raise error for 1-sided confidence bounds with confidence levels below 50%?

[pbstark]

In routines like the binomial confidence interval, the search for the confidence bound assumes that the bound will be between the sample mean and the appropriate a priori bound (e.g., for an upper confidence bound, between \hat{p} and 1). If you call the routine with a confidence level below 50%, that assumption is false and the search algorithm will not converge.

In my experience, I've never seen a 1-sided confidence bounds with a confidence level below 50%. Should we raise an exception (tacitly on the assumption that the caller used \alpha instead of 1-\alpha)? Or should we (correctly) compute 1-sided confidence bounds with confidence levels below 50%?

I get the impression that pythonic style might not require either solution: the user is assumed to be somewhat sophisticated.

@jarrodmillman @stefanv

[stefanv]

When designing APIs, we try and make a parameter mean one and only one thing (i.e., no black magic behind the scenes). You also have the option of a warning here, with something like "α is lower than expected (typically >0.5). Perhaps (1 - α) was provided?".

These warnings can be silenced by expert users.