The Pluralistic Field and the Sample

Franklin H. Giddings

FOR STATISTICAL purposes any plural number of things, qualities, circumstances or happenings, or other items, is a pluralistic field. If the number of items is not too great we can count them and one by one scrutinize them. "Too great" is a relative term, however, meaning too great for our resources of money, number of competent enumerators at command, time, and so on. For the United States Census a hundred million and more individuals are not too many to count. To study them all one by one, would be another matter and practically impossible.

Every observable phase of human society is statistically a pluralistic field in the same sense or way that population is. 'It is resolvable into items, which theoretically may be counted, and one by one scrutinized, but which practically may be far more numerous (even immensely more numerous) than we can either scrutinize or count with such limited resources of energy, time and means as we command. Even national censuses have rarely undertaken to make a complete and trustworthy count of items in any societal field other than that of population. To mention only matters of major importance, there has never yet been in the United States a complete count throughout the nation of either births or deaths. Not until 1920 was there an attempt to count all marriages. No count of religious believers has been satisfactory. Citizens of voting age are enumerated, but those legally qualified to vote are not. In all of these fields, however, incomplete and otherwise imperfect counts have repeatedly been made, and they have cost a great deal of money,

Are these incomplete counts of scientific or of practical value? Is there any way of ascertaining how much or how little they are good for?

The statistician calls incomplete counts "samplings," and we assume that they may be, and often are, of considerable importance. If they are not, quantitative studies of biological, psychological and societal phenomena, including matters economic, legal, and political, made by individuals or private organizations are worthless, for, one and all, they are samplings, and our costly reports on stature and weight, intelligence rankings, unemployment, wages, family budgets, and many other interesting matters, are but litter on our shelves. Theoretically, moreover, this condemnation would necessarily be made sweeping, because, theoretic-ally every known aggregate of things or persons is only a sample of an infinite series; and, to go to the other pole of possibility, an item, or count, which we assume to be a sample, may turn out to be the total aggregate now known or knowable.

In the attempt to determine when and how far a sample is a trustworthy and reasonably adequate picture of an entire pluralistic field, which may safely be used when we wish to proceed with inductive research, we have developed a theory and a technique of sampling.

What then is a sample? The statistician defines it as any item or plural number of items which, we can be reasonably sure, is fairly representative of the entire aggregate.

What, however, do we mean by representative? The root meaning of "represent" (re, again, and praesentare, to place before, to present) has be-come in modern usage "to present in place of something else, to exhibit the counterpart or image of." Thus a painting may represent a landscape or a face. Accordingly, the primary meaning of "representative" is, "fitted to repre-

( 482) -sent," and this phrase, somewhat expanded, be-comes, "fitted to represent" truthfully, without misleading, and therefore justly. Finally, by further development of the implicit idea, we get the meaning, one who, or that which, "stands for" another or for others "as an agent, deputy or substitute," without misleading or injustice. These definitions make sufficiently clear the nature of a true or goad sample viewed as a representative item or count. For scientific purposes a sample is any fact (for statistical purposes any item or count) which adequately and without misleading stands for, or may be taken as a substitute for, an entire pluralistic field.

How and when is such a thing possible?

Obviously any fact of sort or of size, of quality or of quantity, is truly representative and there-fore may without error be taken as a sample of a pluralistic field, if the difference between any item whatsoever of the aggregate and any other item of it is negligible for the purpose in hand. There is no need to pick and choose, and it makes no difference whether we pick and choose or not. We may shut our eyes and take an item, or two or three or more items, at random; or, if we prefer, we may look over the field and deliberately select an item or items according to our whim. Either way there is no possibility of error; the item or the count of items taken is a good sample of the entire lot. Such a field, in which all differences are negligible, we call "homogeneous."

Among all observed pluralistic fields, however, (not to mention all possible ones) the strictly homogeneous aggregates are relatively few. Far more numerous are the approximately homogeneous fields in which the differences between item and item are not quite negligible for the purpose in hand. Whatever item or count is taken from one of these fields as a sample, will be, in appreciable measure, inadequate or misleading. As far as we can we must minimize it. Obviously, we shall only magnify it if we pick and choose, selecting our item or count according to our preference, prejudice, or other bias. Therefore, in taking our sample of such a field we must take it at random, thereby eliminating bias.

This consideration discloses a significant fallacy in our theory of "representation" as a political device. Speaking in severely scientific terms, the representatives that we send to legislative bodies are not strictly good samples of their constituencies. We elect them, that is to say, we permit and expect every voter to exercise choice. He may and does give full expression to his preference, prejudice or whim. To get a true sample of our political population we should resort to the casting of lots, as the Athenians at one time did. Whether that would be good politics or not, is another question.

