I have looked at the probabilities of certain child behavior problems in
adolescents in child protection surveys in two Canadian provinces. I have
found a linear relationship. All problems are less frequent in Province Y,
but they are all in proportion. I did linear regression (I did check for
normality and homogeneous variances) and found that the probability of any
problem in Province Y is linearly related to its probability in Province X,
at a very high level of statistical significance. Okay. What bothers me,
though, is the slope of the line is almost 1. That is, pretty well all the
difference is in the constant: in effect P(of a given problem in Province
Y) = P(of that same problem in Province X) minus K, a constant. Now I can
imagine various effects causing the slope of the regression line to change,
but a slope of almost 1.00 with a different constant puzzles me. What form
of experimental bias or population differences could account for the
regression line being offset by a constant?
I know that responding child protection agencies in Province Y were
instructed to exclude from the sample cases that were "purely" behavior
problem cases. Does the observed result fit that sampling bias? I'm not so
sure.
David
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