It looks like a body of evidence is (at last) slowly coming together on how to teach statistics.
Or at least I like there conclusions
“Many of the problems with students learning statistics stem from too many concepts having to be operationalized almost simultaneously. Mastering and interlinking many concepts is too much for most students to cope with. We cannot throw out large numbers of messages in a short timeframe, no matter how critical they are to good statistical practice, and hope to achieve anything but confusion.”
Was working on a post but maybe just a fine here.
But continued speculation is still in order – jettison as much of the math as possible! There likely will be far many more that can understand statistical reasoning than those who can do that and "get used to the math". Abstract models are unavoidable – counterfactuals are the premise of statistical reasoning. What if something – we can never determine for sure is Null versus Alt – (or actually can never be NULL but we wish to assume so anyways)? What other samples could we have gotten other than the one we did?
But simplified abstractions can "work". I once used NULLS of -1,0,+1 and ALTS of 0,1,2 (all with equal probability) and enumerated all possible sample paths of size 3. Though the students hated it before the final exam – almost all did very well on the final exam that involved novel questions they had not seen before. It is likely all largely a matter of effort as to what works. But here you get the bootstrap for free – its just sampling those enumerated possible sample of 3 paths with sampling with replacement rather than the more sensible sampling without replacement. The real abstraction that I believe is hard to get in the bootstrap – is taking the sample you got as exactly the population! Then realism just needs to be built back up (n > 3 and less simple abstract models) and the pragmaticism of sampling with replacement demonstrated.
My current interest is in model displays rather than data sampling displays – how Prior models and Data model add and various ways to average over tem. The math is trivial but the task of explanation is probably not – at least for zombies – http://www.stat.columbia.edu/~cook/movabletype/ar…
Thanks – I had a look at the online paper http://www.rss.org.uk/pdf/Wild_Oct._2010.pdf that motivated this.
It looks like a body of evidence is (at last) slowly coming together on how to teach statistics.
Or at least I like there conclusions
“Many of the problems with students learning statistics stem from too many concepts having to be operationalized almost simultaneously. Mastering and interlinking many concepts is too much for most students to cope with. We cannot throw out large numbers of messages in a short timeframe, no matter how critical they are to good statistical practice, and hope to achieve anything but confusion.”
Was working on a post but maybe just a fine here.
But continued speculation is still in order – jettison as much of the math as possible! There likely will be far many more that can understand statistical reasoning than those who can do that and "get used to the math". Abstract models are unavoidable – counterfactuals are the premise of statistical reasoning. What if something – we can never determine for sure is Null versus Alt – (or actually can never be NULL but we wish to assume so anyways)? What other samples could we have gotten other than the one we did?
But simplified abstractions can "work". I once used NULLS of -1,0,+1 and ALTS of 0,1,2 (all with equal probability) and enumerated all possible sample paths of size 3. Though the students hated it before the final exam – almost all did very well on the final exam that involved novel questions they had not seen before. It is likely all largely a matter of effort as to what works. But here you get the bootstrap for free – its just sampling those enumerated possible sample of 3 paths with sampling with replacement rather than the more sensible sampling without replacement. The real abstraction that I believe is hard to get in the bootstrap – is taking the sample you got as exactly the population! Then realism just needs to be built back up (n > 3 and less simple abstract models) and the pragmaticism of sampling with replacement demonstrated.
My current interest is in model displays rather than data sampling displays – how Prior models and Data model add and various ways to average over tem. The math is trivial but the task of explanation is probably not – at least for zombies – http://www.stat.columbia.edu/~cook/movabletype/ar…
Happy World Statistics Day!