# Experimental design when having continuous factors

I am studying about experimental design. I understand some of its general steps. I still have a small question:

Can we apply experimental design when having continuous factors ?

What I mean by a continuous factor: is a factor in an experiment taking values continuously. This means that it has no specific levels ( 2, 3 ,..). For example, a factor in an experiment that is allowed to take values in $[0,1]$.

If such continuous case does not exist, Is it possible to have an alternative investigation. For example, is it possible to carry the experiment on (let us say ) $6$ different levels taken in the interval $[0,1]$, and build our design depending on these levels?

Edit : An example to clarify my idea:

suppose I am doing an experiment to test the effect of the 1. Electric flow (voltage) 2. the thickness of the copper wire on the electrostatic force.

Voltage: I have three levels for this factor : $12V$, $15V$, and $20V$. Thickness: this factor take continuous values between $10$ and $20$ nm, i.e. values in $[10,20]$.

My question was, is it possible, for the thickness factor, in order to carry an experimental design, it is possible to select some values from this interval, and say, okay these level (values) represent this factor. In other words, it it possible to choose, for example, Four levels for the thickness factor $10nm$, $13nm$, $16nm$, and $20nm$. Then construct my experimental design depending just on this four factors?

• I think you can do a regression analysis using the voltage as ordinal variable and thickness as continuous variable. If you want to use thickness as ordinal variable too you have to use different intervals and not absolute measures, for example interval1 [8-10 nm], interval 2 [10-13 nm] ecc – GGA Jan 29 '16 at 9:38
• en.wikipedia.org/wiki/Optimal_design – whuber Jan 29 '16 at 14:08