Experimental values are close but are not equal to the factor values in outlined in the DoE.

Question

In my class, students use custom design to plan their experiment. They conduct trials targeting the factor values recommended by JMP. In practice, the conditions of the experiment are a little different for a variety of reasons. I recommend they input the "actual/measured" values when analyzing the results? Am I correct? How does this affect their analyses as the conditions may not be orthogonal as in the JMP design?

Victor_G · Answer

Hi @Raghavan,

Welcome in the Community !

You may find previous answers to posts closely related to your question helpful :

Altering factor values once you have already made the design and the table (CUSTOM DESIGN)

Use of Real instead of target factor values in DoE

You may also encounter similar situations when creating a Custom design with constraints in the experimental space : the values found by the coordinate-exchange algorithm may be very precise/specific (sometimes odd) compared to what is practically possible in the experimental setup:

How are odd factor settings in D-optimal RSM generated

Random decimals incorporated in mixture screening design

To answer your question, I agree with the proposal of @statman to run in parallel both analysis, with design factors values (as they were generated) and with "real" values, to avoid any doubt about the influence and importance of this change in factors values.

In practice, if you only have small deviation in your factors values and sufficiently broad factors ranges, the impact of this change should be minimal and perhaps even not visible. There may be also relatively a larger variation in the response measurements (due to repeatability/reproducibility, measurement errors, ...) that will completely "hide" the influence of the deviation in factors values.

Hope this additional answer may help you,

Raghavan · Answer

For practical reasons, it is not often feasible to hit the set point precisely. For example, I may choose to control flow at X lpm but fluctuation in line pressure may cause the flow to vary +/- 1 Lpm! I like your idea of testing both ways but if the results are different, would you trust the results based on coded values?

statman · Answer

Here are my thoughts:

1. Why can't they use the values for the factors specified by the design (JMP)?

2. The assumption is, in experimentation, that if you set a low level (e.g., -1 coded) and change the level setting and go back to low level, -1, that level is identical to the previous level 1.  This greatly simplifies the analysis and allows for assignment of higher order terms easily.

3.  The reality is, variation exists in everything, so one strategy to overcome the within level variation is to ensure the between level variation is large (e.g., bold level setting).

4. If you want to do use the actual values, depending on how much they vary from the specified level setting, you might lose the ability to assess higher order terms like interaction effects.  If they are not that different, probably doesn't affect the analysis too much .

I'm not sure I would consider your advice "correct" or just one way to analyze the data.  I would try analysis of several experiments using the coded values and the actual values and see how the output of the analysis differs.