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I am looking at some data with a 5 factors and a response variable. The experiment was designed as a factorial experiment, with observations at different levels of each factor. One thing that I have notices, though, is that there is some variability in the readings for the factor levels.

For example, motor RPM is a variable, and readings were supposed to be recorded at 800 RPM, 1000 RPM and 1200 RPM. The experimenters were able to set the RPM at these levels for the experiment. There is an RPM monitor that keeps track of the RPM during the experiment, and is recorded along with the data. However, looking at the data, we see that there are slight variations. For example, when set at 800 RPM, we have readings that range between around 790 and 810 RPM. This occurs for all five of our factor variables. The RPM variability is negligible, but some factors are varying more than 15 percent of the desired factor level. This may be due to some error in the readings of the monitoring equipment.

My question is, can I ignore the variability in the factor levels and assume that we read the observations at those factor levels, or can I take into account the factor level variability when doing the analysis?

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  • $\begingroup$ If you do an initial analysis ignoring the minor variations you may get a estimate of the impact of RPM on the response. If this is reasonably smooth and plausible, you could then adjust your models for the implied impact of the minor variations, and if necessary rinse and repeat. $\endgroup$ – Henry Apr 22 '12 at 12:03
  • $\begingroup$ Thank you for the comment. We are also suspecting that the variations are due to measurement error in our monitoring equipment. Do you want to submit your comment as an answer so that I can accept it as an answer? $\endgroup$ – ialm Apr 22 '12 at 14:58
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If you do an initial analysis ignoring the minor variations you may get a estimate of the impact of RPM on the response. If this is reasonably smooth and plausible, you could then adjust your models for the implied impact of the minor variations, and if necessary rinse and repeat.

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I may be missing something but it seems there is an entirely empirical answer to your question. I think what I'm saying matches @Henry's comment as well. Assess, whether through regression and a plot of predicted vs observed Y, or through a more "vanilla" scatterplot, the relationship between RPM and the response variable. You should be able to tell fairly easily the extent to which cases with values other than 800, 1000, and 1200 are behaving in line with (literally) those that are exactly at those 3 levels. You could even formally test whether residuals differ, in mean or variance, between the "exact matches" and the other cases.

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