To be honest, I'm not that concerned with high schoolers needing "a rigorous and thorough statistical education."
I'm more concerned with the populace at-large being able to understand and apply fundamental statistical concepts. For example, another commenter mentioned Bayes Theorem, and how it's a very powerful idea and not that difficult to grok. Related, predictive value positive and negative, and how they are calculated from (but also very different from) sensitivity and specificity, are extremely valuable concepts to understand.
To what you point out, I think the concept of "p-hacking" is super important to understand, but I'd be less concerned about a student needing to hand-calculate the steps to run a t-test (that's what a college-level class is for). That said, I decided to look up T-test on Wikipedia while writing this comment, and I found this interesting tidbit. Great example of the applicability of statistics, and something that I think would peak the interest of many high-schoolers:
> Gosset had been hired owing to Claude Guinness's policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness's industrial processes.[13] Gosset devised the t-test as an economical way to monitor the quality of stout.
I'm more concerned with the populace at-large being able to understand and apply fundamental statistical concepts. For example, another commenter mentioned Bayes Theorem, and how it's a very powerful idea and not that difficult to grok. Related, predictive value positive and negative, and how they are calculated from (but also very different from) sensitivity and specificity, are extremely valuable concepts to understand.
To what you point out, I think the concept of "p-hacking" is super important to understand, but I'd be less concerned about a student needing to hand-calculate the steps to run a t-test (that's what a college-level class is for). That said, I decided to look up T-test on Wikipedia while writing this comment, and I found this interesting tidbit. Great example of the applicability of statistics, and something that I think would peak the interest of many high-schoolers:
> Gosset had been hired owing to Claude Guinness's policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness's industrial processes.[13] Gosset devised the t-test as an economical way to monitor the quality of stout.