Yet more numerous than approximately homogeneous aggregates are those which are unmistakably heterogeneous. Think of the variety of blossoms in the most unpretentious flower-garden of the kinds of grasses, clovers, and weeds in an old pasture. Go through a forest, and count the species of deciduous trees, or of pines. These all are highly heterogeneous fields, but their heterogeneity is as nothing by comparison with the variegation of the pluralistic fields that make up human society. Think of the range of age classes in any population. Think of the ethnic composition of the American people, the native and the foreign-born, the colour races, the nationalities. How many sects or religious denominations should we find if we could discover them all? How many occupations, each calling for a distinctive proficiency, could we count?

When we reflect upon variegations like these it does not take us long to perceive that no one item or count of items taken at random without other procedure can he an acceptable sample of a heterogeneous field. Chance would give us perhaps a daffodil or a hollyhock as our sample of a garden containing also tulips, roses, pansies, and a dozen other common flowers in their respective seasons. It would give us Catholics or Baptists, as like as not, as our sample of a religious population containing also Presbyterians, Methodists, Second Adventists, Mormons, and fifty-seven or more other varieties of religious experience. What further procedure then is necessary?

Plainly our sample must be a compound affair, and our first step toward obtaining its factors and putting them together is to resolve our pluralistic field into component kinds of items.

Every qualitative kind or quantitative class that is significant for our purpose must be included, and each kind or class must be approximately homogeneous. All items within the kind or class must be alike, and likeness, as was explained in a discussion of classification must be conceived as a difference less than a limiting difference which is

( 483) significant for our purpose. In like manner, a quantitative class must be understood to be a plural number of quantitative items within limits of inequality which are significant for our purpose.[1]

When the entire heterogeneous field has been resolved into component fields, each approximately homogeneous according to foregoing definitions, a sample of each must be taken at random. Each regarded by itself will be approximately adequate and not seriously misleading. Collectively, however, the combination of these samples will be inadequate, and possibly so far misleading as to be worthless, unless one further precaution is taken.

The samples may be equally large or small, or fortuitously unequal, but qualitative kinds and quantitative classes usually are found to be respectively composed of unequal numbers of units. Each is a relatively large group of things, of activities, or of persons, or what not; or it is a small group, as may happen. Unless these in-equalities are allowed for and represented the compound sample is misleading. Therefore, any sampling of a heterogeneous pluralistic field must bring together samples taken at random from each homogeneous field that is a significant component of the entire heterogeneous aggregate, and the size of each sample must be proportionate to the relative quantitative value of the homogeneous field from which it is taken.

Examples of practically bad and scientifically worthless samplings of heterogeneous pluralistic fields made in societal surveys and elsewhere could be multiplied indefinitely. Let us be con-tent for the present with two, which are of generally recognized interest and importance.

One is our sampling of public opinion. A practice has grown up of interviewing individuals in various walks of life to ascertain their reactions to innumerable matters of belief, morals, domestic legislation, and world politics. Another practice is that of taking straw votes. Most of the samples obtained by either of these methods are in-valid; they have little value even as indications of an actual state of public prejudice or conviction. Now and then they are taken at random, and they would meet scientific requirements if each were taken from a homogeneous field ; but attention to this point is rarely discovered. Inter-views and straw votes from employers, wage earners, shop keepers, and professional men, or from Fundamentalists and Modernists, from liberals and authoritarians, from internationalists and nationalists, are jumbled and scrambled. No attempt is made to get reactions from each distinctive component group of the entire hetereogeneous field of makers of opinion, and to see that each is represented in proportion to its relative quantitative importance.

The second example is taken from the practice of representative government, already referred to. Not only, as was said, are our representatives in legislative bodies selections rather than samples, but also, even as preferences they represent constituencies as territorial groups only, or, more precisely, they directly represent them only on a territorial basis. Incidentally or accidentally they may represent them also as interest, or as cultural, or as proficiency groups ; that is to say, as capitalistic or proletarian classes, employer or wage earner ranks, agricultural or industrial blocs, Catholic sodalities or Protestant sects, educated or uneducated consortings, and so on. The soviet scheme of government, by contrast, is theoretic-ally based upon the idea that these interest, cultural, and proficiency groupings, rather than territorial groupings, should be represented in the political scheme. Which plan is politically better we are not now attempting to decide. We are here concerned only with the scientific question whether, in a strictly scientific sense of the term, either plan is representative government, and no further analysis should be necessary to make it quite clear to the statistical mind that it is not. Neither the one plan nor the other gives us representation within a meaning of the word which must be adhered to for scientific purposes. To make a legislative body really representative of a politically organized people it would be necessary to constitute it of deputies from both territorial constituencies and bloc constituencies, which are important enough to be politically significant; and to apportion the representation of the latter as we now apportion representatives of territorial groups, according to the relative quantitative importance of each group.


  1. Methods of measuring heterogeneity (for approximation to homogeneity) and of ascertaining the limits within which differences are significant, are set forth in manuals of statistical theory.

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