Which statistical topics to teach in European Studies study programme? Next year, I will teach statistics in bachelor study programme European studies (Faculty of Social and Economic Sciences, Comenius University in Bratislava). According to programme description, 

the aim of the study is to acquire knowledge of basic categories and terms of political science, European law and economy related to the processes of European integration. The graduate students are acquainted with fundamental terms and theories exploring political and economic developments in Europe which serve them as a tool for analyses the domestic and foreign policies. The students are prepared to continue with study of the M.A. degree in European studies, International relations or related scientific disciplines. Among the basic student competencies belong the ability to collect and explore theoretical and empirical data in the field of interdisciplinary studies of the processes of European integration; the students are prepared for work in various sectors of public administration and public policy; they are able to use international databases and act in media as analysts.

To my best knowledge, the study program is also close to politology (especially elections and polls), sociology and psychology. However, I graduated in Probability and Mathematical Statistics study programme and I am not sure, whether I should teach these students classical topics from probability and mathematical statistics or something else.
Are there any other topics that should be introduced to this study programme?
 A: The scientific literature in (most areas of) experimental psychology is still choke-full of hypothesis tests with authors and reviewers alike expecting a p-value next to every number and very little interest for/understanding of effect sizes, modeling or anything else.
Consequently, a typical psychology graduate will have heard a lot about ANOVA and often think that statistical analysis is a search for a “significant” result complicated by abstract rules (“Am I allowed to do X?”) and mostly consists in the identification of the “right” test based on the level of measurement (ordinal, interval, etc.) culminating in obtaining a p-value.
I am certainly not advocating this as the right way to teach statistics to anybody but your students will need to be able to understand hypothesis testing and its limitations if they need to read the psychological literature or might go on to do a Ph.D. in psychology. This is in fact quite unfortunate as this material is far from easy to digest, probably not all that useful for many other careers/applications, and would eat up a lot of time that could in principe profitably be devoted to other things.
I don't know as much about political science or quantitative sociology but I would expect more emphasis on modeling, regression, the GLM, etc.
A: Thom Baguley, an outgoing editor of the British Journal of Mathematical and Statistical Psychology, wrote a good and effective book for the upper undergraduate level. It is very modern in many respects, including use of R and discussion of the advanced models such as multilevel stuff.
Another good book is "Mostly Harmless Econometrics" about tweaking linear regression to work well when the data are contaminated with intertwined social effects. It is written without matrix algebra at all, but at a level of methodological rigor that is very appropriate at the doctorate level.
If you can somehow combine the two books together, this would be a fabulous course. With a degree in pure math stat, though, either one will blow you mind with the stuff that you have NEVER seen in your scholastic statistics classes.
