Thanks
I can't tell from your picture if this is count data or not. Is your response variable always an integer, or does it include values like 0.5 and 0.87321?
SAS/STAT supports fitting several zero-inflated models. You can use PROC GENMOD to fit zero-inflated models, or you can use PROC FMM to fit the data as a finite mixture.
If that doesn't suffice, what kind of a permutation test are you looking for? What quantity are you comparing between groups?
You could start by testing if the proportion of zeros is the same across b groups:
data myData0;
set myData;
isZero = a=0;
run;
proc freq data=myData0;
tables isZero*b / chisq;
run;
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