I have the one-factor model Y=W*m + e where e ~ N(0, (s^2)*I) and W = I(3) (x) J(6).
The (x) refers to the Kronecker product, I(3) refers to a 3-size identity matrix and J(6) refers to a 6-size vector of ones. Y and e are 18-by-1 vectors, W is a 18-by-3 matrix, and m is a 3-by-1 vector.
My given hypothesis is that m1 = m2 = m and m3 = d*m where d =/= 1 and m is some arbitrary value. Using this information, I am supposed to find an F value (test statistic) and its distribution. I can figure out the hypothesis matrix which is as follows:
[1 -1 0]
[d 0 -1]
[0 d -1]
This is as far as I can go. Anyone know what I should do next?