What are different ways to make sure no errors are involved?
There is no way to eliminate the two errors simultaneously, because they are connected. The only sure way to minimize both is to increase the sample size (but that's also the hardest).
Usually, one of those errors is more important to you.
One example is fraud detection in banks.
Say a false positive there is a transaction flagged as fraudulent when it isn't.
A false negative is a transaction that is determined as alright, when in fact fraudulent.
You can quickly realize that a false positive is easy-peasy. You double-check the transaction, lose some time but realize everything is alright with it, and nobody lost money.
A false negative, however, is the big problem. You designed the system specifically to catch fraudulent activity and you missed it.
In this case, you will be desperately trying to minimize the false negative (Type II Error). This implies, you will be making more of the first type of error. But you are okay with that, aren't you? A bit more work, but at least you are safe.
That's how the reasoning goes usually.
The 365 Team