I am helping my boys, currently in high school, understanding statistics, and I am considering beginning with some simple examples without disregarding some glimpses to theory.

My goal would be to give them the most intuitive yet instrumentally constructive approach to learn statistics from scratch, in order to stimulate their interest in further pursuing statistics and quantitative learning.

Before beginning, though, I have a particular question with very general implications:

Should we begin teaching statistics using a Bayesian or frequentist framework?

Researching around I have seen that a common approach is beginning with a brief introduction on frequentist statistics followed by an in depth discussion of Bayesian statistics (e.g. Stangl).

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#### Best Answer

Both Bayesian statistics and frequentist statistics are based on probability theory, but I'd say that the former relies more heavily on the theory from the start. On the other hand, surely the concept of a credible interval is more intuitive than that of a confidence interval, **once** the student has a good understanding of the concept of probability. So, whatever you choose, I advocate first of all strengthening their grasp of probability concepts, with all those examples based on dice, cards, roulette, Monty Hall paradox, etc..

I would choose one approach or the other based on a purely utilitarian approach: are they more likely to study frequentist or Bayesian statistics at school? In my country, they would definitely learn the frequentist framework first (and last: never heard of high school students being taught Bayesian stats, the only chance is either at university or afterwards, by self-study). Maybe in yours it's different. Keep in mind that if they need to deal with NHST (Null Hypothesis Significance Testing), that more naturally arises in the context of frequentist statistics, IMO. Of course you can test hypotheses also in the Bayesian framework, but there are many leading Bayesian statisticians who advocate not using NHST at all, either under the frequentist or the Bayesian framework (for example, Andrew Gelman from Columbia University).

Finally, I don't know about the level of high school students in your country, but in mine it would be really difficult for a student to successfully assimilate (the basics of) probability theory and integral calculus at the same time. So, if you decide to go with Bayesian statistics, I'd really avoid the continuous random variable case, and stick to discrete random variables.

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