But you are assuming there exists a positive correlation between absence of brown M&M:s and whether the other demands are also filled or not. I don't think you can show that since the M&M demand was singled out. Had they instead randomly inspected once piece of equipment and found an error that would have been totally different.
This is not about rigorous statistics, it's about human nature. In the sixth grade, my math teacher offered a test at the beginning of the year that included quite a lot of complicated instructions. The last instruction told students to ignore all the previous instructions, and just write their name at the top of the paper and turn it in.
Guess how well the typical top scorers in the class did on this one.
That prank is horrible because the document is self-contradictory yet assumes a single correct interpretation, unless the document is very carefully written and formatted using an agreed semantics.
A well-written document would be a great illustration of Haskell-style lazy evaluation, though
But you are assuming there exists a positive correlation between absence of brown M&M:s and whether the other demands are also filled or not. I don't think you can show that since the M&M demand was singled out.
Yes, that is the assumption. Many mathematical models make assumptions like that. It seems much more likely than the opposite assumption which is that they are independent.
Since you're attempting to model human behavior you are going to have to make assumptions that are ultimately incorrect. That's how humans process information. We join the dots and infer things in countless ways that mean we could be incorrect, but which none-the-less are better than wildly guessing (http://en.wikipedia.org/wiki/List_of_cognitive_biases). It would be probably better, if you are trying to model this, to think of it as a machine learning classifier. Brown M&Ms existing would be a prominent feature, not proof.
First of, now we know from another commentor that that the M&M-test didn't work at all since catering was handled by a completely different crew than those setting up the stage equipment (https://news.ycombinator.com/item?id=7754636).
Second, let's imagine that M&M:s and safety is handled by the same people. Then brown M&M:s could easily be negatively correlated with equipment errors because a competent technician would spend more time double-checking equipment than full-filling bullshit demands.
