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Everyday we allocate mortgages between two investor platforms. Within each risk segment and term (length of mortgage in years), mortgages are allocated based on investor demand randomly. ie 70/30 split.

Mortgages/borrowers can have a number of attributes, fico, dti, loan amount, borrower income, number of revolving accounts, etc.

I want to validate that the random allocation is truly random across time and across various attributes.

I am thinking of using Welch's t-test and testing each attribute separately (unequal sample sizes and unequal variances). Is this approach valid or should I look at some type of multivariate test? ie Hotellings T-squared.

On some days, there are only a handful of loans per platform, so I think using a window size of couple days, a week or even month. What do think for the time dimension and monitoring the overall process on an ongoing basis?

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You could do a Chi-Square test. Search for Chi-Square test for fair dice. It is pretty much the same problem.

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