I would like to know what topics are considered 'core knowledge' for a statistician. Please keep in mind I know very little about statistics.

At my university, I hear statistics students discuss topics such as: Time series analysis, Descriptive statistics, Non-parametric statistics, ANOVA, Regression Analysis, Statistical learning, etc. Assuming these are distinct courses, I am curious what topics like these are considered 'core' for a general statistician?

Before anyone marks this as a duplicate, I have read through a good few similar threads. For instance:

If there was a certification exam for statisticians, what would be the syllabus?

Mathematician wants the equivalent knowledge to a quality stats degree

However I find none of these really answer my question specifically. I don't want references. I'm interested in a specific list of topics (if one exists) that every statistician would be expected to know, with a brief description of what that topic actually is.

Perhaps to give an example: I am a maths and theoretical physics student. It seems to me that, no matter what field of expertise a maths/physics student may eventually choose, there are a number of central topics they would be expected to know. For instance, one can list the following topics that are standard for most maths degrees:

  1. Set Theory
  2. Category Theory
  3. Point Set Topology
  4. Real analysis (Calculus, Measure Theory, Functional Analysis)
  5. Complex Analysis
  6. Abstract Algebra (Group, Ring and Field Theory)
  7. Number Theory
  8. Differential Geometry
  9. PDEs
  10. Algebraic Topology
  11. Algebraic Geometry
  12. etc

Whether a student has taken a full course in this area or not, most maths students would be expected to know at least the basics in these 'core' areas. For physics, one can come up with a similar list.

My question is:

Can one come up with a similar list summarising the basic topics a statistician should know? If so, please give a basic description of each topic in the list (even just one or two sentences).

I understand such lists are never a perfect (or even good) way of summing up the core knowledge for a field. Nevertheless, I am interested in getting a rough idea of what topics a statistician has studied.


Statisticians are an extremely diverse set of professionals/researchers, so the set of core topics that all of them should know is actually quite small. If you visit websites of statistics graduate programs in the US, you'll see that the common core topics are as follows: probability theory; theory of statistical inference; theory of (generalized) linear models; and basic computer programming skills.

  • $\begingroup$ So are you saying it is unlike maths, physics and other subjects, where there is a roughly agreed upon set of core topics? It is really just a case of knowing basic programming, probability and a few statistical concepts and then they starting to 'specialise' from there? $\endgroup$ – leob May 29 '20 at 14:13
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    $\begingroup$ @leob: I would say that what you said above is almost correct but replace "a few statistical concepts" with solid knowledge of math-stat and regression concepts. $\endgroup$ – mlofton Jun 2 '20 at 14:09
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    $\begingroup$ you also need linear algebra at least, if not some calculus (calculus, you may actually not use and eventually forget, you do use linear algebra a lot though) $\endgroup$ – carlo Jun 2 '20 at 14:22

I agree with @Bayequentist but would go further.

"Statistician" is a broader term than just people with a PhD in statistics. My PhD is in psychometrics, but I've worked as a statistician for more than 20 years. (When talking to statisticians, I call myself a data analyst).

I know less theory than a lot of people (probably less than almost all the regular answerers on this site) but I've got a lot of practical experience with data.

So, e.g. I'd expect anyone called a statistician to know something about various kinds of regression. But what about them? Need we all be able to prove various theorems? I don't think so. Need we all be able to take a messy data set and figure out how to model it (and know how to interact with the substance-matter expert)? I don't think so.

(I can do the second, but not the first).


Applied statisticians should know

  • conditional probability inside and out; this is the source of a great deal of misunderstandings about p-values and type I assertion probability $\alpha$ as well as holding back more usage of the Bayesian paradigm
  • experimental design, sources of bias and variability
  • measurement properties and how to optimize them
  • how to translate subject matter knowledge into model specification
  • which modeling assumptions matter the most, and which type of model flexibility should be prioritized (e.g., in many situations nonlinearity is more damaging than non-additivity)
  • how to specify and interpret details of regression models (at least up to specification of nonlinear interaction terms)
  • model uncertainty and how it damages inference, and understanding that trying multiple models can destroy inference
  • understand that getting a Bayesian posterior probability of normality is better than trying to use the data to decide whether to assume normality or not
  • how to specify flexible models so that you don't need to worry so much about model uncertainty
  • instead of learning all the standard statistical tests and ANOVA, learn how to accomplish them through modeling (this includes standard nonparametric tests such as Wilcoxon and Kruskal-Wallis)
  • $\begingroup$ Can you provide a citation or any info on the “ Bayesian posterior probability of normality ” bit? This sounds like Bayesian goodness of fit testing, which seems... weird. $\endgroup$ – JTH Jan 19 at 14:28
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    $\begingroup$ Watch out for the frequentist model uncertainty all-or-nothing GOF trap. Don't think of goodness of fit testing (which in effect assumes a power of 1.0 for testing GOF). Think of model specification, with relaxed assumptions. A prior for degree of non-normality favors normality but allows data to override this assumption smoothly while providing exact inference all along the way. Details at hbiostat.org/doc/bbr.pdf p. 5-29 (physical page 116) and later. $\endgroup$ – Frank Harrell Jan 19 at 14:40
  • $\begingroup$ On the topic of flexible modeling, are you referring to GAMs, decision trees, and other semi-parametric ideas? $\endgroup$ – Guilherme Marthe Jan 19 at 15:11
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    $\begingroup$ Primarily to semiparametric models (left hand side of model) and flexible spline functions on the right hand side, plus penalization if needed. $\endgroup$ – Frank Harrell Jan 19 at 17:41

A statistician, as in a Mathematical that is specialized in Statistics, as in my experience, has a basic set of theorical knowledge in:

  1. Probability Theory (most importat one)
  2. Mathematical Inference
  3. Mathematical optimization
  4. Regression
  5. Basic Programming
  6. Exploratory Data Research
  7. Stochastic methods

Keep in mind that, even if it's not as complex as other fields of the Mathematics at face value, it's deeply rooted in Mesure theory, so it's still a specialization of an already specialized cience that it's the mathematics. Now, recently, due to the technological advancement, computer knowledge has become a very sought after skill in the field, so knowledge in Big Data and basic Data Science it's becoming the 8th item in the list above.

Every statistics degree with a rigorous basis of theorical knowledge would contain every element in the list above.


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