# Is there a word for believing events are independent when they are not?

This is sort of like the opposite of the gamblers fallacy, although it's not the "inverse gamblers fallacy". For instance, if I observe that in some condition, the expression of Gene A is elevated with p-value 1e-3, and the expression of Gene B is elevated with p-value 1e-4, I might say that this event has p-value = 1e-7. Except that implicitly assumes these two genes are uncorrelated (which is not usually true in practice even under the null hypothesis of neither gene being associated with the condition).

Is there a name for this kind of error?

• This error (which I don't really have a specific name for, but let's call it the "independence fallacy*) often goes hand in hand with the prosecutor's fallacy (conflating P(innocent|evidence) with P(evidence|innocent), also called the conditional probability fallacy) by first lining up a string of conditions that are treated as independent (making P(E|I) low). Possibly the most famous instance of your independence fallacy combined with the prosecutor's fallacy is People v. Collins Feb 1, 2016 at 0:09
• @Glen_b The prosecutor's fallacy sounds like it's mixing up likelihood and and posterior probability, not quite the same. This recently came up for me in the context of discussing the Sally Clark trial, where one "expert" witness makes both mistakes. "Independence Fallacy" sounds good. I was thinking "amateur statisticans fallacy" because it seems like a mistake people make when they know just a little bit of statistics. Feb 1, 2016 at 7:58
• My characterization of it as P(E|I) vs P(I|E) comes from the wikipedia page. Not that this is any reason to think it's correct of course; the wikipedia page can easily be wrong. Feb 1, 2016 at 8:01