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TRENDS in egg production and egg weight during the first year of production have been studied by many investigators, but data relating to the trend in hatchability appear to be somewhat scanty. This paper presents data on the average hatchability of eggs, during each month of the first year of production, from pullets receiving low-protein and normal diets, together with data on average egg production and egg weight for the same birds which have been included for purposes of comparison with the hatchability data. The data herein reported were obtained as part of a study of the effects of some nutritional factors on hatchability, conducted by the staffs of the nutrition and physiology laboratories at the U. S. Animal Husbandry Experiment Farm, Beltsville, Maryland. The observations were made over a period of three years, a different group of pullets being used each year. The experimental work was usually begun during . . .

IN A recent paper Amiet (1936) suggested that the methods of statistics might be used to good advantage in record of performance inspection work. As a contribution to this field, Hendricks (1937) showed that the familiar chi-square distribution may be employed to test the accuracy of trap-nest records. Although the development of the test invloved some mathematical theory with which flock inspectors and supervisors are usually not familiar, the practical application of the test is quite simple. The present paper offers a detailed explanation of the practical application of the test to those workers who may have some occasion to employ it. The test is designed to determine whether or not the numbers of eggs produced by a given flock of birds on inspection days, when the trap-nesting is done by the inspector, differ significantly from the numbers of eggs which would be expected on the basis of the production . . .

(1944). The Relative Efficiencies of Groups of Farms as Sampling Units. Journal of the American Statistical Association: Vol. 39, No. 227, pp. 366-376.

When observations in a random sample of n are classified into k categories with n i falling into a given class, the usual estimate of the corresponding probability is ni/n. When a priori information about the distribution of the probabilities is available, more precise estimates can be derived from data in any one sample of n. When the a priori distribution is not specified completely, but its general form can be inferred, the parameters of that distribution can be estimated from the average of the ni/n and their estimated sampling variances. The computations are analogous to those that arise in regression theory with the bivariate normal frequency distribution when Y = X + e and the expected value of X for a given Y is estimated from the regression of X on Y. The parameters of the distribution of X have to be estimated from the observed distribution of Y and the sampling errors in the individual values of those observations.

This paper presents data on the early growth of nine lots of White Leghorn chicks, hatched at different seasons of the year and used as “control” pens in a series of nutrition experiments conducted at the U. S. Animal Husbandry Experiment Farm, Beltsville, Maryland. The analysis of the data was made primarily for the purpose of obtaining an estimate of the average growth made by White Leghorn chicks between the time of hatching and various ages up to 15 weeks under the conditions imposed by the above-mentioned series of nutrition experiments. It was hoped that the analysis would show the degree of variability in growth made by different lots of chicks, hatched at different seasons of the year and reared under similar conditions. Although the conditions were not strictly comparable, the writers believe that they were similar enough to justify the use of the data in such an analysis. The . . .

THE value of statistical methods in interpreting the results of agricultural research has been quite generally recognized in recent years. This has resulted in a desire on the part of many investigators to avail themselves of those methods without inquiring into the mathematical theory upon which they are based. One can certainly concur with Fisher (1934) in the view that the methods of statistics can be extremely useful in the hands of investigators who may not have the time to master the theory involved. However, an investigator who is not thoroughly familiar with the theoretical background of a procedure may occasionally make the error of applying it to particular cases in which its use is not justified. Many modern statistical procedures are so new that they are particularly susceptible to this kind of abuse, even by competent statisticians, although many a venerable classical formula has received the same inglorious treatment. . . .

THE utilization of feed by growing chickens is a subject of considerable economic importance as well as of general scientific interest. The daily feed intake of a growing chicken must serve a variety of needs; only a portion of the total feed eaten is available for producing a gain in live weight. A study of the utilization of that portion of the feed intake which remains to be used for growth, after the requirements for other metabolic processes have been satisfied, should be of much help in devising suitable diets for growing chickens. In a recent paper the authors (1931) suggested that the curve of the diminishing increment might be useful in making a preliminary study of this problem. The differential form of the equation of the curve of the diminishing increment was written: dW dF = C − mW in which the constant, C, was interpreted to represent the gain in live weight which the . . .

