I have 2 input variables, $X_1$ and $X_2$ that affect output variable $Y$. I can run experiments where I modify the inputs and measure what happens to the output.
Now, if $X_1$ and $X_2$ were binary, I could just run four sets of experiments, collect $Y$ and use t-test to figure out if any combination affects output differently. Most importantly i can use power tables to check what should the sample size for each experiment be in order to achieve a desired power level.
However, if $X_1$ and $X_2$ are continuous between 0 and 1 I am not sure how to compute sample size and power. I am willing to assume some form of continuous function connecting $Y$ to $f(X_1,X_2)$ although not necessarily a linear one, but I am unclear about what my power is when I check, for example, if the difference between $f(X_1,X_2)$ and $f(X_1,X_2+h)$ is significant or not.
And given this, can I figure out what the sample size ought to be?