Showing papers in "Annals of Mathematical Statistics in 1934"

The Method of Path Coefficients

Abstract: The Method of path coefficients was suggested a number of years ago (Wright 1918, more fully 1920, 1921), as a flexible means of relating the correlation coefficients between variables in a multiple system to the functional relations among them. The method has been applied in quite a variety of cases. It seems desirable now to make a restatement of the theory and to review the types of application, especially as there has been a certain amount of misunderstanding both of purpose and of procedure.

On the Relative Stability of the Median and Arithmetic Mean, with Particular Reference to Certain Frequency Distributions Which Can Be Dissected into Normal Distributions

Abstract: In any statistical investigation in which an average i's to be used as a summarizing figure for a frequency distribution the question arises, which average best describes the distribution. That this is still a debatable question among writers on economic statistics is shown by a perusal of the many papers dealing with the measurement of seasonal variations which have appeared in recent years.2 Each of the proposed methods of isolating seasonal variations involves an averaging, either of monthly items or of relatives of monthly items, but whether this averaging is best accomplished by use of the arithmetic rimean, the median, or the mean of a middle group of items seems to be a moot point. Persons3 employs the median of link relatives of monthly items, since by this device the influence of large non-seasonal variations may be greatly moderated. Hart4 in justifying the use of the arithmetic mean has shown that the method of monthly means gives the actual

The Adequacy of "Student's" Criterion of Deviations in Small Sample Means

Abstract: The origin of the movement toward precise evaluation of probabilities based on the statistics of small samples would generally be located by practical statisticians in the work of "Student" (1908). The problem he considered is of such importance, not only from the historical aspect, but also from a consideration of the elements of statistical interpretation, that we wish to return to an analysis of the adequacy of his solution. "Student" was concerned with the problem of determining the significance to be attached to the deviation of the mean, X, of a small sample from a probable (or possible) supplyt mean, m, when the dispersal of variates in the supply is unknown. The solution he suggested was based upon derivation of the probability integral of the quantity

The Accuracy of Computation with Approximate Numbers

Abstract: 1. General Considerations. The number of figures necessarily free from error in the result of a piece of computation may be determined by studying the relation between the number of digits in the result and the number of digits in the maximum error of the computation. It is the purpose of this essay to derive rules for the determination of the, number of digits which are certain to be correct in computations based on measurement, but it must be understood that these rules state the minimum number of correct digits so that the resuk of a specific piece of computation may be accurate for more places than the rules indicate. 2. Notation. Since the location of the decimal point has no connection with significant figures in a given number, it is assumed that the decimal point follows the last significant figure in each of the original numbers, the argument being somewhat simplified by this assumption. Accordingly the greatest error in the statement of the original numbers is ? 0.5. Let / and .B be the true values of two numbers such that A tQ /Oand B5i . , where m and n are positive incegers and where 0.1 < a < 1.0 and where 0.1 & < 1.0. Then by the convention adopted above, the number of significant figures in A and B are m and no respectively, and the observed values are not less than A 0.5 and B0.5 and not more than

Mathematical Foundation for a Method of Statistical Analysis of Household Budgets

Abstract: The object of this paper is to offer a satisfactory method of statistical analysis of household budgets in accordance with the general principles of mathematical logic. I have, therefore, taken these words of Fourier: "Mathematics has no symbols for confused ideas"1 as my guiding light, and set out to effect a simple and comprehensive analysis of the general type of statistical data which is included under the heading "household budgets," i. e. monetary incomes and expenditures of these incomes. I have tried to lay the greatest stress, accordingly, on the clarity and terseness of the exposition rather than inclusiveness, attempting to diminish to the utmost the number of undefined ideas and the undemonstrated propositions. I make no special claim to originality and base my method upon the works of numerous previous investigators, summarizing analytically old principles and ideas on the bases of mutual consistency and reducibility to more fundamental principles. This paper is specially framed to relieve the feeling of intellectual discomfort which of late has been troublesome to conscientious investigators in our field, so overcrowded with revelations of numerous parts, rather than with indications of the mode of combination of the major components within the whole. I address here the properly instructed mind and so dispense at times with the elaboration of some statements. In this summary, therefore, we shall be concerned with laying down a rigid method for analysing the budgetary data, defining their scope formally to include only the monetary incomes and

On the Systematic Fitting of Straight Line Trends by Stencil and Calculating Machine

Abstract: Whenever there is only one plotting point corresponding to IV successive abscissal values equally spaced, it is possible greatly to simplify the fitting of straight lines to the empirical observations. Let the N several absicissal values (ordinarily time) be X % , X2 1 X3, Let these several % values be replaced by a series of transmuted steps.. X. ( ?, 3, -} a)1 Let the several corresponding ordinates be y,, y., y3). . The situation is represented in Figure 1.