I switched to the combination of problems that have the answers in the back and those that don't, just like you were thinking. The ones that are in the back give them a way to make sure they are doing things correctly, while the ones that aren't there gives me a way to know they aren't just copying from the back of the book.
I also require that they do some problems using SPSS. For those problems I typically go through an example with screen shots in the notes and then provide a sample data set that the homework questions ask about. For example, I recently covered both independent and repeated measures t-tests, so I gave them an abbreviated version of a data set I had from a study a few years ago. The study involved both a pre-test and post test for two groups, so I could ask question about differences between groups at the beginning and end as well as differences within the groups across time. By going through similar examples with another data set (also provided to them) they could work through the example to get a feel for how to do things and then go on their own for the actual homework problems.
I tend not to worry about the hand calculations for things beyond descriptive statistics (and DF formulas) since after this class they will almost always have access to a computer with SPSS to do the calculations. Instead I use the formulas as a way to conceptually show them what is going on. It took me a while to get away from wanting the hand calculations though. At first, my reservation, and one I still hear in my department, is that having students work through the formulas by hand gives them a better understanding of what is going on. But, after really looking at things it seemed only those students who had a really good grasp of math were able to do this. The majority of my students ended up viewing the class as one of simply plugging in numbers to crank out a number at the end without really understanding why the numbers went where they did. Moving to the more conceptual less calculation approach has allowed me to spend more time in the why and less on the how.
At times I feel like I'm in the minority with this approach, but for me it really came down to thinking about what would be expected of them later on in other classes, in graduate school, and/or on the job. They are expected to know which test(s) are appropriate for a given scenario, a little about what the test is doing, how to "perform" the test, and how to interpret the results. When having students calculate things by hand I ended up spending so much time on the "how" that not enough was going into the why a test would be appropriate and what it was doing. By moving to SPSS for most of the calculations, I could focus on those what and why questions more as well as the interpretation issues. Also, those students that came into the class with high math anxiety were put at ease somewhat because they didn't have to worry about their math skills as much so they could focus more on what each test was really trying to do and when it was appropriate to use. Also, when I really sat and thought about it, when would a student be asked to do the calculations by hand after the class ended? I really couldn't think of a time other than perhaps for a really small data set or an example in some class. 99.9% of the time they would have access to a computer to do the analysis and would be dealing with much larger data sets. By using SPSS now, I can actually have them working with those larger data sets in class and gaining skills that they will be more likely to use in the future. I even had one student who swore up and down throughout both stats and methods that he'd never use those skills. As it turns out he ended up getting a research/data analysis job with the military making about $10k more a year than he expected because he had those skills... that was one of the best thank you notes I've received, and it really made me commit more to teaching the class this way.
This approach seems to work well for me and the students I tend to have in class which are often highly math phobic. I admit that it was a bit of a challenge at first because I found myself having to explain things in more conceptual detail than I was used to at the undergraduate level, but in the end I really believe the students are getting more from the stats class than they were in the past when more than half of their energy was spent making sure they remembered to carry the 1 in a formula correctly.
Okay, longer than I intended but hopefully helpful... - Marc
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