Datis

“ Since all data suffer from a lack of mathematical precision through being of a certain size and somewhat vague in outline, it is plain that if such a notion as that of a point is to find any application to empirical material, the point must be neither a datum nor a hypothetical addition to data, but a construction by means of data with their hypothetical additions. It is obvious that any hypothetical filling out of data is less dubious and unsatisfactory when the additions are closely analogous to data than when they are of a radically different sort. ”

“ As data, though entitled to a certain limited respect, they cannot be placed on a level with the facts of sense or the laws of logic. The kind of respect which they deserve seems to me such as to warrant us in hoping, though not too confidently, that the hard data may prove them to be at least probable. Also, if the hard data are found to throw no light whatever upon their truth or falsehood, we are justified, I think, in giving rather more weight to the hypothesis of their truth than to the hypothesis of their falsehood. ”

“ Asking questions at the design stage can save headaches at the analysis stage: careful data collection can greatly simplify analysis and make it more rigorous. Or, as Sir Ronald Fisher put it: “To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. ”

“ Still, there are generally certain surviving data, in place-names, natural features, and so forth, which enable those who can detect them, and make use of them, to piece together something like a connected outline of what we may take, with some degree of probability, as an approximation to what have been actual facts, although lacking, at the time, the chronicler to record them. ”

“ Statistics belong, like chronology, to the domain of the organic, to fluctuating Life, to Destiny and Incident and not to the world of laws and timeless causality. As everyone knows, statistics serve above all to characterize political and economic, that is, historical, developments. In the “classical” mechanics of Galileo and Newton there would have been no room for them. ”

“ And perhaps even those who call them sense-data, may, in part, be attributing to them properties which it may be doubtful whether they possess. If we want to define a sensation or a sense-datum, in a manner which will leave it not open to doubt what sort of things we are talking of, and that there are such things, I do not know that we can do it better than by saying that sense-data are the sort of things, about which such judgments [Pg 232] as these always seem to be made—the sort of things which seem to be the real or ultimate subjects of all such judgments. ”

“ Any fact which we know or have been told about our problem is called a datum. The number of pounds of sugar we are to buy is one datum; the price per pound is another.
The plural of datum is data. It is a good plan to write all one's data on one column or page of the paper and work one's sum on the other. This leaves the first column clear for adding to one's data if one finds out any fresh one. ”

“ In any science other than psychology the datum is primarily a perception, in which only the sensational core is ultimately and theoretically a datum, though some such accretions as turn the sensation into a perception are practically unavoidable. But if we postulate an ideal observer, he will be able to isolate the sensation, and treat this alone as datum. There is, therefore, an important sense in which we may say that, if we analyse as much as we ought, our data, outside psychology, consist of sensations, which include within themselves certain spatial and temporal relations. ”

“ It would place us in that position of more advanced knowledge, in which the probabilities, to us, would be different from what they were before; and in estimating these new probabilities we should have to proceed on a totally different set of data, furnished no longer by mere counting of possible suppositions, but by specific knowledge of facts. Such data it should always be our endeavor to obtain; and in all inquiries, unless on subjects equally beyond the range of our means of knowledge and our practical uses, they may be obtained, if not good, at least better than none at all. ”

“ The development of statistics is causing history to be rewritten. Till recently the historian studied nations in the aggregate, and gave us only the story of princes, dynasties, sieges, and battles. Of the people themselves—the great social body with life, growth, sources, elements, and laws of its own—he told us nothing. Now statistical inquiry leads him into the hovels, homes, workshops, mines, fields, prisons, hospitals, and all places where human nature displays its weakness and its strength. ”

“ Such is the great complexity of our mental life that it is not possible to deny that constant mean values, when obtained, are of the nature of such statistical constants. To test that, I examine the distribution of the separate numbers represented in an average value. If it corresponds to the distribution found everywhere in natural science, where repeated observation of the same occurrence furnishes different separate values, I suppose—tentatively again—that the repeatedly examined psychical process in question occurred each time under conditions sufficiently similar for our purposes. ”

“ In statistics, it is evident that empirical laws may sometimes be traced; and the tracing them forms an important part of that system of indirect observation on which we must often rely for the data of the Deductive Science. The process of the science consists in inferring effects from their causes; but we have often no means of observing the causes, except through the medium of their effects. In such cases the deductive science is unable to predict the effects, for want of the necessary data ”

“ He uses the results of statistical inquiry because the method of obtaining and presenting them is scientific, and because he recognizes with the German Schlosser, that "statistics is history ever advancing," and that if he wishes to grow with advancing history and keep himself fully and thoroughly informed of progress in every direction, he must use the statistical or historical method ”

“ I shall give the name sensibilia to those objects which have the same metaphysical and physical status as sense-data, without necessarily being data to any mind. Thus the relation of a sensibile to a sense-datum is like that of a man to a husband: a man becomes a husband by [149] entering into the relation of marriage, and similarly a sensibile becomes a sense-datum by entering into the relation of acquaintance. It is important to have both terms; for we wish to discuss whether an object which is at one time a sense-datum can still exist at a time when it is not a sense-datum. ”

