Recommendations for non-technical yet deep articles in statistics The inspiration for this question comes from the late Leo-Breiman's well-known article Statistical Modeling: The Two Cultures (available open access). The author compares what he sees as two disparate approaches to analyzing data, touching upon key ideas in classical statistics and machine learning. However, the article is intelligible to a wide audience--arguably to anyone who works with data, regardless of whether they've pursued statistics at the doctoral level or have only taken an introductory course. Moreover, the article is stimulating. That is, it readily generates discussion (as is evidenced by the series of lively commentaries published in the same issue).
I'm curious to discover more articles with these qualities. That is, articles that:


*

*Touch on fundamental concepts in statistics/data analysis

*Can be understood by a wide audience in terms of variation in research-focus and formal statistical training

*Stimulate discussion, whether through insight or controversy

 A: Ioannidis, John P. A. "Why Most Published Research Findings Are False." PLoS Medicine (2005)
Ioannidis, John P. A. "How to Make More Published Research True." PLoS Medicine (2014)
Must reads for every researcher/statistician/analyst who wants to avoid the dangers of using and interpreting statistics incorrectly in research. The 2005 article has been the most-accessed in the history of Public Library of Science, and it stimulated lots of controversy and discussion. 
A: Tukey, J. W. (1960) Conclusions vs Decisions Technometrics 2(4): 423-433
This paper is based on an after-dinner talk by Tukey and there is a comment that 'considerable discussion ensued' so it matches at least the third of your dot points.
I first read this paper when I was completing a PhD in engineering and appreciated its exploration of the practicalities of data analysis.
A: Efron and Morris, 1977, Stein's Paradox in Statistics.
Efron and Morris wrote a series of technical papers on James-Stein estimator in the 1970s, framing Stein's "paradox" in the Empirical Bayes context. The 1977 paper is a popular one published in Scientific American.
It is a great read.
A: Well, despite the greater interest in Roy Model is among economists (but I may be wrong), its original paper "Some Thoughts on the Distribution of Earnings" from 1951, is a insightful and nontechnical discussion about self selection problem. This paper served as inspiration for the selection models developed by the nobel prize James Heckman. Although old, I think it matches your three bullet points.
A: Although it’s a full-length book and not just an article, Judea Pearl’s The Book of Why admirably meets all three of your criteria.
It addresses a foundational question of statistics—under what conditions can statistical analyses yield causal conclusions—in a way that successfully targets a general audience.  Philosophers, AI researchers, trial lawyers, climate activists, and of course statisticians will all find much of interest in this remarkable, cross-disciplinary book.
Among statisticians with a serious interest in causality, Andrew Gelman’s review is less enthusiastic than most because Gelman finds Pearl’s causal graphs and do-calculus less useful than do most textbooks on causal inference. Gelman likewise takes issue with many of Pearl’s grander generalizations about the history of statistics.  But stirring up controversy and directly influencing the discipline both count as stimulation:
https://statmodeling.stat.columbia.edu/2019/01/08/book-pearl-mackenzie/
A: No Interpretation of Probability (Schwarz, 2018) is a favorite of mine.  It touches on a lot of deep and persisting interpretational issues in statistics, and offers a refreshingly deflationary resolution to many (but not all) of them.
The Reference-Class Problem is Your Problem Too (Hájek, 2007) is a pretty good summary of the fundamental impossibility of assigning statements of probability to uniquely interpretable empirical quantities, much in the vein of the first article.  I think it is a little unduly harsh on frequentism, but not so much that it hurts the article.
Prior Probabilities and Transformation Groups (Jaynes) is a nice overview of how symmetries in our problem-framing can be used to inform our choice of priors.  Jaynes is always a pleasure to read, if a bit dogmatic.
All of these require very little in the way of formal mathematical background, but touch on extremely important concepts that are relevant more or less everywhere in application.
A: Shmueli, Galit. "To explain or to predict?." Statistical science (2010): 289-310.
I believe it matches your three bullet points.
It talks about explanatory versus predictive modelling (the terms should be self-explanatory) and notes that differences between them are often not recognized. 
It raises the point that depending on the goal of modelling (explanatory vs. predictive), different model building strategies could be used and different models may be selected as "the best" model.
It is a rather comprehensive paper and an enjoyable read. A discussion of it is summarized in Rob J. Hyndman's blog post. A related discussion on Cross Validated is in this thread (with lots of upvotes). Another (unanswered) question on the same topic is this.
A: 
Lehmann, Erich L. "The Fisher, Neyman-Pearson theories of testing hypotheses: One theory or two?." Journal of the American Statistical Association 88.424 (1993): 1242-1249.

It is not known to many but when the giants of the profession were still among us, they did not get on well with each other. The debate on the foundations of hypothesis testing specifically, whether it should be inductive or deductive,  saw some pretty serious insults flying around between Fisher on the one hand and Neyman-Pearson on the other. And the issue was never settled during their lifetimes.
Long after they have all passed, Lehmann tries to bridge the gap and in my opinion does a good job as he shows that the approaches are complementary rather than mutually exclusive. This is what students learn nowadays by the way. You need to know a few basic things about hypothesis testing but you can otherwise follow the paper without any problems.
A: Wilk, M.B. and Gnanadesikan, R. 1968. 
Probability plotting methods for the analysis of data. 
Biometrika 55: 1-17. Jstor link if you have access
This paper is, at the time of my writing, almost 50 years old but still feels fresh and innovative. Using a rich variety of interesting and substantial examples, the authors unify and extend a variety of ideas for plotting and comparing distributions using the framework of Q-Q (quantile-quantile) and P-P (probability-probability) plots. Distributions here mean broadly any sets of data or of numbers (residuals, contrasts, etc., etc.)  arising in their analyses. 
Particular versions of these plots go back several decades, most obviously normal probability or normal scores plots. which are in these terms quantile-quantile plots, namely plots of observed quantiles versus expected or theoretical quantiles from a sample of the same size from a normal (Gaussian) distribution. But the authors show, modestly yet confidently, that the same ideas can be extended easily -- and practically with modern computing -- for examining other kinds of quantiles and plotting the results automatically. 
The authors, then both at Bell Telephone Laboratories, enjoyed state-of-the-art computing facilities, and even many universities and research institutions took  a decade or so to catch up. Even now, the ideas in this paper deserve wider application than they get. It's a rare introductory text or course that includes any of these ideas other than the normal Q-Q plot. Histograms and box plots (each often highly useful, but nevertheless each awkward and limited in several ways) continue to be the main staples when plots of distributions are introduced. 
On a personal level, even though the main ideas of this paper have been familiar for most of my career, I enjoy re-reading it every couple of years or so. One good reason is pleasure at the way the authors yield simple but powerful ideas to good effect with serious examples. Another good reason is the way that the paper, which is concisely written, without the slightest trace of bombast, hints at extensions of the main ideas. More than once, I've rediscovered twists on the main ideas covered explicitly in side hints and further comments. 
This isn't just a paper for those especially interested in statistical graphics, although to my mind that should include everyone interested in statistics of any kind. It promotes ways of thinking about distributions that are practically helpful in developing anyone's statistical skills and insights. 
A: A recent surge in Causality and machine learning give rise to Pearl's framework moving into mainstream data science and statistics practice. In this direction, an article from Judea Pearl is a great starting point on the intricacies of Causal Inference in Machine Learning:

The Seven Tools of Causal Inference, with Reflections on Machine Learning .
Judea Pearl.
Communications of the ACM, March 2019, Vol. 62 No. 3, Pages 54-60.

