Three-way ANOVA lost DFs

[#1]

Hello,

I learned JMP in class using "perfect" dataset but now I am trying to use it for my research work by running a three way ANOVA using the attached data. Generally, there are three different factors (Current, HRT and Temp) and I would like to see to sig. effect and interaction of each factor on the result (Inf pH). However, the "Effect Test" from the analysis showed "Lost DFs" instead of p-values. I have a pretty small dataset (33 points) so could this be the problem? 

Here is what I've done:

1) Analyze -> Fit Model

2) Insert "Inf pH" as Y variable

3) Insert Current, HRT and Temp as Model Effects with * interaction (I also tried doing 2-way ANOVA using only two factors)

4) Run using "Std Least Squares" as Personality (I tried other personalities as well but did not work)

I would really appreciate any inputs on how to work around this dataset, in order to get the "Effect Test" p-value result! Thank you very much!

Ji Yeow

[#2 · Accepted solution]

Ji Yeow,

The issue you have is that your effects are confounded with each other.  You really only have 2 groups.  One group has a Current=100, HRT=8 and Temp=10.  The second group has Current=300, HRT=12 and Temp=22.5.  Without having measurements made for the different combinations of Current, HRT and Temp, the analysis can not be performed.  That is, you need to have measurements where Current=100, HRT=8 and Temp=22.5, measurements where Current=100, HRT= 12 and Temp=10, and the other combinations of the 3 factors.  For a "Full Factorial" analysis, you need to have measurements made for each of the possible combinations of the 3 factors.  A "Partial Factorial" analysis could also be run, however, for it to be a valid analysis, the design needs to be be developed using DOE(Desing of Experiments), to make sure the final analysis will be valid.

The only analysis that you could do with your current data is a Oneway analysis.  If you chose to use Fit Model, just specify one of the factors. 

[#3 · Accepted solution]

Just adding a bit to Jim's insightful reply:

The confounding is not perfect between Current and HRT, but it is likely that the correlation of the estimates is strong enough to preclude enough power to determine their significance, especially if you include the interaction effect in the model.

Going back to Jim's reply and assuming for the moment that the three factors are perfectly confounded, you can estimate the one-way ANOVA model with this data but the choice of which factor is subjective and arbitrary. The data cannot be used to determine which one is, in fact, attributable to any effect on the response.

[#4]

Mark is correct......I missed the few rows at the bottom where current is 100. 

[#5]

Yes, Jim, but your point essentially stands.

A designed experiment, possibly smaller than this data set, could have provide much more information. Live and learn!

[#6]

Thanks a lot Jim and Mark! This is a great explanation and is definitely helpful with my analysis!