Minor scale

“ A scale might be formed, graduated according to the decrees of a combined ratio of intensity, duration, connexion, periods of recurrence, and utility, which would be the standard, according to which all ideas might be measured, and an uninterrupted chain of nicely shadowed distinctions would be observed, from the faintest impression on the senses, to the most distinct combination of those impressions; from the simplest of those combinations, to that mass of knowledge which, including our own nature, constitutes what we call the universe. ”

“ I saw, methought, a pair of golden scales hanging by a chain in the same metal over the table that stood before me; when, on a sudden, there were great heaps of weights thrown down on each side of them. I found upon examining these weights, they showed the value of everything that is in esteem among men. I made an essay of them, by putting the weight of wisdom in one scale, and that of riches in another, upon which the latter, to show its comparative lightness, immediately "flew up and kicked the beam." ”

“ The progression from pre-word to notation, and in our days from literacy to illiteracy is paralleled by the progression of scale. Numbers as such-how many people in a given area, how many people interacting in a particular practical experience, the longevity of people under given circumstances, the mortality rate, family size-are almost meaningless. Only when relations among numbers and circumstances can be established is some meaningful inference possible. Scale is the expression of relations. ”

“ The point-scale method has the merit of indicating directly the rate, or annual increments of intellectual growth. We do not claim for our measurements a high degree of accuracy, especially in the case of the early years of childhood. ”

“ Then if the purpose be to establish such a standard of measurement, the scale must be expressed in units of the same denomination as that of our own nature—you cannot divide miles by ampères—and it is because the scale of our potential being is laid out in the same denomination as that of the Spirit of Life itself that we can avail ourselves of the standard of "the Word made Flesh." ”

“ But the ability of an individual in one distribution can hardly be compared with that of an individual in another distribution in a biologically significant way by their actual positions on the physical scale. A physical unit, does not measure the same sort of fact of development in a scale for the immature that it measures in the scale for adults or that it measures in another dynamic scale for the immature. This can be seen when a physical unit is compared with the amount of standard deviation which it measures in the different scales. ”

“ Consequently, Nature herself supplies us with an ascending scale or Alphabet of angles for half a degree up to 60°, Specimens of which are placed in every Elementary School throughout the land. Owing to occasional retrogressions, to still more frequent moral and intellectual stagnation, and to the extraordinary fecundity of the Criminal and Vagabond Classes, there is always a vast superfluity of individuals of the half degree and single degree class, and a fair abundance of Specimens up to 10°. ”

“ The Binet scale, it must be understood, is an instrument of precision, not to be handled except by one who has been thoroughly trained in its use. It looks so simple that any student is apt to say, "Why, I could give those tests!" ”

“ If the unit of the scale is some measure of the variability of a defined group, as it is in the majority of our present educational scales, this median point may well be calculated to the nearest tenth of a unit, or, if there are two hundred or more individual measurements in the distribution, it may be found interesting to calculate the median point to the nearest hundredth of a scale unit. Very seldom will anything be gained by carrying the calculation beyond the second decimal place. ”

“ In the one case, the child makes the best production he can and measures its quality by comparing it with similar products of known quality on the scale. Composition, handwriting, and drawing scales are good examples of scales for quality of products. In the other case, the scales are placed in the hands of the child at the very beginning, and the magnitude of his achievement is measured by the difficulty or number of tasks accomplished successfully in a given time. Spelling, arithmetic, reading, language, geography, and history tests are examples of scales for quantity of achievement. ”

“ Arbitrary Scales.—An arbitrary scale can be constructed by selecting any physical property of a substance which varies regularly with the temperature, such as the volume of a liquid, or the pressure or density of a gas, or the electrical resistance of a metal. ”

“ After careful thought and a comparison of different scales, I have come to the conclusion that the scale for standards of size given in the accompanying Table is the one I would recommend to be adopted. I have endeavoured to arrange one which would be easily intelligible to the ordinary workman, and that would in every possible case coincide with the old system, so as not to cause more expense in altering the present sizes than may be absolutely necessary. ”

“ Ordered, for instance, to practise her scales for an hour each day, without receiving any explanation as to the usefulness of such practice, the girl naturally regarded scale-playing as a fresh device for annoying her. ”

“ Why are we so interested in the type of scale that measures a dependent variable? The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable. ”

“ These graphs represent the normal form of distribution usually expected when any fundamental ability is measured in a random group. If the number of cases at each unit of measurement are plotted by a point placed relatively as far above the scale, used as a base line, as the number of cases found at that unit of the scale, it will be discovered that these points arrange themselves in the form of a symmetrical curve high at the middle and flaring out 257along the base-line scale. ”

“ since, again, they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modelled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. ”

“ When we think of curves of general ability we must, therefore, keep in mind the light which might be thrown on them by an analysis of the various processes tested in the particular scale used.
Another feature of all developmental curves which is apparent as soon as the causes of development are considered, is that growth in an individual is the result of several factors. ”

