation of definitions, a strict causal relationship has been disavowed.1

The failure consciously to acknowledge the statistical nature of many of the central problems of economics tends to take the edge from the tools of economic research. When economists speak of "tendencies," and qualify their statements by "other things being equal" they are dealing fundamentally with statistical factors. Failing to employ appropriate instruments, their statements tend to be loose and ambiguous, their conclusions to lack precision and their "laws" to lack authority. Methods of research and methods of stating and applying conclusions in economics should be adapted to the data being handled. These data are masses of events related not in terms of certainty but of contingency; our knowledge of these

1 The attitude of W. Stanley Jevons, as expressed in the following passage, is in harmony with the statistical view as applied to economics:

"... it seems to be impossible to discover more than an approximate law (of human mortality). It may perhaps be urged that in such subjects no single invariable law can be expected. . . . The results observed may in fact be aggregates of an immense number of separate results, each governed by its own separate laws, so that the subjects may be complicated beyond the possibility of complete resolution by empirical methods. This is certainly true of the mathematical functions which must some time be introduced into the science of political economy." Principles of Science, 500-1.

events is knowledge in terms of aggregates and averages. Methods appropriate to these conditions must be employed.

No one method may be put forward as constituting the royal road to economic knowledge, and it is far from the purpose of the present paper to present any such claim. All methods must take account of the underlying conditions, however, and if the view here presented be correct, these underlying conditions are statistical in character. A recognition of this fact is at all times necessary; it is imperative when methods involving measurement are employed in economic study.

There is, I think, general agreement among modern economists as to the necessity of measurement if the science of economics is to have a valid claim to recognition. Alfred Marshall's great work centers about the statement "The raison d'être of economics as a separate science is that it deals chiefly with that part of man's action which is most under control of measurable motives. Even the strongest advocate of a deductive science of economics would admit the necessity of employing quantitative methods for testing and verifying his conclusions. Granted the necessity of measuring, questions arise as to how we are to measure, as to what tools are appropriate to the data we are handling. If we accept the statistical view of nature, insofar as affairs economic are concerned, we must perforce employ the tools of statistics, and base our reasoning upon the fundamental conceptions of averages, approximation and probability. When dealing with mass phenomena the quantitative method means the statistical method, and our results have the degree of authority given by that method and the limitations inherent in that method. For an understanding of these limitations the distinction between statistical description and statistical induction is of fundamental importance.

Given a body of material, as a number of commodity prices, wage figures, interest rates, or individual incomes, the statistical method affords a means of describing concisely the characteristics of the group. Since there is a high degree of individual variation we are precluded from using the historical method. The intensive study of an individual case will not give us the essential characteristics of the group. By a process of averaging the essence of the aggregate may be distilled into a single typical figure representing the central tendency or the most common value. The degree of "scatter" or dispersion about this central value may again be described in summary fashion by a single figure, a measure of variation. The characteristics of the group as a whole with respect to symmetrical arrangement may be described by a third figure. Other distinctive

group features are capable of statistical description in the same way. The three or four resulting values have replaced the hundreds or thousands of individual figures representing the individual members of the group. The individual case has disappeared, has been submerged in the group. The measures secured relate to the group as an entity. Knowledge of the individual cases has been sacrificed deliberately, to the end that our knowledge of the group may be increased

Again, the problem may be that of describing the relationship between two variable factors. We may be seeking to describe, in summary fashion, the development of wheat production during the last fifty years, the relation between gold production and prices, or between capital expenditures on land and the yield per acre. Here we enter a field in which the economist is particularly interested. Most of his problems concern such relations-between prices and rents, between wages and productivity, between demand and price, between supply and price, between population and land values. How may we measure in quantitative terms the relationship between two variables of this type?

The problem is precisely the same as that facing the physical scientist when he seeks to establish empirically a "law" which describes the relationship between variables in his field. An example from a physical science and another drawn from a field in which the economist is directly interested will illustrate the method and will serve to exemplify the generalizations characteristic of these two types of data.

In Figure 1 are plotted fourteen points, representing corresponding values of the terminal voltage and the current in a 118-volt tungsten filament incandescent lamp.1 The problem is that of securing a statement in quantitative form of the functional relationship between these two variables, together with a measure of the degree to which this relationship actually holds in experience. This latter measure will lie somewhere between zero, which indicates complete independence, and unity, which indicates a perfect cause and effect connection. The curve fitted to the fourteen points by appropriate methods represents an empirical approximation to the law which describes the relationship between these factors. The measure of correlation in this case has a value of .99987, which approaches unity so closely as to indicate an almost perfect causal connection. We stand here virtually at the conceptual limit of complete certainty and

1 This example is taken from Steinmetz, Engineering Mathematics, 235-8.