Data on farm labor supply and demand as per cent of normal were collected from farmers by the Department of Agriculture from 1918–45. No detailed study of these data has been made previously. The present analysis shows the nature of the relationship between those data and corresponding data on numbers of workers employed in Agriculture and numbers of persons available for employment. The series on supply and demand as per cent of normal seem to have reflected the farm labor situation fairly well. Supply as per cent of normal, as reported by farmers, seems to reflect the number of persons available for hire at current wage rates but not yet employed in agriculture. Reported data on demand as per cent of normal seem to reflect the number of vacant jobs that farmers were trying to fill by recruiting workers.

AS A result of several years of investigation relating to the effects of feeding inorganic sulphur compounds to laying hens, data have become available at the U. S. Animal Husbandry Experiment Farm, Beltsville, Maryland, which lend themselves quite readily to a study of the molt of White Leghorn hens and its effect on their egg production. * Observations on the molt were made on three groups of White Leghorn hens, each group representing a separate year’s work The first and third groups consisted of four lots each, and the second group, of three lots. The birds were kept in colony houses and were permitted a limited amount of grass range. The nutrition of the birds in any one group was the same, except for the composition of the mineral supplements for the various lots. However, the composition of the basal diet fed to the first group differed from that fed to . . .

THIS paper presents an analysis of a set of feather measurements obtained at the Beltsville Research Center during the course of an experiment designed to determine the effects of certain mineral supplements, particularly inorganic sulphur compounds, on the molt of White Leghorn hens. Since the molt is usually accompanied by a cessation of egg production, the importance of favorably influencing the growth of feathers, if it is possible to do so, is obvious. In view of the fact that feathers contain considerable amounts of sulphur, it was thought that the feeding of sulphur compounds might have some effect on the rate of growth and mature length of the new tail and wing feathers which were grown after the old feathers were dropped during the molt. The general plan of this experiment, including a description of the sulphur compounds fed, has been given in an earlier paper (Hendricks, 1933). Three groups . . .

IN A RECENT paper Hays (1936) reported an attempt to separate the distribution of “age at first egg” for 230 Rhode Island Red pullets, reared at the Massachusetts Station, into two normal components. This dissection was attempted in order to test the hypothesis that the group of birds under consideration consisted of two distinct phenotypes for “age at first egg.” The results obtained served as the basis for the conclusion that there appeared to be a definite phenotype with an age range from 130 to 179 days, but that the group of birds with an age range from 180 days upward consisted of more than one phenotype. It appeared to the author of the present paper that the above-mentioned data could be adequately explained by the hypothesis that only two phenotypes were involved and that the distribution of “age at first egg” for this particular group of birds could be . . .

The method of least squares offers a precise method ofc fitting a curve describing the relation between two or more related, measurable variables, but certain criteria must be fulfilled to justify its application. First, the type of equation selected for fitting must be the true mathematical expression of the law governing the relationship of the variables. Secondly, all errore of measuremeiit, made in obtainiing the observed values of the variables when the data were collected, must be distributed according to the wellknown laws of probability.' This paper is concerned with the latter of these two criteria. The fundameintal theory upon which the method of least squares is based can be found in any text-book on the subject and need not be elaborated upon here. However, it may be well to point out a very pertinent, if somewhat elenientary, aspect of the theory which facilitates the ready visualization of the fundamental concepts involved.

THE DESIG N OF A SAMPLE usually involves some method of taking account of heterogeneity in the universe to reduce the size of the random sampling error. The degree of success with which this objective is attained depends upon the extent and precision with which various contributions to the variability of the individual units in the universe are isolated and measured before the sample is designed. The amount of pertinent information about the universe that is available before a sample is selected is sometimes meager and sometimes quite far-reaching; it may have become available from previous sampling investigations or from previous contacts with every individual in the universe. But regardless of how much information is available, or how it was obtained, an experienced sampler takes advantage of it. Mathematically, the heterogeneity of the individuals in a universe with respect to a variable X can be expressed as a series of sums of squares which add up to the total sum of squares S(X m)2, where m is the average of all values of X in the universe. The number of component sums of squares into w-hich such a total can be resolved is limited only by the amount of available information concerning the universe and the number of individuals in the universe. This simple algebraic identity serves as a basis for constructing the formula for the sampling variance of a mean, x, computed from a sample with a specified design. The synthesis of such a formula can be accomplished in more than