# How to analyze results of this experiment?

I used a Definitive Screening Design plan to examine which of the parameters $A_1, A_2, \ldots, A_6$ have significant influence on the response $Y$. The design plan consists of $13$ treatments. A treatment is a combination of low, medium and high levels of the factors. I have repeated all the treatments on the same set of subjects. The number of subjects is $n=30$. Let $Y_{i,j}$ denote the response measured in the $j$th subject when exposed to the $i$th treatment.

I am not certain how to proceed. Can I compute the average response for each treatment: $$\overline{Y_i} = \frac{1}{n}\sum_{j=1}^{n}Y_{i,j}$$ and then try to fit a linear model to these $13$ data points? For example: $$\beta_0 + \beta_1A_1 + \beta_2A_2 + \beta_{11}A_1^2 + \beta_{34}A_3A_4$$ I would then test the hypotheses $H_0: \beta = 0$ vs $H_a: \beta \neq 0$ for each $\beta$. A DSD plan that I used allows us to estimate main effects and also pure quadratic and two-way interaction terms.

• Treatments are combinations of low, medium and high values of the factors, chosen in a specific way to order to allow estimation of main effects, two-way interactions and pure quadratic effects of the factors. So, I need to find out how each of the factors $A_1, A_2, \ldots, A_6$ influences $Y$. This is why I don't think that dummy coding treatments would help, or at least, I don't get why it would. :( Can you, please, elaborate more on that and 'moderation'? – Milos Oct 21 '16 at 14:16
• No, factors are $A_1, A_2, \ldots, A_6$, and a treatment is a combination of their values, e.g.: [Low $A_1$, Low $A_2$, High $A_3$, Medium $A_4$, Low $A_5$, High $A_6$]. :) – Milos Oct 22 '16 at 1:13