I am trying to understand the meaning of the goodness-of-fit estimate in section 15.2, fitting data to a straight line. We compute a and b to minimize the chi-square in 15.2.2. Then I read the following: "The probability Q that a value of chi-square as poor as the value (15.2.2) should occur by chance is Q = ...."

I interpret "as poor as" to mean "as large as" or "as bad as". Since the chi-square is to be minimized, I would think this should say "as good as" since a random pair of a and b would likely result in a much larger chi-square value. However, the authors' emphasis placed on the word "poor" makes me think I'm missing something.

The text goes on to say that Q > 0.1 indicates a good fit, that Q < 0.001 should call the validity of the model into question. This also seems backwards to me since a high probability (Q near 1) of the chi-square value occurring by chance indicates that randomly selected a and b would have served just as well. Similarly, a low probability of this chi-square occurring by chance sounds like a good thing, yet with smaller Q we are to have less, rather than more, confidence in the model(?).

I am hopeful that someone can explain this, perhaps in slightly different terms, and help me understand.