Discrepancy measure for space filling design

[#1]

Hello, how is the "discrepancy" measure calculated? I read in the docs that "The discrepancy value shown below the table is the integrated difference between the design points based and a uniform distribution." Is this the L1 distance? or something else? The DiceDesign R package has a boatload of different (L2) discrepancy measures. Any help appreciated.

[#2]

@Mark_Bailey explains discrepancy in this previous thread.

"The discrepancy measure is a relative measure of the quality of a space filling design solution. It is useful when comparing two or more space filling designs. A smaller discrepancy indicates a better design.

Discrepancy is the difference between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution."

I am not sure which discrepancy measure this corresponds to in the R package. The documentation for the R package does not have a lot of detail.

Perhaps you might want to generate a space-filling design in JMP and then run it through diagnostics in the R package to see which measure is the same. Alternatively you might want to contact technical support to see if they can get more statistical details ([email protected]).

I hope that helps,

Phil