for good reason. It will be argued that jobs are not so easily found as all that. They would be if the government put through the proposed scheme of public works before mentioned. Here the value of the identification card would prove itself. If the man appearing before the court could prove, by his filled in identification card, that he had been working a reasonable time out of the last six months, surely the judge, exercising some of the wisdom for which he is proverbially known, would extend the proper treatment toward the man.

If, however, an individual should be arrested for begging, stealing, or train jumping, a more stringent law could be invoked. This man should not become a burden upon the community, for then the community would not, as they do now, shift the burden on to their neighbors. The court could sentence this man to hard labor for a period of one to six months, or, if the case deserved greater severity, the time could be extended. The man would be placed on a public-service work gang at the standard rate of pay, of which he would draw one-fourth on the expiration of his sentence; out of the remaining three-fourths his board would be deducted and the balance go to pay the guards who were hired to insure his staying on the job.

For the more vicious types of migrants, mentioned above, we have a sufficient number of laws on the statutes. These, however, should be made uniform throughout all the states, and each conviction should be turned over to the federal bureaus for placement in the labor gangs. While there might be a large number of convictions during the early application of the law, and consequently large labor gangs, the state would benefit in having its public improvements progressing at a rapid rate, and at the same time rid itself of such undesirable parasites as the criminal tramp, the tramp criminal, and the jocker with his prushon. The road kid and the prushon would be cared for under different laws.

Housing and control of camps.—In order to insure proper sanitary conditions in both the federal and the private labor camps, the government might do well to institute a housing commission who would be empowered to inforce certain suitable laws designed to meet the conditions that are found.

There is little or no profit in conducting a hotel of the type that would cater to migrants, so the government would not be competing with existing interests by the installation of federal hotels at convenient centers. Here for a minimum of cost the migrant might obtain food, shelter, and have his other needs cared for. The hotels, after the initial cost, could be nearly, if not entirely self-supporting. It would not be looked upon as a charitable institution any more than our federal grant colleges are looked upon as charitable institutions.

The prime consideration to be borne in mind while considering these suggestions is that to be successful in their operation and to accomplish what they are designed for they must be nation-wide in their scope. The competitive element enters so strongly into all lines of industry that, if the people of one state were to enact laws and introduce measures similar to these or others destined to accomplish the same end, they would be competitively embarrassed if their neighboring states were not also subjected to the same conditions. By having these remedies under federal jurisdiction, the initial cost need not fall heaviest on any one group of individuals, but would be shared by all, as the elimination of the migrant problem would be a common benefit enjoyed by all.

THE STATISTICAL DEFINITION OF A

SOCIETAL VARIABLE

F. STUART CHAPIN

University of Minnesota

ABSTRACT

One of the basic problems for the sociologist is the discovery and definition of his constants and the description of his variables. The statistical method supplies a tool for the quantitative measurement of societal variables. This paper seeks to use the statistical method in defining the societal variable-room overcrowding among the families of Chicago workers-and is based on data gathered by the former School of Civics and Philanthropy. The group of 212 Italians from the Plymouth Court district is selected as a typical case for statistical definition. The coefficient of correlation, mean, standard deviation, and standard error of the mean, are computed for this group. In terms of these indexes it is possible to define with some precision the relationship between room occupancy and cubic air capacity, the average condition of occupants, the degree to which this average condition represents the series, and the probable representativeness of the sample. Further statistical analysis discovers the mathematical law of the distribution of cubic air contents per occupant. This procedure has made it possible to define our variable on seven quantitative counts.

This procedure is now applied to the ten remaining groups and the results compared. We conclude that: there is less variation among the means of the samples than in any series of observations in a single sample; the standard errors of the means of the samples confirm this conclusion; these findings establish a strong mathematical probability that the original samples were well chosen, although the reports of field work do not in themselves establish this point to the satisfaction of the critical statistician; the tabulated results conform to the normal law of error; the coefficients of correlation of the samples are quite uniform, so that the studies probably represent the actual conditions; the statistical analysis made in this paper suggests a way in which it is possible to check back upon original fieldwork investigations and is an example of the practical value of applying refined statistical methods in sociology.

1. Societal phenomena consist of variables. The analysis of social relationships is an analysis of data of observation, in which there are few if any constants. One of the basic scientific problems for the sociologist is, therefore, the discovery and definition of his constants and the description of his variables. As a matter of pure logic, the distinction between a constant and a variable is one of degree rather than of kind. Now, this distinction is one of greatest service to the sociologist in identifying his problems, because in so far as he is successful in completely describing some social variable, he has by this very process transferred the phenomenon from the

realm of an unknown variable to the realm of a known variableand a known or a more or less fully defined variable is as near to being a constant as the sociologist can probably ever come.

2. At this point in analysis the statistical method supplies the sociologist with a refined tool for the quantitative measurement and definition of societal variables. It is the purpose of this paper to illustrate the use of the statistical method to measure and define quantitatively a definite societal variable. The variable taken for study is room overcrowding among the families of unskilled workers in Chicago, 1910-15. The data of observation consist of ten studies of housing conditions in Chicago conducted by the former Chicago School of Civics and Philanthropy, and published in the American Journal of Sociology. Tabular analyses of room overcrowding given in the quantitative terms of cubic feet per occupant were selected for the purpose of analysis in this paper rather than the tables of rent per apartment, because the former variable seemed to have somewhat greater significance for pure sociology than the latter. For example, room overcrowding has a closer connection with personal morality, family solidarity, and the spread of communicable diseases than does room rental.

II. THE STATISTICAL DEFINITION OF ROOM OVERCROWDING

3. Before subjecting all of this material to statistical analysis and definition, it will be useful to attempt first a full quantitative description of a simple case. Let us select the study of 212 Italians living in the Plymouth Court district. If no overcrowding existed and every room was perfectly adjusted to the regular needs of its occupants, we should find that the cubic feet of room space increased directly with the number of occupants, or, statistically speaking, that the correlation of air space and occupants was unity. As a matter of fact, the survey showed that 33 per cent of the cases shown in Table I were overcrowded in terms of legal definition. Statistically, we find that the coefficient of correlation instead of being +1 is r = -.185.044. This means that there is 18 per cent of a tendency for a larger number of room occupants (x) to be

'XVI, 145-70, 289-308, 433-68; XVII, 1-34, 145-76; XVIII, 241-57, 509-42; XX, 145-69, 289-312; XXI, 285-316.

2 Ibid., XVIII, 539.

associated with a smaller air space (y). We may describe the situation differently in terms of the regression equations:

y=1277-74.03x

x=2.344 .0002y

The first equation means that for every increase in occupancy of one additional child the cubic room capacity diminishes by 37 cubic feet. The tendency in each case is shown in the columns in the table below:

4. We have taken the first step in statistically defining the variable. Let us now inquire into some other aspects of the variable. We may ask: What is the average room space? Computation shows that the mean is equal to 1,122 cubic feet or m1 = 1,122 cubic feet. We may next inquire how typical of the varying cubic contents of the sleeping-rooms is this mean cubic capacity. The answer is found by computing the standard deviation of the series. This is found to be σ =338 cubic feet, which means that theoretically 68 per cent of the cases lie within a range of ±σ, or ±338 cubic feet of the mean 1,122 cubic feet. As a matter of fact, a range of 784 to 1,460 cubic feet from 1,122 cubic feet includes. 165 or 77 per cent of all cases.

5. If now we regard the group of 212 Italians as a fair sample of overcrowded conditions among Chicago Italians, we may ask how