Full Factorial Analysis with added blockingDear JMP Community,
Initially, I have designed the following experiment using full factorial - 3 factor (2 continuous + 1 categorical) - process chamber being the categorical factor.
For the process of concern, it is already known that there will be chamber-to-chamber variation, but all chambers must be operable within a certain specification limit. Hence, the initial decision to include the chamber as categorical parameter.
In total there were 20 runs. The experiment has been performed and data have been collected.
1. Would be better if Full factorial with blocking being used in the first place, since the chamber can be considered as random effect? If yes, then i'm screwed. 
2. Is there any other way to use the existing data collected to properly analyze the data?
Thank you in advance
AmirSS
DOERe: Full Factorial Analysis with added blockingWhy do you think that the chamber should be considered as a random effect?
You would model a factor effects as a random effect if you expect to see important differences between levels of the factor and you can't control the levels.
A classic example is DAY when you have multiple runs on each day and you would expect differences in the response between days because of one of more "noise" factors (e.g. ambient temperature, humidity, daily instrument calibration, shift operators, ...) that vary from day to day and you are not able to control.
You can include a random effect for DAY to take care of the day-to-day noise factor variation and separate it from the variation due to the fixed effects of interest. In this way, you have a better estimate of the effect of the factors that you are able to control. But you can't make specific predictions about a day in the future because you have no information about what the random effect of DAY will be.
Now, on the other hand, you might suspect that there is a predictable DAY effect in the way it varies by day of the week. Maybe you expect higher response on Monday and Tuesday. In that case you would model DAY (M, Tu, W, Th, Fr) as a fixed effect. With your model you could make predictions about the response that you might see on a certain day of the week.
Hopefully that makes sense.
The question for you therefore is whether Chamber is like the "noisy" effect of DAY in the first example or is it like the predictable effect of DAY in the second example.
I hope I have not added to your confusion!
Phil
Re: Full Factorial Analysis with added blockingPhil advice and explanation is excellent. My thoughts:
1. Are you actually interested in experimenting (understanding causal structure) or testing (picking a winner)? Do you want to understand why you would be getting potentially different effects of the 2 continuous variables for each chamber?
2. Curious as to why you are not trying to understand and possibly reduce the chamber to chamber variation?
3. Is there any significant within chamber variation? How about measurement system error?
4. Are there only 2 chambers? If so, are you trying to find the settings that work best in each chamber?
5. You can certainly analyze the data set you have. It seems you have a 3^2 factorial replicated over 2 chambers. You could analyze the results for each chamber separately (if you are just looking to find the appropriate effects for each chamber) or if you actually want to get clues to understanding the effects and why they might be different for each chamber, you can include chamber and all chamber by factor interactions in the model.
