> It's a simple case of reversing positive and negative.
> 
> When allergy tests are positive, they indicate that you are allergic.
> 
> (A positive test is not such a happy outcome, and thus one might 
> think that's a "negative" thing).

Another way to look at it is to see what question does the test try to answer.

In case of the allergy tests, the question is "did the person react to the substance?"
Positive means: Yes, the person had a reaction.
Negative means: No, the person did not have a reaction.

Thus, a positive result usually means that you are allergic.
However, a negative result is not as conclusive since the administrator of the test may not have observed a reaction in these particular circumstances but your body may still react in different circumstances.

A challenge (repeated a couple of times) has a higher degree of confidence in ruling out allergies.

Best wishes,
Alex.