I am trying to run a three way Anova analysis on my data. The problem is that when I run a full factorial (with the three-way and the two-way interactions) the table does not contain the data regarding the main effects and the two way anova- only for the three-way anova. in the row of the 3 main effects and the 2 interactions, there is a "dot" where there should be F ratio or P-value, and in the DF clumn it sayes for all the effects besides the three way interaction: "0", and at the end of the row "LostDfs", what thus that mean? I do not have enough N cases to prefom this analysis?
Yes, based upon your description it seems as if you do not have enough experiments to delineate all the terms in your model. Have you tried entering all of the terms for your model and performing a Stepwise regression?
How did you obtain the data for your analysis? Did you use a DOE? Did you select a DOE that can support the model that you want to fit and the terms that you want to test?
For example, with three factors you could use a Custom Design and specify the full factorial model or you could use Factorial Design and add the interaction terms in Fit Model.
DOE stands for Design of Experiments. The purpose of a designed experiment is to provide the necessary data to fit a given model.
If you select DOE > Custom Design, define your response (outcome) and factors, then specify the full factorial model. This way you can see which treatments are missing your data set that prevent you from estimating and testing all of the terms.
I should add that it is not the quantity of runs alone that matter. Sure, you can't fit a fifteen-term model with three observations. But it is also a matter of having the right observations - that is, the right treatments in your data set. For example, if you replicated your experiments five times, I bet that you still could not fit the model with all these terms.
I recommend that you design the experiment for the desired model. I bet you already have some of the trials in your data set but this way will show you the specific gaps that need to be filled to fit your model.