APPROXIMATION OF CHI-SQUARE BY PROBITS AND BY LOGITS
成果类型：
Article
署名作者：
BERKSON, J
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2280157
发表日期：
1946
页码：
70-74
关键词：
摘要：
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;< [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.