Let's say I compare two diagnostic procedures (A and B) and want to check if one outperforms the other one using the metric diagnostic accuracy where diagnostic accuracy is commonly described using sensitivity and specificity. I want to test for significant improvement for this metric using some statistical test, do I then already need to apply some sort of correction for multiple testing?
My guess would be yes as even though I only have one hypothesis (concerning diagnostic accuracy) I need to check for significant improvement of both its sub-components sensitivity and specificity (i.e. two hypothesis?)