W. Edwards Deming

Sample design in business research

Responsibilities in Planning a Survey. Some Remarks on the Theory of Sampling. The Frame and Elements of a Sampling Plan. Operational Definitions of Expected Value and of Standard Error. Uncertainties Not Attributable to Sampling. Some Simple Replicated Designs. A Survey of Business Establishments with Correction for Nonresponse. Examples in Sampling Accounts. Evaluation of Inventory of Materials. Exercise in a Replicated Survey of a Small Urban Area. General Theory and Procedure for Replicated Sampling of a Large Area. Field Procedure for the Creation of Segments and for the Selection of People Within Families. A Statistical Aid to Supervision. Sampling New Material. Stratified Sampling. Evaluation of Expected Value and of Bias in Sampling Procedures. Theory of Variances. The Poisson Series and the Square-Root Transformation. Optimum Number of Segments Per Block. Theory for the Formation of Strata. Choice of Zoning Interval and Number of Subsamples. Index.

On a population sample for Greece.

Abstract Samples of households and of names from electoral lists were compared in connection with the work of the Allied Mission for Observing the Greek Elections. Only the sample of households taken in the summer of 1946 is described in detail here. The 3052 sample households were drawn from a primary sample of about 200 areas. Villages, towns, and cities were classified on the basis of their 1940 populations, and a sample of areas and households was drawn, conforming closely to the principle of optimum allocation of resources and manpower. Geographic distribution was obtained automatically by drawing the areas at systematic intervals from the 1940 Census lists, which were arranged in geographic and alphabetic order. The sample gave an estimate of .988 for the ratio of the 1946 to the 1940 population, with a standard error of 2.1 percent. This ratio corresponds to a 1946 population of 7.26 ± .15 million. Numerous other population characteristics such as distribution by sex and age, literacy, and employme...

LXVII. On the application of least squares.—II

Abstract A solution of the general problem in least squares, together with examples of its applications to several special cases, was given in a previous paper. The author now presents further illustrations of the adjustment of observations and determination of parameters, together with suggestions for systematic procedure in computation. The problems here treated are the logarithmic decrement of a balance, the exponential law, and the laws represented by the equations yax =b, yzx =b, and yzx =w, wherein a and b are parameters, arid x, y, z, w are observed coordinates. The last three equations are respectively the ones needed in the determination of e and h (electronic charge and Plancks constant) under the three situations: (a) neither e nor h directly observed, (b) direct observations on e included, (c) direct observations on both e and h included. Provisions in the general solution allow any relation, between e and h to be forced. In particular, the normal equations are set up and illustrated with Edd...

IV. Temperature distribution along a heated filament used as a catalyst

Abstract An expression was found for the temperature gradient at any point along a heated molybdenum filament used as a catalyst in the decomposition of ammonia. The temperature at any point along the length was obtained by graphical integration of this expression. The integrated resistance for the whole length of filament was compared with the measured resistance and found to agree within ·27 per cent, at four different temperatures. Knowing the distribution of temperature, it was possible to determine the equivalent length of the filament effective as a catalyst at the maximum temperature. From considerations of the thermal losses to the gas, a value of the heat of dissociation of ammonia was found that was in good agreement with that obtained by Lewis and Randall from Habers data.

XXXI. On the application of least squares.—III. A new property of least squares

Abstract It is shown that when a curve is fitted by least squares, Σ(wx U x V x ) + wy U y V y =0 to within higher powers of the errors, which are assumed to be small. The summation is taken over all the fitted points, wx and V x denote the weight and residual of the x coordinate of an observed point; U x denotes the true error of the calculated xcoordinate, w y V y , and U y are similarly defined. In the simple case of observations on a single magnitude, the general proposition reduces to the familiar statement that the algebraic sum of the residuals is zero.