I've done a number of these data analysis 'tests' as part of interviews for data scientist / analyst roles. They typically vary -- usually (hopefully!) the data set & questions are highly specialized for the company + the role you are applying for. So as for ways to practice.... I'm not sure. If you're skilled in R / Python / Matlab / SQL or whatever the role requires... you should be fine.
General advice:
1. Be explicit: if you are making an assumption in your code, write why. Write out your logic & reasoning at every step.
2. Watch out for missing / 'bad' data. Write out how you would deal with messy data in real life.
3. Pay attention to the time limit. If you don't know, contact the recruiter to ask what's expected.
4. Interpret your results! If they ask you to, say, find the R^2 correlation between x and y, give them the number and then tell them what that might mean.
Don't stress. Hopefully the 'test' is fun and well thought out. I've always found them extremely helpful in understanding the problems that I would be solving if I were to end up at the company. On the other hand, I've heard that some companies don't put a lot of time into making these assignments relevant, so for me, that would be a warning sign.
