The angular transformation may be used in two ways in the analysis of quantal data. Transformation of the observed response (Eisenhart, 1947) leads to a quick noniterative but approximate solution. If the expected response is transformed, an exact iterative maximum likelihood solution is available. Comparisons have been made which indicate the practical similarity of the two methods, though where additional accuracy is required one cycle of the maximum likelihood solution following the method of Eisenhart seems all that is required. To overcome difficulties with regions of 0 and 100% response in factorial experiments, parallelogram designs have been introduced.
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CLARINGBOLD et al. (1953) studied this question.