This is a quick overview of the topic: http://www.siop.org/_Principles/pages31to34.pdf
An interesting thing is that the predictive bias is reduced for open-form response questions vs. select-one tests. It's an indication that there is more at work than just subgroup differences.
One of the people looking at the results then looked at the breakdown of questions by group and noticed immediately that questions like "The cup goes on the a) saucer b) floor c) table d) shelf" where consistently "wrong" (correct answer was a) for the poorer group at which point he realised that working class children drink tea from mugs and saucers where a middle class thing.
The story might be apocryphal but its stuck with me since I was 12-13 whenever I run into any kind of standardised testing/results.
How do we know the tests are fair? For a given test score, life outcomes like income and criminal conviction rate are the same.
I'm intrigued, is the "bias" because the test is unfair to one racial or more racial sub-groups or because the test is "fair" and that is how they actually perform or is it a language thing.
I do reasonably well on standardised IQ tests but I suspect if I did a German one I might struggle.