Approximation of Chi-Square by "Probits" and by "Logits"

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Abstract
In biological assay, when death rates, q, are plotted against dosage, the resultant sigmoid curve may be interpreted as a cumulated normal distr. or as a logistic. Either approaches linearity (against log. dosage) upon transformation into pro-bits or logits respectively where the probit, pr, is defined as (5 + x) and x is taken from a table of the normal curve oriented in q, and the logit, lr = log.e[long dash][long dash][long dash]-[long dash]. For testing goodness of fit of a function Q to the rates q, x2 for the ith rate qi based on ni individuals is: -ni (qi [long dash]Qi)2. Estimated Z2 by probits, x2 [long dash]ni -p7c (pr [long dash]Pr)2 where Z is the ordinate [center dot]f V* of the normal carve at q. Using logits: x2[long dash]m;<Z (1 [long dash]2<)(/< [long dash]Li)2 and in hypothetical examples this approx. is better than the probit approx. The latter may be too large or too small while the logit approx. is always too small.

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