Let's say I have 4 doses of the same medication, and record some Y response variable for a couple of patients for each dose.
If I want to test linear trend of Y for doses, I find in the SAS documentation
PROC GLM DATA=... ;
CLASS dose ;
MODEL y = dose ;
CONTRAST "linear trend" dose -3 -1 1 3 ;
RUN ; QUIT ;
and that if the contrast test ends up with a p-value small enough according to my sample size, I accept the linear trend.
If someone can explain in a mathematical (or in plain English) how come the inequality that -3 Mean(Y|dose=1) - Mean(Y|dose=2) + Mean(Y|dose=3) + 3 Mean(Y|dose=4) ^= 0 is equivalent to "Mean of Y increases linearly with dose", I'd be really delighted.
I've asked french Tech Support, but got no real explanation until now (just "that's how it works" but no further justification).