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Revision of Introductory Statistics Courses Could Close Divisions

1 March 2014 794 views One Comment

Terry Speed’s comments in “Trilobites and Us” (January 2014) refer to omissions in the fields described in the International Year of Statistics conference—social and government, in particular. This connected me with the areas in which our community was said to have been guilty:

F. Generally poor teaching, particularly to large classes of non-specialists
H. Failing to articulate our core to the world at large

F and H seem to me to follow almost automatically from the fact that we do not have a unified profession upon which the basic principles are agreed. The divisions within the community are most clear between official and academic statisticians. In Australia, the Australian Bureau of Statistics (ABS) was concerned for many years by the failure of academic statistics courses to teach adequately (or at all) sampling procedures and the design-based approach to inference. The ABS had to retrain university statistics graduates in these areas before they could be useful in ABS work. Graduates found a major disconnect between their academic courses and the work of the ABS, and this contributed to high turnover of new graduates recruited to the ABS.

Over the same period, but especially since the 1990s, there has been an increasing disconnect between the traditional Fisher-Neyman-Pearson (FNP) math statistics course and the demands for complex analysis in many application areas. The failure of classical maximum likelihood methods to deal effectively with complex models and the success of MCMC-based methods has led to a similar situation: The undergraduate FNP course does not prepare students for these models, and Bayesian MCMC retraining courses are needed to prepare graduates for these applications.

It might be argued that advanced courses training graduates in new areas (as GLMs and GLMMs once were) will always be needed, so this is nothing new. However, the point is that the classical FNP course does not now train students effectively for any subsequent career, except research in extending the FNP paradigm and teaching it at undergraduate and graduate levels.

Progress in closing these divisions, and improving F and H, would be greatly accelerated by a revision of introductory statistics courses for undergraduate math statistics students.

An immediate introduction to real finite populations is needed (small socio-medical populations are interesting to students for this purpose, like the StatLab population of Hodges, Krech, and Crutchfield, 1975), as well as the sampling processes for learning about population quantities.

Starting with Bernoulli models and progressing to categorical variables before continuous ones allows likelihoods (including the sample design contribution) to be developed quickly.

Of course, statistical computing is an essential element, and both Bayes and maximum likelihood (from a log-quadratic likelihood approximation) can be introduced with these simple models.

In dealing with continuous or discrete variables, the Bayesian bootstrap approach—with sampling from the posterior Dirichlet distribution from the multinomial population model—allows a great deal of analysis without specific parametric model assumptions. These can be introduced later through exponential family and other useful models.

Beyond this point, courses will evolve depending on the individuals designing the courses, but the introductory course components above seem to me to be both essential and practical.

Murray Aitkin
Honorary Professorial Fellow
Department of Mathematics and Statistics
University of Melbourne

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