they are omitted? To include them would be to add weight to the value arrived at on the basis of other sales, providing the value thus determined is warranted. If it is not warranted, then their inclusion only tends to support a case which in and of itself is incorrect, and weight would normally be given to the conditions under which the sales were made. Their inclusion, on the other hand, may change materially the values assigned to a given district, and yet from every side the evidence is clear that they represent true value. The only consideration against them is the relations of the grantees and grantors relations which will normally not be allowed in the use of sale statistics for the determination of land values. Moreover, how many sales are necessary to establish a unit value? With twenty sales the unit value is $100 per front foot; with twenty-five sales the unit value is $105, and with eighteen sales $95. How many sales should be included and to what districts should they apply?

Such considerations as these are vital, and their force is constantly being experienced in actual statistical work, no matter whether it applies to land valuation, price determination, studies of wages, cost of living, or what not. The function of the editor calls for the possession of sound judgment and the exercise of keen discrimination.

VI. CONCLUSION

This chapter has to do with the sources of secondary and the collection process of primary data. The aim is to discuss the practical steps to be followed in statistical work. Both are held to be anterior, but at the same time vital, to all other considerations in the statistical process. The discussion is intended primarily as a manual of instruction rather than as an encyclopedic treatment. If the points of view

here developed are kept constantly in mind, and there is real desire to profit by them, subsequent steps will be easier and the reader will have the assurance that he is employing in a scientific manner a delicate, though frequently abused, instrument of study.

The personal element stands out as an important factor in all that has been said. Statistics do not answer questions or support conclusions independently of the one who manipulates them. Judgment, candor, and integrity are necessary at every step. One must not only know the field in which he is working, its statistical possibilities, and what has been done, but he must also realize the difficulties under which data are collected, the precise manner in which they are used, the sources and possibilities of error and bias, etc., and the ways of detecting and eliminating them. In a word, he must understand what is involved in the preparation of an intellectual tool, and then in the light of his knowledge use it intelligently for the purpose in mind. If it is faulty he should know and acknowledge it. If it is well fitted for his purpose, that fact should be evident in the uses which are made of it. To be a good statistician one has to be more than a technician, but technique cannot be ignored.

REFERENCES

King, W. I. Elements of Statistical Method, Chs. IV, V, VI, and VII, pp. 39-64.

Bowley, A. L.-Elements of Statistics, pp. 23–63.

-Elementary Manual of Statistics, Ch. VIII, pp. 64-70. United States Occupation Statistics, 13th Census, Washington, D. C. 1910. Vol. IV, pp. 17-23.

CHAPTER III

UNITS OF MEASUREMENTS IN STATISTICAL STUDIES

PASSING from the more general statement of the principles involved in the collection process, and of the methods of collecting statistical data, the significance of such expressions as units of measurements, purposes of studies, schedules, etc., will be clearer if they are discussed separately and studied in connection with concrete problems. This is done in the following two chapters.

I. THE MEANING OF STATISTICAL UNITS OF MEASUREMENTS

The statistical approach to a subject is always numerical. Things, attributes, and conditions are counted, totaled, divided, subdivided, and analyzed in this approach. We do not deal alone with single instances or with rare occurrences, but rather with aggregates.1 The statistical process is both analytical and synthetical, and numerical considerations and preponderances of evidence are the chief bases for conclusions.

The numbers of aggregates dealt with always relate to units of measurements characteristic of the things or conditions studied. It is not 1000 as an abstract unit of frequency which is considered, but 1000 farms, industrial establish

1"Statistics. . . does not deal with a single homogeneous mass but with a complex body composed of multitudinous units differing in form and action one from the other; and it is with the complex not with the units that it is concerned." Bowley, A. L., Elements of Statistics, p. 262.

ments, loans, mortgages, etc. Numbers as abstract units may be combined, separated and divided indefinitely because they are homogeneous, the more or less merely indicating presence or absence of a condition represented abstractly. In physical measurements we are accustomed to add, subtract, and otherwise treat numerically units of length, width, and volume as it suits our fancy or as necessity demands. This is generally done without any necessity of re-defining the units since they are homogeneous, standardized, and unvarying as respects time, place, and condition. They do not have to be adjusted to each purpose for which they are employed. A linear foot remains 12 inches, a meter 39.37 inches, an American gallon 231 cubic inches, etc., for all uses to which they apply, and they may be combined with like units and frequently converted into terms of each other without any serious inconvenience or risk of misunderstanding or confusion.

The same cannot be said of most units of measurements which are dealt with in economic statistics. Respecting such a unit as the ton-mile, while the physical measurements remain constant, in applying them to concrete problems many counter considerations are involved. While a ton is invariably a ton, and a mile a mile, all tons, except as to the one quality weight, are not the same, nor are all miles, except as respects distance, equivalent. One ton may be bulky, low-grade freight; another ton may be compact, high-grade freight. One may be the measure of a quantity of stovepipe elbows, the other of a quantity of silks. Likewise, one mile may be of easy grade in a prairie, the other of heavy grade in mountainous tunnels. The conditions necessary to the movement of one ton one mile the ton-mile - may be wholly dissimilar in spite of the common, name which is assigned to the service. Units must be referred to the condi

tions which they describe, and since these are widely different, combinations of them should be made only with care and circumspection. The point sought to be emphasized is that in statistics while abstract units of size, dimension, and frequency are employed they are not dealt with as abstract units, but only as reflecting conditions which produce them. and for purposes to which they apply.

Respecting most units, with which the student of economic statistics deals, the fixity and definiteness which characterize such a unit as the ton-mile do not hold. Abstract quantities or frequencies representing relative abundance or absence

a more or a less are still employed, but the conditions which they measure and the purposes for which they are used are so different for each unit that a clear declaration of purpose must always precede their definition and use. The problem is not so much that of counting units describing different degrees of intensity, abundance, or absence of the same thing, as it is counting different things which have been given the same general name. An illustration will give point to this contention.

If our problem were simply to enumerate the number of manufacturing establishments in a given district, the definition of this unit would obviously be determined by the following conditions: (a) The meaning of manufacturing as distinct from trading, mercantile, transporting, agricultural, etc., pursuits. (b) The meaning of an establishment. The definitions employed will depend upon the purpose in mind in using them. If it is to learn the number of such enterprises when the criterion of individuality is ownership, one condition maintains; if the criteria are independent existence respecting the processes involved and the management over them, independence respecting housing conditions or contiguity, independence respecting relative location, etc., then other