I built a detector to detect a binary outcome and then took a random sample from the population. From this, I can create a signal detection/confusion matrix (hit, miss, false alarm, correct rejection) [aka: TP, FP, FN, TN] and then calculate metrics such as Recall and Precision.
My question: How do you calculate confidence intervals for the Recall and Precision of the population from which I sampled?
I was thinking of this formula: p - z * sqrt(p*(1-p)/n) < p < p + z * sqrt(p*(1-p)/n)
where p = the statistic (e.g., Recall) and z = z-score for the desired confidence