Using only one side of a two sided confidence interval

Question

Say that I compute a two-sided confidence interval. For example say I compute a confidence interval for a binomial proportion with significance level $\alpha$ as

lower, upper = conf_interval(count=95, trials=100, significance=$\alpha$)

If I only use the lower bound than I can call instead

lower, _ = conf_interval(count=95, trial=100, significance=$2\alpha$)

and similarly if I only use the upper bound.

Now, say that I am computing a function

out = f(lower, upper)

where the output is guaranteed to equal either out = f(lower, 1) or out = f(0, upper) but I don't know in advance which one of the two it is. In other words, the output of the function is identical to using either the lower bound or the upper bound.

Am I still allowed to use $2\alpha$ in this case since my function will never "use" both lower and upper simultaneously?

Answer 1

No. If you want to use a one-sided p-value, or a one-sided confidence interval, you need to specify the hypothesized direction in advance. If you only want to know the upper limit, then you only compute and report the upper limit -- even if the data actually went the other way.