1. ## Hypothesis test

Hi all,

How do I conduct a hypothesis test as follow

$H_0: \mu_{trt,time(j+1)}-\mu_{trt,time(j)} \ge \mu_{trt,time(j)}-\mu_{trt,time(j-1)}$

as opposed to

$H_0: \mu_{trt,time(j+1)}-\mu_{trt,time(j)} < \mu_{trt,time(j)}-\mu_{trt,time(j-1)}$

To simplify this: Let look into 1 particular treatment with j=2:

$H_0: \mu_{time(3)}-\mu_{time(2)} \ge \mu_{time(2)}-\mu_{time(1)}$

Let say I have $\bar Y_1, \bar Y_2, \bar Y_3$ and $\sigma_{11},\sigma_{22}, \sigma_{33}, \sigma_{12}, \sigma_{23}, \sigma_{13}$

I was thinking maybe I can shift the equation into left hand side to form:

$\bar Y_3-2\bar Y_2+\bar Y_1$ as the estimate, but what about the S.E?

My guess is: $1/n\sqrt{(\sigma_{11}+2*\sigma_{22}+\sigma_{33}+??)}$ These variables are correlated.