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A simplified method of evaluating dose-effect experiments.

J T LITCHFIELD, Frank Wilcoxon

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Abstract

The increased emphasis on quantitative biological studies in recent years has resulted in the widespread use of statistical methods for evaluating biological data. Much of this data is of the all-or-none type and, consequently, it is neces-sary to solve a dose-per cent effect curve. By converting doses to logarithms and per cent effects to probits (1), logits (2), or angles (3), a straight line may be fitted by the method of weighted least squares. From the viewpoint of many biologists, such procedures are not pleasant to contemplate because the data must be converted to units which are meaningless to many and the calculations are difficult, tedious and often quite incomprehensible. It is not surprising therefore that there is widespread use of a variety of approximate methods for solving dose-per cent effect curves. It may be argued that such methods are undesirable because they do not make use of all of the information contained in the data, and are therefore inefficient in a statistical sense. On the other hand, the computations necessary in using efficient methods are often so time-consum-ing and laborious that the busy experimenter is deterred from using them, and

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The increased emphasis on quantitative biological studies in recent years has resulted in the widespread use of statistical methods for evaluating biological data. Much of this data is of the all-or-none type and, consequently, it is neces-sary to solve a dose-per cent effect curve. By converting doses to logarithms and per cent effects to probits (1), logits (2), or angles (3), a straight line may be fitted by the method of weighted least squares. From the viewpoint of many biologists, such procedures are not pleasant to contemplate because the data must be converted to units which are meaningless to many and the calculations are difficult, tedious and often quite incomprehensible. It is not surprising therefore that there is widespread use of a variety of approximate methods for solving dose-per cent effect curves. It may be argued that such methods are undesirable because they do not make use of all of the information contained in the data, and are therefore inefficient in a statistical sense. On the other hand, the computations necessary in using efficient methods are often so time-consum-ing and laborious that the busy experimenter is deterred from using them, and

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Available abstract

The increased emphasis on quantitative biological studies in recent years has resulted in the widespread use of statistical methods for evaluating biological data. Much of this data is of the all-or-none type and, consequently, it is neces-sary to solve a dose-per cent effect curve. By converting doses to logarithms and per cent effects to probits (1), logits (2), or angles (3), a straight line may be fitted by the method of weighted least squares. From the viewpoint of many biologists, such procedures are not pleasant to contemplate because the data must be converted to units which are meaningless to many and the calculations are difficult, tedious and often quite incomprehensible. It is not surprising therefore that there is widespread use of a variety of approximate methods for solving dose-per cent effect curves. It may be argued that such methods are undesirable because they do not make use of all of the information contained in the data, and are therefore inefficient in a statistical sense. On the other hand, the computations necessary in using efficient methods are often so time-consum-ing and laborious that the busy experimenter is deterred from using them, and

Key concepts: Confidence interval, Computation, Mathematics, Statistics, Logarithm, Simple (philosophy), Line (geometry), Range (aeronautics)

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