4
$\begingroup$

I am planning to develop a course which I tentatively call as 'Quantitative Reasoning'. The goal of the course is to equip a typical undergraduate student with sound quantitative reasoning skills so that they can critically evaluate statistical and related quantitative claims they may encounter as part of their personal/professional lives.

In contrast to the traditional 'Intro to Statistics' type of courses the focus of this course will not be on derivation of formulas, use of statistical tests etc but on interpretation and understanding of statistical concepts. Towards that end I have developed a rough list of topics that I would like to cover in this course:

  • Logic of hypothesis tests
  • Interpretation of p-values and clarify common misconceptions.
  • Bayesian statistics and its relationship to frequency statistics (at an informal level)
  • Conditions required for causality
  • How to assess/test for causality?
  • Advantages & disadvantages of experiments, surveys etc

In light of the above, I have three questions:

  1. What else should you think I should include/exclude from such a course?

  2. Are there any textbooks that may be useful given the above goal?

  3. Are you aware of any other course that attempts to accomplish the above? Links to syllabus would be very helpful.

If it matters, the target student for the above course is an undergraduate student in the US possibly at the freshman or sophomore level.

$\endgroup$
  • 1
    $\begingroup$ Have them read Innumeracy by J. A. Paulos for "real-life" perspective. Not all of it is directly related to probability and statistics, but a lot of it is. And nearly all of it is good for thinking about critical thinking. $\endgroup$ – cardinal Sep 6 '11 at 16:51
  • 1
    $\begingroup$ Define "typical undergraduate" in more detail, please. $\endgroup$ – StasK Sep 6 '11 at 18:18
  • 1
    $\begingroup$ @Stask I want the course to appeal and be useful to students of all backgrounds. So, in the US context, think of the course as a core course that all freshmen or possibly sophomores need to take irrespective of what they eventually major in. So, all type of students- english, arts, history, social sciences, math, physics, business ... etc. Does that help? $\endgroup$ – Algo Sep 6 '11 at 18:22
  • 1
    $\begingroup$ @Algo: it does clarify the original question, but of course a diverse audience will make it very difficult to find common themes. For one thing, physics and math majors will have a math background very different from an English major; on the other hand, I found natural science and engineering resist the very idea of uncertainty, and have hard time conceptualizing it. You might find something useful at math.smith.edu/natscistats.php and/or causeweb.org. $\endgroup$ – StasK Sep 6 '11 at 18:29
  • 1
    $\begingroup$ Converted to CW because this question is on topic but it has no objectively best answer and effectively asks for a list. $\endgroup$ – whuber Sep 6 '11 at 21:42
4
$\begingroup$

Good for you! There are lots of people working in this area trying to improve on the "traditional" Intro to Statistics course, and there are more and more great resources every year.

The GAISE (Guidelines for Assessment and Instruction in Statistics Education) recommendations are a good place to start, though broad and not perhaps as specific as you'd like.

Project AIMS (Adapting and Implementing Innovative Material in Statistics) and Project CATALST are two recent projects that have developed curriculum for classes like this that you might be able to use. CATALST also has a blog.

One specific course you might look into is Andy Zieffler's ESPY3264 at the University of Minnesota.

$\endgroup$
2
$\begingroup$

Sounds like a great idea. Some other key concepts to consider including are Effect Size, Power, Multiple Comparisons, and The Importance of Graphing Data.

An excellent text relevant to several of your topics would be Michael Oakes' Statistical Inference: A Commentary for the Social and Behavioural Sciences (see my review). I should add that it would require a good deal of commentary and class discussion to be comprehensible to freshmen and sophomores.

$\endgroup$
2
$\begingroup$

This sounds like a great course to have. I'd go for trying to teach it as essentially a literature critique course - students will be reading alot of papers, whether or not they're ever called upon to do statistics themselves, and I think a course like that would be useful.

Other things I would consider including, based on my encounters with "lay-level statistics" in recent days:

  • Power and sample size. It seems many people have this idea that having a small sample size is bad, but have no idea what a small sample is (or indeed that it will change by question). I've seen studies with ~300 some subjects be met with "yeah, but their sample size is small" when they were properly powered.
  • Sampling. A huge amount of bias in otherwise okay looking studies emerges from how you got your study population. Perhaps you could use one of the recent Autism-Vaccine surveys for this. They outright copy a CDC study design (good) and then apply it to a biased population (bad).
  • Visualization, as you mentioned.
  • A brief treatment of logical fallacies. Even if the statistics are perfect, if a paper author "digs too greedily, and to deep" for meaning and a good headline, that's a problem. So not only the statistics and what they mean, but how far you can interpret what you have.

It's more work for you, but I'd go for exemplar papers put into a coursepack or the like. But that's just because I've never run across a book like that which was suitable for your audience.

| cite | improve this answer | |
$\endgroup$
2
$\begingroup$

If you are in need of a text on causality with minimal mathematical assumptions, Angist & Pischke's "Mostly Harmless Econometrics" is a book that presents regression via sums of squares (no matrices thank you), yet talks about very deep concepts in causality, counterfactuals, propensity and such. If your "typical" undergraduate audience is coming from social sciences, that would be good reading for them.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.