"Mm, not the Science!tific way of thinking about it, exactly, but not at all bad, either.  You even simplified the math some."

"Though, saying they got artifact-headbanded is not what the original experimental spec was.  We were specifying natural all-14s which will probably give us noticeably different results.  One does want to learn to think precisely about that sort of thing."

"To compute that number there, let's observe it'll be the square of 6^3*4^2/5^5, or 216*16/3125, 2160+1296 is 2160-4+1300=3456, divided by 3125... about 1.1, since 3456 is around 3125+312, squared is about 1.2."

"So the results you saw are 1.2 times more likely if the all-10s have 40% pass rates, and the all-14s have 60% pass rates, compared to everyone having 50% pass rates."

"Now, I realize this ought not to go in a 'published-experimental-report', but what do you happen to believe, seeing that?"

"Mm, not the Science!tific way of thinking about it, exactly, but not at all bad, either.  You even simplified the math some."

"Though, saying they got artifact-headbanded is not what the original experimental spec was.  We were specifying natural all-14s which will probably give us noticeably different results.  One does want to learn to think precisely about that sort of thing."

"To compute that number there, let's observe it'll be the square of 6^3*4^2/5^5, or 216*16/3125, 2160+1296 is 2160-4+1300=3456, divided by 3125... about 1.1, since 3456 is around 3125+312, squared is about 1.2."

"So the results you saw are 1.2 times more likely if the all-10s have 40% pass rates, and the all-14s have 60% pass rates, compared to everyone having 50% pass rates."

"Now, I realize this ought not to go in a 'published-experimental-report', but what do you happen to believe, seeing that?  What would you believe if you saw that in real life?"