When using the data-randomization strategy we have to condition our inference on an auxiliary random variable – the
order of the observations – which has no relation to the parameter of interest. Apart from the fact that this creates the false
impression of an interval which does not rely on an external random variable, a major problem is that we then lose the rather
natural property of invariance under permutations of the sample. Consequently, a statistician who reads the sequence from
the left to the right may end up with a different interval than a statistician who reads the sequence from the right to the left.
Care should be taken when using data-randomization: in most binomial experiments it is arguably neither reasonable nor
desirable that the order in which the observations were obtained affects the inference.