Solved – What should be taught first: Probability or Statistics

teaching

I have newly joined as a faculty member in a math dept. of a reputed institution. I will be teaching the course Probability and Statistics at the undergraduate level. The institution already has a syllabus for this course which I am not very much satisfied with. In that syllabus, statistics is covered first, also estimation part is missing. I always thought basics of probability should be taught before teaching statistics. Can someone give some opinion on this? Also a suggestion for the topics that should be covered in such a course is greatly appreciated.

Best Answer

It doesn't seem to be a question of opinion any more: the world appears to have moved well beyond the traditional "teach probability and then teach statistics as an application of it." To get a sense of where the teaching of statistics is going, look at the list of paper titles in last year's special edition of The American Statistician (reproduced below): not a single one of them refers to probability.

They do discuss the teaching of probability and its role in the curriculum. A good example is George Cobb's paper and its responses. Here are some relevant quotations:

Modern statistical practice is much broader than is recognized by our traditional curricular emphasis on probability-­based inference.

What we teach lags decades behind what we practice. Our curricular paradigm emphasizes formal inference from a frequentist orientation, based either on the central limit theorem at the entry level or, in the course for mathematics majors, on a small set of parametric probability models that lend themselves to closed-­form solutions derived using calculus. The gap between our half-­century‐old curriculum and our contemporary statistical practice continues to widen.

My thesis ... is that as a profession we have only begun to explore the possibilities. The history of our subject also supports this thesis: Unlike probability, a scion of mathematics, statistics sprouted de novo from the soil of science.

Probability is a notoriously slippery concept. The gap between intuition and formal treatment may be wider than in any other branch of applied mathematics. If we insist that statistical thinking must necessarily be based on a probability model, how do we reconcile that requirement with goals of making central ideas “simple and approachable” and minimizing “prerequisites to research”?

As a thought experiment, run through the basic concepts and theory of estimation. Note how almost all of them can be explained and illustrated using only first-­semester calculus, with probability introduced along the way.

Of course we want students to learn calculus and probability, but it would be nice if we could join all the other sciences in teaching the fundamental concepts of our subject to first year students.

There's far more like this. You can read it yourself; the material is freely available.

References

The special issue of the American Statistician on "Statistics and the Undergraduate Curriculum" (November, 2015) is available at http://amstat.tandfonline.com/toc/utas20/69/4.

Teaching the Next Generation of Statistics Students to “Think With Data”: Special Issue on Statistics and the Undergraduate Curriculum Nicholas J. Horton & Johanna S. Hardin DOI:10.1080/00031305.2015.1094283

Mere Renovation is Too Little Too Late: We Need to Rethink our Undergraduate Curriculum from the Ground Up George Cobb DOI:10.1080/00031305.2015.1093029

Teaching Statistics at Google-Scale Nicholas Chamandy, Omkar Muralidharan & Stefan Wager pages 283-291 DOI:10.1080/00031305.2015.1089790

Explorations in Statistics Research: An Approach to Expose Undergraduates to Authentic Data Analysis Deborah Nolan & Duncan Temple Lang DOI:10.1080/00031305.2015.1073624

Beyond Normal: Preparing Undergraduates for the Work Force in a Statistical Consulting Capstone Byran J. Smucker & A. John Bailer DOI:10.1080/00031305.2015.1077731

A Framework for Infusing Authentic Data Experiences Within Statistics Courses Scott D. Grimshaw DOI:10.1080/00031305.2015.1081106

Fostering Conceptual Understanding in Mathematical Statistics Jennifer L. Green & Erin E. Blankenship DOI:10.1080/00031305.2015.1069759

The Second Course in Statistics: Design and Analysis of Experiments? Natalie J. Blades, G. Bruce Schaalje & William F. Christensen DOI:10.1080/00031305.2015.1086437

A Data Science Course for Undergraduates: Thinking With Data Ben Baumer DOI:10.1080/00031305.2015.1081105

Data Science in Statistics Curricula: Preparing Students to “Think with Data” J. Hardin, R. Hoerl, Nicholas J. Horton, D. Nolan, B. Baumer, O. Hall-Holt, P. Murrell, R. Peng, P. Roback, D. Temple Lang & M. D. Ward DOI:10.1080/00031305.2015.1077729

Using Online Game-Based Simulations to Strengthen Students’ Understanding of Practical Statistical Issues in Real-World Data Analysis Shonda Kuiper & Rodney X. Sturdivant DOI:10.1080/00031305.2015.1075421

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout the Undergraduate Curriculum Nathan Tintle, Beth Chance, George Cobb, Soma Roy, Todd Swanson & Jill VanderStoep DOI:10.1080/00031305.2015.1081619

What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum Tim C. Hesterberg DOI:10.1080/00031305.2015.1089789

Incorporating Statistical Consulting Case Studies in Introductory Time Series Courses Davit Khachatryan DOI:10.1080/00031305.2015.1026611

Developing a New Interdisciplinary Computational Analytics Undergraduate Program: A Qualitative-Quantitative-Qualitative Approach Scotland Leman, Leanna House & Andrew Hoegh DOI:10.1080/00031305.2015.1090337

From Curriculum Guidelines to Learning Outcomes: Assessment at the Program Level Beth Chance & Roxy Peck DOI:10.1080/00031305.2015.1077730

Program Assessment for an Undergraduate Statistics Major Allison Amanda Moore & Jennifer J. Kaplan DOI:10.1080/00031305.2015.1087331

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