[aaronjg]

In the clinical trial literature Anscombe's approach is considered Bayesian, and Armitage is frequentist. From Armitage's 1963 response to Anscombe's paper:

'Anscombe takes the Bayesian view that inferences should be made in terms of the likelihood function... An immediate consequence is that stopping-rules are irrelevant to the inference problem.'

Page 6 of the Anscombe paper that I cited may be helpful in your understanding of the approach.