I thought that the OP was clear on the statistics; 45 2.1 has cast doubt on that clarity. After reviewing the OP, I don't know how to make the explanation clearer, better, or simpler. The first post has the explanation.
For those who are interested in, or have questions about, the statistics, I'll be happy to explain-but not here, where most are not interested. I'm at: firstname.lastname@example.org.
I'll be happy to send anyone a copy of my Statistics book, just ask.