Allow me to elaborate.

Let us take that example question and use it in a faux conversation.

Bewildered Scientist: You didn’t just drop that vial of Anthrax?

Clumsy Scientist: Yes.

Bewildered Scientist: Do you mean “Yes, I did drop it” or “Yes, I didn’t drop it”?

Clumsy Scientist: What do you think I meant?

Bewildered Scientist: Dammit James, answer the question! We could have a biological pathogen on the loose!

Apparently James: I did answer you fool! You haven’t activated emergency protocol A11-CCX?

Bewildered Scientist: What? No!

Apparently James: Do you mean “No, I didn’t activate it” or “No, I did activate it”?

At this point both scientists suffer a massive brain embolism completely unrelated to the unbroken vial of anthrax.

I believe my point is well illustrated. Now, allow me to present you with the correct way of answering a question asked in the negative.

Bewildered Scientist: You didn’t just drop that vial of Anthrax?

Clumsy Scientist: Correct, I didn’t.

Bewildered Scientist: Oh, OK then. So how does Chili’s sound for lunch?

Clumsy Scientist: Oh, no can do. Margaret and I are going to the wedding planners to look at cake designs.

Bewildered Scientist: Oh, OK. Some other time then?

Apparently Margaret’s Betrothed: Sounds great.

Bewildered Scientist: Say, why are we handling potentially dangerous vials of Anthrax anyway?

Apparently Margaret’s Betrothed: We aren’t. We work at a book store.

At this point both scientists turn around and go back to restocking the shelves with pulp sci-fi novels, silently pondering how little use their PhDs in astrophysics and bio-engineering actually are.

Now you can clearly see exactly how to deal with a question asked in the negative. Either reply with “Correct” or “Incorrect” as the situation depends.