“ Knowledge being scientific, as it can apply number and measure, an attempt is in order to see if a scientific order of values cannot be built "on a number and measure scale of force," ascent in the scale signifying increase of value, descent diminution of value—all other estimations being prejudices, naïvetés, misunderstandings. ”

“ This view raises clearly the question how far the curve of average development represents a common tendency of different individuals in development. Are the individual curves of development so varied in form that an average curve does nothing but obscure their significance? ”

“ The two relations of fatherhood and sonship appear in considering the same two beings according as we regard one with reference to the other or the second with reference to the first. The embodiment of the scale from the point of view of which we consider another we shall here call the referred scale, the embodiment with regard to which we consider it the scale of reference. ”

“ Of mechanical ones the most familiar is that of the scales. If accurately made and not clogged by dirt or rust, a pair of scales cannot be perfectly balanced: eventually one scale will descend and the other ascend—they will assume a heterogeneous relation. ”

“ Each scale is divided into one hundred parts, which are marked from five to five. A slide that can be moved up or down, shows the measure of the qualities therein specified each one possesses, or believes himself to possess. ”

“ Waiving the question whether annual increases or the range of measurements relative to the age norms would be satisfactory indications of the change in the rate of growth, it seems to be fairly clear that neither of these criteria would be adequate unless we first knew that the units in which they were measured were equivalent at different portions of the scale. ”

“ When reducing by scales, it is obviously not essential to use the same scale as that to which the original is made; the dimensions on one scale may be readily transferred to any other, and the student will do well to make himself familiar with the operation. ”

“ The question is, therefore, to decide whether a given response contains as much and as good interpretation as we have a right to expect at the age level where the test has been placed. It is imperative for any one who would use the scale correctly to acquaint himself thoroughly with the procedure and standards described above. ”

“ The median point of any distribution of measures is that point on the scale which divides the distribution into two exactly equal parts, one half of the measures being greater than this point on the scale, and the other half being smaller. When the scales are very crude, or when small numbers of measurements are being considered, it is not worth while to locate this median point any more accurately than by indicating on what step of the scale it falls. ”

“ The placing of objects of a known size near, to give scale, is a useless expedient in such a case. At times it may be successful, often of use; but if the scale of the main object is false, the other object of known size, instead of giving size to the main one, as it is intended to do, will be itself dwarfed by it. ”

“ Where we see a body raised in a scale, we are sure that there is in the opposite scale, however concealed from sight, some counterpoising weight equal to it; but it is still allowed to doubt, whether that weight be an aggregate of several distinct bodies, or one uniform united mass. ”

“ The main condition in the matter of scale appears to be that we cannot afford to ignore the average human standard. As we may say that the human frame itself contains the elements and principles of all ornamental design, so its proportions and scale control the proportions and scale of all design. ”

“ Equivalent Units Of Ability When The Distributions Are Normal. In considering the curves of development it is desirable first to notice the differences between measurement in equal physical units and measurement in equivalent units of ability or of development. ”

“ The question of whether special technical studies of an arbitrary nature, such as scale studies, should be extensively used is one which has been widely debated, and I fear will be debated for years to come. ”

“ That is to say, if we make a seriation of measurements relating to the sitting stature of an indeterminate number of individuals, we find a numerical prevalence of those corresponding to the medial measurement marked upon the axis of the abscissæ; and the number of individuals will continue to decrease with perceptible symmetry on each side of the centre, i.e., toward the higher and lower statures. ”

“ Take for example the question of increase in weight. We can compare the mean figures given by the authorities with the ascertained weight of some particular child of a given age, so as to keep an empirical check upon the normality of its growth. But since we know that an individual in the course of evolution undergoes [Pg 179] profound alterations in the volumetric proportions of the different organs in respect to one another, we cannot obtain from the total weight any light upon this extremely important alteration in proportions. ”

“ The extended scale over which beings are distributed may at first sight seem to be an assemblage of unconnected objects, but seen with the eyes of science, it is perceived to be a delicately worked chain, whose links present, as we advance, greater beauty and perfection. ”

“ Contenting ourselves, however, with our own small value-scale, as we needs must, and assuming it to be adequate, the most important thing to consider is the value-key of our picture. Assuming the whole scale of values from the deepest black to the purest white to be represented by the number 100, the question arises as to what proportion of this number we shall use in the particular work which we are proposing to execute. ”

“ We may now divide this art of measurement into two parts; placing in the one part all the arts which measure the relative size or number of objects, and in the other all those which depend upon a mean or standard. Many accomplished men say that the art of measurement has to do with all things, but these persons, although in this notion of theirs they may very likely be right, are apt to fail in seeing the differences of classes--they jumble together in one the 'more' and the 'too much,' which are very different things. ”

“ As representative of the first form of scale we may refer to the widely used Binet-Simon scale for the determination of mental age. Whatever we mean by intelligence, it is a characteristic which is essential to vocational activity. It is furthermore a characteristic which normally tends to increase in its degree or manifestation from infancy up to at least ten or twelve years of age. Beyond that point there are, to be sure, striking individual differences in that characteristic which we call intelligence, but beyond this point it does not seem so dependent on the physical age of the organism. ”