Teaching statistics - can I leave aside assumptions testing?

[Hibush]

Update: I have decided to not talk much about assumptions in class, but to make a power point with assumptions for each test available to the students. This way, interested students who can absorb the extra nuance have those resources (which I'm happy to discuss with them in office hours), but the other students don't get bogged down in something the aren't really able to understand.

It's probably also a good idea to demonstrate what can go wrong if you blindly apply a statistical test or measure when the assumptions are violated, to drive home the point that the assumptions matter to the validity of the test.

Doing only tests for which the data sets sufficiently meet the assumptions is so important. Grad students make this mistake more than any other. I like the idea of having the students do (or see) an analysis where the data come close enough, realistically imperfect compared to a similar one where the data stray from the assumptions enough to give false inferences.

[dlehman]

How about not teaching NHST at all?  Personally, I think the assumptions are more important than the test.  The tests invite binary thinking (always wrong) and divert attention from what can and cannot be learned from the data.  Assumptions are part of that picture, but probably a minor part.  Most problems with studies are not that the assumptions have been violated, but that the data measurements (data quality) are poor and/or the data has been improperly filtered/selected/aggregated.  So, students should be aware that there are assumptions, but there are so many more important things they need to understand. 

[Hibush]

How about not teaching NHST at all?  Personally, I think the assumptions are more important than the test.  The tests invite binary thinking (always wrong) and divert attention from what can and cannot be learned from the data.  Assumptions are part of that picture, but probably a minor part.  Most problems with studies are not that the assumptions have been violated, but that the data measurements (data quality) are poor and/or the data has been improperly filtered/selected/aggregated.  So, students should be aware that there are assumptions, but there are so many more important things they need to understand.

The binary thinking is a killer. Completely agree that it prevents interpretation (and even collection of) informative data.

I would include data quality and appropriateness of filtration among the assumptions one wants to be aware of. E.g. can we assume the sampling error is a lot smaller than the natural variation? Can we assume the outlier was a data-collection error? My (biology) grad students have a lot of trouble developing objective approaches to answering even such fundamental questions. I think it is well worth my effort to give them a better foundation.