“ The treatise of Achenwall, the German philosopher who originated the word, laid the foundation of many of the greatest reforms in modern legislation. Statistics are state facts, facts for the consideration of statesmen, such as they may not neglect with safety. It has been truly said that ‘statistics are history in repose; history is statistics in motion.’ If we neglect the one, we shall deserve to be neglected by the other. ”

“ Simple inspection of the data enables us to perceive them; and one inspection is as effective as a million for engendering in us the conviction that between those data that relation must always hold. To change the relation we should have to make the data different. 'The guarantee for the uniformity and adequacy' of the data can only be the mind's own power to fix upon any objective content, and to mean that content as often as it likes. ”

“ If this is to be the case in the world of one man's sense-data, and if each sense-datum is to have not less than a certain finite temporal extension, it will be necessary to assume that we always have an infinite number of sense-data simultaneous with any given sense-datum. Applying similar considerations to space, and assuming that sense-data are to have not less than a certain spatial extension, it will be necessary to suppose that an infinite number of sense-data overlap spatially with any given sense-datum. ”

“ It is a great step to know the mean fall of, say ten years, at any place in the United Kingdom; inductions may be drawn from this; by comparing results at different places; different theories may be evolved, or light thrown on some leading view. At all events, a body of statistics furnishes even an outside labourer with something on which to work. It is every one’s part who is at all interested in the study to contribute what he can of time and observation towards supplying additional facts on our rainfall. ”

“ Ellis, late of the Royal Observatory, Greenwich, has sought to show by a seemingly powerful array of statistics that the idea now under consideration is unfounded, but I consider that we have here only one more illustration of the familiar statement that you can prove anything you like by statistics. ”

“ In our tables every figure is set to work. Our idea of missionary statistics demands that they should be a basis for action. We think that it is waste of time to collect statistics from which no conclusion can be certainly drawn both by the compiler and the reader—a conclusion which ought to be suggestive when taken alone by itself, and, when considered in relation to the conclusions suggested by similar tables, compelling. ”

“ The science of statistics, by which facts are so gathered as to embody truth, and so interpreted as to afford knowledge, is of recent origin. It is a singular fact that our young republic was the first government in the world to take a census at stated intervals. ”

“ In all cases of sense-data capable of gradual change, we may find one sense-datum indistinguishable from another, and that other indistinguishable from a third, while yet the first and third are quite easily distinguishable. Suppose, for example, a person with his eyes shut is holding a weight in his hand, and someone noiselessly adds a small extra weight. If the extra weight is small enough, no difference will be perceived in the sensation. ”

“ It may also cause surprise that we ask for estimates in some cases where exact information is not immediately accessible. It may be said that statistics are misleading, but estimates are hopelessly misleading: let us have correct figures or none. That attitude is easily understood, but under the circumstances it is vain. "Correct figures," that is, meticulously exact figures, are unattainable. An estimate is in nearly all matters of daily life and business the basis, and rightly the basis, of our action. ”

“ Tinkering around with the data, also known as exploratory data analysis, is often the most informative part of the analysis. Exploratory plots can reveal data quality issues and outliers. Simple summaries, such as means, standard deviations, and quantiles, can help refine thinking and offer face validity checks for hypotheses. Many studies, especially when going in completely new scientific directions, are exploratory by design; the area may be too novel to include clear a priori hypotheses. Working with the data informally can help generate new hypotheses and ideas. ”

“ Every one who is engaged in statistical inquiry must acknowledge the possibility of natural laws governing such statistical facts. Hence we must allot a distinct place to numerical information relating to the numbers, ages, physical and sanitary condition, mortality, &c., of different peoples, in short, to vital statistics. ”

“ It may be asked, as Mill asks, Why spend so much trouble in calculating from imperfect data, when a little trouble would enable us to render a conclusion certain by actual trial? Why calculate the probability of a measurement being correct, when we can try whether it is correct? But I shall fully point out in later parts of this work that in measurement we never can attain perfect coincidence. Two measurements of the same base line in a survey may show a difference of some inches, and there may be no means of knowing which is the better result. ”

“ All that is necessary to make the examples appropriate is that we should admit that in their case statistical data are our ultimate appeal in the present state of knowledge. Of course if the empirical laws can be resolved into their component causes we may appeal to direct deduction, and in this case the employment of statistics, and consequently the use of the theory of Probability, may be superseded. ”

“ We may succeed in actually defining the objects of physics as functions of sense-data. Just in so far as physics leads to expectations, this must be possible, since we can only expect what can be experienced. And in so far as the physical state of affairs is inferred from sense-data, it must be capable of expression as a function of sense-data. ”

“ When we ask what are the kinds of objects with which we are acquainted, the first and most obvious example is sense-data. When I see a colour or hear a noise, I have direct acquaintance with the colour or the noise. The sense-datum with which I am acquainted in these cases is generally, if not always, complex. This is particularly [211] obvious in the case of sight. I do not mean, of course, merely that the supposed physical object is complex, but that the direct sensible object is complex and contains parts with spatial relations. ”

“ It is that the different statistics with which we are presented should not in reality offer materially different results, If, for instance, we were enquiring into the probability of a man aged forty dying within the year, we might if we pleased take into account the fact of his having red hair, or his having been born in a certain county or town. 396 Each of these circumstances would serve to specialize the individual, and therefore to restrict the limits of the statistics which were applicable to his case. ”