Joseph Berkson

Minimum X2 and Maximum Likelihood Solution in Terms of a Linear Transform, with Particular Reference to Bio-Assay

Abstract An old and commonly used device for fitting a curve y = F(x, α, β) is to find a function of y which is linearly related to x, or a function of x which is linearly related to y, or functions of y and x which are linearly related to each other. The linearly related functions are plotted against one another, and a line is fitted to the points, usually by eye, sometimes by “least squares” in terms of the transforms. Texts dealing with empirical curve-fitting characteristically use this scheme [6]. Before Bliss and Fisher [2], no attempt was made to adjust the transforms systematically in order to achieve a fit that fulfilled defined criteria in terms of the original measures y and x, nor was it known that such adjustments were possible. These authors presented for the bio-assay experiment a method in terms of probits, which as shown by Garwood, [5] accomplished a maximum likelihood estimate of the integrated normal curve, when the observations were distributed binomially. Following the procedures use...

Laboratory Standards in Relation to Chance Fluctuations of the Erythrocyte Count as Estimated with the Hemocytometer

The method in general use for routine estimation of the erythrocyte content of the blood is to dilute the specimen of blood in a calibrated pipet in the ratio of 1 to 200, and, after mixing, to spread a droplet in a graduated counting chamber. When this chamber is examined under the microscope, it is seen to be divided into small squares, each of which demarcates a volume of 0.00025 cu. mm. In routine practice two rows of such squares are examined, each row containing 20 squares; the process is repeated in the same or another chamber, and the proportions are such that if the sum of 4 rows examined this way is multiplied by 10,000, the result gives the mean number of cells per cu. mm. of blood in the original specimen. Another common method is to count the cells in 5 groups of 16 squares each, in either 1 or 2 chambers.