4. Data-randomized intervals
4.1. Modifying externally randomized intervals
The main objection against externally randomized confidence intervals is that different statisticians may produce different
intervals when applying the same method to the same data. As pointed out by Decrouez and Hall (2014), if the result of
each of the n independent trials are recorded, one can put the first n1 observations in the first subsample and the other n2 observations
in the second subsample, so that the randomness in the split sample interval only comes from the data itself. This
means that there is no ambiguity about the interval, that there is no need to discuss the range of the upper bound and that
two different statisticians always will obtain the same confidence interval when they apply the procedure to the same data.