A 'Thirsty Arab' is a term referring to a hypothetical unexpected factor that can or has thrown off the result of an experiment or measurement.
The expression is reminiscent of the term 'bug', which currently means a fault or defect in a computer program, system, or machine, but originally referred literally to insects getting physically caught in machinery and in that way causing it to malfunction.
The origin of the term came from the following anecdote, told by razzbar:
In 8th grade geography class, the teacher was talking about how dry the Sahara desert was, saying that in some parts it can go for years without raining.
A student raises his hand and asks, "How do they know that, since there's nobody living there?"
The teacher replies that scientists leave rain gauges (those being a cup-like measuring device) out to catch rainwater, and see how much water was in them.
The student then asks, "Well, how do they know some thirsty Arab didn't come along and drink all the water?"
Scientist 1: It appears that all evidence we've gathered over the past 3 years confirms my original hypothesis that all ginger left-handed one-breasted midget prostitutes in Zanzibar wipe their asses back to front, instead of the clearly superior front to back.
Scientist 2: Have you ruled out a possible 'Thirsty Arab' scenario?
Scientist 1: What's that?
Scientist 2: I can't go into it now, I'm playing hide and seek. Look it up on UrbanDictionary.com.
Scientist 1: That's on the... inter-net... correct?
Scientist 2: Is that the one that's a series of tubes?
Scientist 1: I think so.
Scientist 2: Yes, that's the one.
Scientist 1: OK, I'll do that.
Scientist 2: Good.