how did you control for the socio-economic statuses of each of the individuals in your sample? without specific knowledge of each one your conclusion is fundamentally flawed, and as such completely expendable, and arguably dangerous because you're tossing around unsound data under the guise of scientific derivation.
If your socio-economic status is such that you can't afford to leave a proper tip, then you do not have the disposable income to be eating out in the first place.
I have reached no conclusions, in my opinion it has to far more to do with culture than anything else.
Race has absolutely nothing to do with it.
I do not tip less than 20% EVER.