I am performing measurements on a system for different values of the independent variable $X$.
For the sake of simplicity, let's say that:
- I have 5 values of $X_i$ I am interested in: $\{X_0, X_1, X_2, X_3, X_4\}$.
- I repeat each measurements 32 times per $X_i$.
What I want to know is what test I can do to figure out whether or not $X_i$ affects my measurement. Said otherwise, I want to know whether the slope of my measurements vs $X_i$ is zero.
NB: I know about t-tests (my measurements are normally distributed). However it seems to me that using t-tests between pairs $\{X_i, X_j;~ i\neq j\}$ is far less powerful than leveraging the fact that I have 5 cases which I know to grow linearly with $X$ iff $X$ actually has an effect.