A Statistically Precise and Relatively Simple Method of Estimating the Bio-Assay with Quantal Response, Based on the Logistic Function

so that, if the logit P is plotted against x, the points will fall on a straight line, with a as the intercept and ,B the slope. The function (1) has had many statistical applications [37] and has been advanced for use in bio-assay by, among others, Emmens [17] Wilson and Worcester [46], and Berkson [7]. In bio-assay x measures the "dose"' and P the "response." If the response is measured, not in terms of a continuous scale such as weight or length, but in terms of the observed proportion p affected out of n "exposed," the response is said to be "quantal," and in this statistical model it is assumed that the observation p at x can be considered a random variable binomially distributed around the "true" P at x, with variance o -2 = PQ/n. For this situation, the present writer has advanced a method [71 of calculating a and b, which are estimates of a and a respectively, presently called the "minimum logit X2 estimate," based on a minimization of the following quantity, called the "logit X2.",

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