Very different ranges auf factor levels

[#1]

In one experiment, I have several factors whose factor levels (maximum vs. minimum value = range) differ substantially in their real-world dimensions. For one factor, the range is about 4%, for another factor about 16%, with several other factors lying in between. At present, these are only estimates of the minimum and maximum factor levels chosen so as not to impair the overall function of the object.

However, the factors are interdependent in such a way that, for example, the range of the factor with 16% could be reduced, while the ranges of other factors could be increased. In this way, it might be possible to achieve ranges of about 9–10% for all factors.

What is the better approach: leave the ranges as they are, or equalize them?

Regards

Klaus

[#2]

Really difficult to provide advice as there is virtually no context. Are you asking about mixture designs?

[#3]

No, it is not a mixture design. These are characteristics such as length, width, and height, which form two volumes similar to a Helmholtz resonator. The properties of the resonator certainly depend on the two volumes, which can be dimensioned independently of each other (i.e., there is no fixed total volume defined by the sum of the two volumes, as would be required for a mixture design). However, it may not only be the size of the volumes that matters, but also the shape—that is, the possible combinations of length, width, and height. The same volume can be achieved through different combinations of these parameters. These parameters—length, width, height, etc., in millimeters—are also varied in the experiment, and their ranges differ considerably. That is what the question refers to.

[#4]

Thanks, that helps a bit. Perhaps consider volume as an intermediate y. It is a function of dimensional characteristics of the shape. This is known (geometry). Seems to me you want to experiment on the dimensional x's, record the volumes as an output and record the measures of the resonator (frequency, wavelength, decibel of whatever it is you measure).  To experiment on those factors, consider coding the levels, equidistant. centered on 0.

[#5]

Thank you very much for the reply. In principle, however, we will carry it out in exactly the same way, including the coding of the factors. Nevertheless, the actual spread is very different, by about a factor of four. That means that something which would have the same effect size in reality would show a signal four times stronger in the experiments. The weak effects therefore run the risk of not being detected. Hence the question: would it make sense, at the expense of the very large spread, to increase the smaller spreads so that they can be detected more reliably?

[#6 · Accepted solution]

I can't say I understand exactly what you are asking, but, in general, the hidden assumption of experimentation is that level setting across all factors is similar (e.g., the design space is relatively symmetric).  As you suggest, if one factor level setting is much bolder than others, you likely have biased that factor effect and that factor may overwhelm the others.  Of course, the challenge is how to set similar levels across completely different scales (e.g., temp is in ºF, time is in seconds, force is in Nm)? The advice I give is to set factors as bold as is reasonably possible across all factors (at least in early experiments). First rank order model effects, then fine tune the level setting. Many engineers are leery of such bold level setting. My hypothesis is they aren't really trying to understand mechanisms, they are trying to pick a winner.

Just a side note, your statement: "That means that something which would have the same effect size in reality would show a signal four times stronger in the experiments." is not necessarily true.

[#7 · Accepted solution]

Thanks for your answer, that sounds good for me. But please could you explain the following:

Just a side note, your statement: "That means that something which would have the same effect size in reality would show a signal four times stronger in the experiments." is not necessarily true.

Regards

Klaus

[#8]

If, for example, there is curvature, having levels 4 times larger might entirely miss the factor effect.