Fractional Factorial Design of Experiments DOE Data Analysis Example | How To

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One thing I'm wondering... Say we were looking at one continuous factor x and a reponse y. The true relation between y ~ x is y = x^2 (unknown to us of course). Say, for whatever reason we decide to take the levels of x to be {-2, 2} and measure the response. We observe that in both cases, the response y is the same, thus effect_x=0 and we would incorrectly count it as insignificant. How do we avoid this mistake?

Let me give a concrete example: In the "comfort ~ humidity, temperature" example you keep using, when you run ANOVA on that example, you get a p-val of something like .1 and .2 for the factors, neither of which are significant and so if we were just looking at these p-val's, we'd throw out the terms. However, later you run a few more experiments at the star points for these terms and fit a response surface. We see clearly now that the comfort is quadratic function of the factors and they are important. How would we avoid throwing out possibly important factors too early?

Josiah