Knowledge that Transforms

IN the United States there has been much agitation of late for a shorter work week. In the spring of 1933 Senator Black of Alabama introduced a bill in the United States Senate to limit the work week to thirty hours. This bill passed by a vote of 53 to 20, but was held up on a motion to reconsider. Simultaneously Representative Connery introduced a similar bill in the House. Support given to these bills undoubtedly assured the passage on June 13, 1933, of the National Industrial Recovery Act, one purpose of which was to increase purchasing power by decreasing working hours (thus spreading work) and by increasing wages. Decreasing hours without increasing hourly wage rates to compensate was impossible politically. Prior to the Black and Connery Bills, the United States had been literally covered with the publicity and propaganda attendant upon the pronouncements of Technocracy. Although most of the claims of Technocracy have been proved to be false, the notion persists that great strides have been made in improving machines during the last decade, especially during the depression. In view of the debatable character of shorter work week proposals, it seems desirable at this time to examine some of the facts and to see how these are related to economic theory. In particular, it seems desirable to consider the economic experiment of the shorter work week carried out by the N.R.A., and to discover how hour shortening and attendant wage raising might lead to recovery or further depression. Figure I shows how gainful workers by the different classes of workers varied from 1880 to 1930. In 1880 about 8 per cent of all gainfully employed were professional workers compared with about 25 per cent in manufacturing and mining. About 47 per cent were engaged in agriculture and fishing. Employment percentages, however, did not remain static. The change has been very considerable in the last thirty years. For example, percentage of those engaged in agriculture and fishing in 1930 was 23 per cent, compared with 47 per cent in 1880. In manufacturing and mining a slight decrease occurred over the previous ten-year period. Table IV shows changes in workers in manufacturing and man-hours required during the period 1920-1933. During the period of industrial expansion, we were opening new manufacturing industries and building up our own industrial plants. Improved manufacturing technique and things of that sort were displacing workers and thus fewer were needed in manufacturing, but employment in trade

IN SUCH fields of investigation as economics, psychology, and anthropology, where observations on several variables are taken into account simultaneously, it is at least as important to study relationships among the variables as to consider the variables separately. In fact, if there are significant relationships within a system of variables, a considerable part of the information furnished by the observations will be lost unless the relationships are taken into account. In general, very little is known a priori about such a set of variables, and hence our knowledge of them and their various interrelations must be inferred from observations. Questions relating to the problem of making inferences from observations resolve themselves into those of, (1) devising suitable functions of the observations for estimating parameters which characterize the hypothetical population of the variables and (2) determining frequency laws from which the degree of credibility to be placed in the departure of these functions from expectation can be evaluated. The more complicated the hypothesis concerning the interrelations of the variables, the more complex, of course, will be the functions of observations for measuring the relationships and testing the hypothesis. It frequently happens in multivariate analysis that a number of variables can be rationally classed into several mutually exclusive categories. For example, certain measurable traits of individuals may be classed as physical or mental. In the study of wholesale prices of farm products in a certain region over a certain period of time, the products may be classed as (1) fruits, (2) vegetables, or (3) dairy products, and the deviations of the prices of products within each group from seasonal and secular trends may be taken as the variables. When variables can be grouped in such a manner the question naturally arises as to whether or not there is any significant relationship between the groups of variables. That is, on the basis of the available observations, with what degree of credibility can we assert that the groups are mutually independent, so that knowledge relative to one of the groups gives us no significant information about the others? If they are significantly non-independent how can we measure the amount of dependence? It will become apparent as we proceed that statistical functions' and significance tests more general and comprehensive than I See R. Frisch, Correlation and Scatter in Statistical Variables, Nordielk