Coefficients

Coefficients, a mathematical concept. In algebra, a coefficient is understood as a factor expressed in numbers and standing before a monomial. Thus, in the monomial 6a²b²c, the number 6 is the coefficient of this monomial. By statistical coefficient in the ordinary sense of the word is meant a quantity showing the frequency of occurrence of a given phenomenon in the environment where it occurred. For example, the mortality coefficient is understood as the quotient of dividing the number of deaths in a given calendar period of time (usually a year) by the average number of the population in the environment of which cases of death were observed; for the convenience of comparison, this quotient is reduced to some common base, usually to one with several zeros (1,000, 10,000, etc., or, as is customary to call it, pro mille, pro decimille, etc.). Thus, the statistical coefficient, like the coefficient in algebra, is essentially one of the factors; the other factor is the denominator of the fraction, and their product constitutes the absolute magnitude of manifestations of the trait in the population under study. From the point of view of derived statistical quantities, statistical coefficients are special cases of expression of the so-called relative numbers of frequency or intensity. Depending on the content of the populations brought into relation to each other, statistical coefficients are divided into general and special coefficients. In the case when the population taken as the denominator of the relation (environment) is in a close genetic connection with the population indicated in the numerator (the phenomenon under study), the coefficient has a special meaning. With a different nature of connection between the related populations, the coefficient acquires a general meaning. General coefficients serve only for general orientation, in contrast to special coefficients, which give a more precise measure of the phenomenon and allow for more precise conclusions about it. An example of a general coefficient can be the birth rate coefficient, an example of a special coefficient is the fertility coefficient. The number of births (stillbirths excluded) in Leningrad in 1923 amounted to 31,906 people; the average population in the same year was 1,093,000 people; hence the birth rate coefficient is ³¹1⁹.o^в93^Xooo°^{0(>== 29} '²°/°^{0 (}P^{Г0 тШе}>. Although this coefficient gives an idea of the reproductive capacity of the Leningrad population, especially in comparison with the general mortality rate, it is still a very conditional quantity, since in its denominator it contains a significant part of the population not participating in the production of births shown in the numerator (the elderly, children). Moreover, the birth rate coefficient given is also conditional because it does not properly reflect the family and age composition of the population, which is the main factor among all others determining the degree of fertility of the population. In order to clarify the latter, it is necessary to calculate a series of special coefficients, namely: the general fertility coefficient, the marital fertility coefficient, and age-specific marital fertility coefficients. The first of these is equal: number of births × 1,000

" тт

31,906 × 1,000 on л пг по г. Leningrad -^:₀₀₂-= 89,4 %₀; the second coefficient (marital fertility) is: number of births in marriage × 1,000______ number of married women aged 15-49 years' for the same time and space conditions 26,821×1,000 нг-л лсм j» те -_{173 627} = 154,4°/_0o; the third type, the fertility coefficient, is constructed as follows: number of births to married women of given ages × 1,000 number of married women of the same age

' or for Leningrad in the part of women in on ел

~"~"" ^/0°^-. Along with the presented, most common interpretation, the term in question was and is often used in statistics for a number of other reasons. Most often it is used to denote the measure of the ratio between different numerical characteristics of series. Thus, in this sense, they speak of the coefficient of variation (^⁼⁼~д^%)» ° coefficient of asymmetry (-^~), of coefficient of regression (в£ = г ?*), of coefficient of correlation (r= -_N*' -) - P. Kuvinshnikov. (For details on coefficients of variation and correlation--see, Variation Statistics, Correlation). Coefficient of efficiency of the human body-the ratio of the amount of mechanical work performed to the energy expended. Usually two coefficients of efficiency are distinguished. To calculate one of them, the so-called gross efficiency coefficient, the amount of mechanical work T is divided by the total energy expenditure D and this coefficient of efficiency is denoted by the letter η. To calculate the net efficiency coefficient, a different approach is taken: from the total energy expenditure D, the energy expenditure at rest for the same period of time D_s is subtracted, and the amount of mechanical work is divided by the difference obtained from this subtraction, or in other words, by the so-called dynamic energy expenditure (D - D_s = D_d). Consequently, the net efficiency coefficient can be expressed by the formula: K = jj-, while the gross efficiency coefficient is calculated by the for- t

