# Factorial experiment (2x2x2) analyzed with ANOVA or multiple regression?

#### JossHeme

##### New Member
Hello!

I am working in my Master Thesis and I have some questions regarding the design of my experiment and the analysis of the data, could you please help me?
I am looking at the effect of Temperature, Ionic strength and pH in the solubility. For this, I followed the following steps:

1) I first look into the independent effect of each variable:
a) Temperatures (20, 70, 80 and 90) vs solubility
b) pH (3, 4, 5, 6, 7, 8) vs solubility
c) Ionic strength (0.5%, 1%, 1.5%, 2%)

My objective by doing this was to analyze the relation between each independent variable and the dependent variable. For temperature and ionic strength , I obtained a linear relation, but in the case of pH I obtained a curve (U-form).

2) Now, I would like to perform a 2 level factorial experiment (2^3) to look at the combined effect of the independent variables. I will choose the minimum and maximums for each variable based on the results of the previous experiments. By doing this, I would have 8 experiments to perform.

3) Now, I would like to obtain the coefficients of each independent variable and of their combination. Should I use MANOVA or multiple regression?
I was reading that in the case of multiple regression I need at least 30 samples to have significant results. What does it mean? That I have to repeat 4 times the 2 level factorial experiment? or that 2 levels (min and max) are not enough for conducting a multiple regression?

I will really appreciate any suggestion or guidance,

Joss

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#### Miner

##### TS Contributor
I recommend that you consider a response surface central composite design instead of a 2^k design. You already know that pH is not linear, so your design should take that into consideration.

#### JossHeme

##### New Member
Thank you very much for your answer. Does the 2^k design presuppose linearity between the independent variables and the dependent variable?

#### Miner

##### TS Contributor
Yes, 2^k designs are typically used to first screen variables for significance. Center points may also be included to determine whether curvature is present. If no curvature is present, you may then model the response, but if curvature is present, you need to use response surface designs to model the curvature.