Someone else's PhD student is not getting proper advising on methods. Should I interfere? How?
I think that an important criteria in deciding what action to take is how severe the effect on the research quality actually is.  Practices that look horrifying to an expert in the practice may actually have only a minor effect on the actual validity of scientific experiments that do not depend closely on the details.

I would recommend selecting a response based on how severe the likely issues caused by the sloppiness of statistical analysis actual is:


If the analyses are actually actively fraudulent (e.g., taken with intent to deceive), then you've got a responsibility to blow the whistle (though you must take care in confirming and in how you go about it in order to avoid destroying your career).
If the analyses appear likely to cause a major qualitative change in the interpretation, such that retractions would be appropriate, then it is reasonable to warn both your student and your colleague of the issue and to point out exactly how and why such issues are likely to arise.  If they understand the issues and still choose to go in that direction, it is not your responsibility to save them from embarrassment and possible retraction.
If the analyses are incorrect and probably distorting results but the effects they are working with are strong enough that the distortions are unlikely to radically change the results, then you can point it out, but don't be surprised if they ignore you for the sake of expediency and "good enough" approximations---and indeed, they may be correct to do so!