I have a design matrix , columns are factors with 2 levels, rows are experiments, see pics. I want to evaluate the design for aliasing (also called confounding). I obviously want a design that is free of confounding. I thought as part of doing this i would take XT * X of my design to get the dot products across each column. If there is no confounding id expect 0 in every off diagonal term. When you do this lets say in R very clearly there are off diagonal terms out of a possible |22| some off diagonal terms are at most around |6|, see pics. However when I evalute this design in JMP and look at the alias matrix the off diagonal factor terms are zero i( i messed around with the alias model terms to evaluate the main effects only). This seems like some simple linear algebra but perhaps I am having some fundamental misunderstanding. If the dot products of the column vectors are not zero then they are not orthogonal. Maybe this is an incorrect way to think about this but 6 out of possible 22 seems like a pretty substantial amount of confounding. What is JMP doing that I am missing, or where is my understanding wrong, surely i am wrong. 
Hi,
It is hard to tell what you did outside of JMP without seeing any report/calculations.
Designs with no confounding between the main effects might show an alias matrix like you are getting. This should be the usual expected behaviour for screening design types.
When I build a custom design in JMP only including the main effects the color map of correlations looks like this:
You can see that there is no correlation/cofounding between the main effects (yellow area), but a lot of correlation between higher order terms.
The alias matrix has a different purpose which Ryan explained down below.
Usually you want check the color map of correlations in your report for correlation/confounding properties of the design.
edit: fixed a misleading statement about the alias matrix
Here is what the color correlations look like. I used only the main effects in alias terms. The alias matrix is a 1s and 0s, but the color correlation map has some off diagonal terms that are not 0. next reply i will show what i did outside JMP.
Dot products of 16 columns of the design matrix (i.e. the 16 factors over 22 experiments) leads to a 16 by 16 matrix.
again it looks like there are off diagonal terms. And based on the scale of 22 for -6 looks like a decently large relationship in an absolute value sense. Perhaps i have some very fundamental misunderstanding. Another possibility is there is some cutoff at which off diagonal terms are ignored. But then i would suggest a confounding that is on the order of
heres another image , iused main effects in model terms, and added both main efects and 2nd order interactions in the alias terms. You can see in the color map correlations the dark block of 2nd order vs 2nd order. but main effects vs main effects and main effects vs 2nd order are about the same light grey color . Why then does the alias matrix list 0s for the main effects vs main effect off diagonals but various numbers for the main effect vs 2nd orders. Again im sure its just something im not understanding.