t mule:g=^ or _{D D} . Of course, before division, they express the amount of mechanical work in large calories (dividing the number kg/m by 425) or, conversely, energy expenditure is converted to kg/m (multiplying the number of large calories by 425).-The coefficient of efficiency of any machine characterizes the quality of its work. The higher the coefficient of efficiency, the more economical and better the machine works, the less energy is spent, relatively, to perform the same mechanical work. The healthier and more trained a person, the more rationalized his work, the higher the efficiency of his work, the greater the coefficient of efficiency. As shown by Herbst, people with diseased hearts, emphysematics, and tuberculars give a smaller coefficient of efficiency during muscular work than healthy people. The magnitude of the coefficient of efficiency has enormous significance for the physiology of labor. On the one hand it indicates the condition of the worker, on the other it characterizes the work itself, its organization and the degree of rationalization.-Training in any work increases the coefficient of efficiency. For example, Atzler in 1924 showed that the net coefficient of efficiency changes from day to day as follows: 1st day.....12.9% 8th day.....19.4% 2nd.....10.3% 9th.....19.4% 3rd.....12.3% 10th.....19.9% 4th.....15.0% 11th.....20.4% 5th 12th.....20.6% 6th.....16.0% 13th.....20.6% 7th.....18.1% 14th.....21.0% Thus it is seen that the coefficient of efficiency grows parallel to training at first quickly, then more and more slowly until it reaches its maximum value (21%). The increase in the coefficient of efficiency is explained by the constantly improving coordination of movements as a result of training, whereby unnecessary movements of synergistically working muscle groups disappear. On the second day of training a certain decrease in the coefficient of efficiency is observed, caused apparently by the transition from old work methods to new ones and the destruction of old coordination connections (relearning). A beginning worker always expends more energy on the same work than an experienced adult worker. For example, Amar found that in planing the beginner spends 4.9 large calories per 1 g of shavings (coefficient of efficiency = 6.72%), while the experienced worker only 2.5 large calories (coefficient of efficiency = 9.42%). The first works unevenly, often gets tired, his pulse rate increases on average by 35% (instead of the usual 20%) and his breathing rate by 54% (instead of 30%). It is clear that the intensified work of the heart and respiratory apparatus increases the magnitude D_d and therefore decreases the coefficient of efficiency.-As stated above, the coefficient of efficiency characterizes not only the condition of the organism and the degree of training of the worker, but also gives indications of the rationality of the organization of the work itself. Man, like a machine, works most economically only within certain limits of speed and load ('optimal zones'). As an example, one can cite the data of Chauveau, relating to work on an ergometric bicycle: Speed (number of revolutions per min.) Net coefficient of efficiency [ 70 { 80 ( 90 j 90 0 25.1% 26.7% 28.4% 30.6% 25.8% From this it is seen that man works with the highest coefficient of efficiency, and therefore with the greatest economy, at a speed of 90 revolutions of the wheel per minute. A similar dependence exists between load and coefficient of efficiency. This circumstance represents enormous theoretical and practical interest, as it allows the construction of work in accordance with the data of labor physiology. 'Overload', caused by work at high speed and load, leads to a whole series of pathological processes (diseases of the heart, overfatigue, etc.). As labor physiology develops, labor regulation will be increasingly based on physiological data.-The coefficient of efficiency changes during the work itself, usually reaching a maximum on the 2nd hour of work and decreasing under the influence of fatigue by the end of the work. The effect of exercise (at the beginning of work) and fatigue (at its end) is especially clearly reflected in the coefficient of efficiency.-The magnitude of the coefficient of efficiency for different works is different. On average, it can be considered that the net coefficient of efficiency is 20% and only in the case of habitual work and training of performers it can reach 33% (walking). The gross coefficient of efficiency is much lower, and its value fluctuates between 7% and 10%. In industrial work, the coefficient of efficiency, in the opinion of some researchers, is 4-6%. These figures are much lower than the coefficient of efficiency of various machines (steam engines-12-20%, internal combustion engines-about 35%, electric motors-90-98%), which, in connection with the low power of man (1/10 horsepower) and the high cost of the 'fuel' he consumes (proteins, fats, carbohydrates), has led and continues to lead to the replacement of the human engine by the machine engine. k. Keecheev. The coefficient of absorption in agglutination is an indicator of the ability of a given agglutinogen to bind the agglutinin of a given serum and depends on the avidity (see) of the reacting bodies. The indicator of the coefficient of absorption is the ratio of the amount of absorbed agglutinin to that which is present in the given serum (to the titer of the latter). The methodology for determining the coefficient of absorption was proposed by Eisenberg and Volk, Barikin and Fries.