Im fairly new to JMP and im in the process of setting up a DOE to look at the effects of several ingriedients within a mixture on a specific response. Im only interested in the main effects and the two way interactions. Do I need to check all the assumptions of equal varaince and normal distributions before I fit the model? I generally do when perfoming one way and two way ANOVA, but is it necessary for a DOE?
In general DOE data is analysed using regression models. The assumptions that you talk about are typically applicable to the residuals rather than the raw data, so in that sense you need to build the model first and then validate the assumptions. This can be done by inspecting the residuals. Bear in mind that with a DOE the quantities of data are usually small so it is sufficient to do this visually.
Thanks for this Dave. Im in the process of analysing my results. The response values from the DOE are not normally distributed, but when I screen my factors and build the model around the relevant ones, im saving the residuals of the reponse which when analysed, are normally distributed. Is this the correct way to go about validating the assumptions?
Yes that's the correct way to go about it. You would not expect your response variable to have a normal distribution because you are peforming the DOE explicitly to induce changes in the response so that you can understand the influence of the predictor variables. However, once you have a model you are left with residuals which ideally should be normally distributed. I personally wouldn't worry hugely about this assumption (if you do then it is nolonger an assumption!) - you are unlikely to have enough data points to perform a test that refutes the assumption - however, studying the residuals can be useful to diagnose problems with a model or for areas of improvement.
Mixture DOE's are a unique type of DOE because the factors or parameters are interdependant. They behave differently than regular DOE's so I would suggest that you read a review by John Cornell on Mixture DOE to understand their unique statistical properties.
The definitive book on Mixture Designs is available by John Cornell
Thanks for the advice LouV and Dave. I was going to use a mixture design, but from what I understand, this approach is used if the proportion of ingriedients is important. Reducing the amount of one ingriedient will not effect the the amounts of the other ingriendients in my case. Im just interested in finding out whether the presence or absence of a particular ingriedient effects my response. Am I right in thinking that im able to use a screening DOE to do this?
Sounds like you are good to go then on a screening design. You could also use the Custom Design platform, specify main effects and two-way interactions for your model and enter the number of runs that you desire. The Custom Design platform gives you more flexibility with respect to handling your experimental scenario.
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