I have an electrochemical process where 5 variablea can affect the results, I am testing the maximum reachable value of each variable separately while the other variables are constant.
The question is, how to statistically analyze and relate these separately tested results in the light of all of them affect the same process?
Dear Ahmed AbdElnaby Rezk
In order to analyse the component effects of a known set of active causes you may need to model a multi-dimensional cross-dependency which could in principle also exhibit nonlinearity. If (as in your case) you can predetermine each significant cause and effect as a distinct relationship, developing an appropriate analytical model is a relatively straightforward task.
Step 1. Produce an experimentally derived scalar plot of effect as a function of cause for each variable.
Step 2. Linearize the model (if necessary) by fitting an accurate curve such as a polynomial, or spline function, to each scalar plot.
Step 3. Normalize the resulting tabular product across the dimensions of effect in order to equate the relevant scalar effect values.
Finally derive a relative value an N-dimensional cross-dependency matrix such that each row represents the effect of a single variable and is quantified by the above experimental data and each column represents the observed effects of mixing them. In effect you now have a full set of predictive equations for the overall cross dependent phenomenon. In the absence of the above calibrating single variable data, a much more complex Fourier analysis would be required.
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