First look at the statistical thesaurus

Part of my work at the Institute for the Study of Teaching and Learning in the Disciplines, or ISLTD for short, is to develop a handbook for statistical design and analysis.

The clients of the ISTLD are Simon Fraser University faculty across all disciplines that are looking to incorporate new teaching ideas and methods into their courses. This handbook is intended for faculty and grad student research assistants with little statistical background. As such, the emphasis is on simplicity rather than accuracy.

One wall I've run into in making this document as accessible as possible is terminology. Different fields use different terms for the same statistical ideas and methods. There's also a lot of shorthand that's used, like "correlation" for "Pearson correlation coefficient".

Why is spatial autocorrelation referred to as 'kriging'? Why is spatial covariance described in terms of the 'sill' and the 'nugget'? Because those are the terms that the miners and geologists came up with when they developed it to predict mineral abundance in areas.

Why are explanatory variables still called 'independent variables' in the social sciences even though it causes other mathematical ambiguities? Because they're trying not to imply a causal relationship by using terms like 'explain' and 'response'.

For the sake of general audience readability field specific language will be kept to a minimum, and shortenings will be used whenever a default option is established, as it is with correlation. However, the alternate terms and shortenings will be included and explained in a statistical thesaurus to be included with the handbook.

Here are three pages from the rough draft of that thesaurus. Since such a thesaurus, to my knowledge, has not been published before, I would very much appreciate your input on its readability, or what terms should be included.


https://docs.google.com/document/d/15IWtH9a_bpfhu2cvvtBOCL6FCCaH7zyPwDDsLEXz7d4/edit?usp=sharing

Thanks for reading!
- Jack

Sabremetrics, A.K.A. applied metagaming.

In baseball, sabremetrics started a push for batters to hold off for more and better pitches. By 2011 or 2012, strikeout rates were higher than they were in a century, probably in part of the reduced hitting but also due to pitchers throwing more pitches, knowing they would be swung at less often. How long until batters adapt and capitalize on the higher quality pitches they are receiving to increase hit rates and home runs instead of waiting for many pitches?

This is an example of perfect imbalance, as explained in this video by Extra Credits.  Players of strategic games that involve a lot of pre game decisions often refer to these decisions and the information leading to them as "the meta game". In MOBA games like League of Legends or fighting games like Smash Bros. or Soul Caliber this amounts to selecting one's avatar character and the bonuses they will bring into the start of a match. In collectible and living card games like Magic: The Gathering and Android: Netrunner the meta game is one's deck building process and the popular types of decks among one's opponents.

The pre game decisions, the meta game, in sports include who to hire and how to train. In sports where game-to-game fatigue is a factor, such as hockey with goalies or baseball with pitchers, the meta also involves choosing who will start the game, and how well that matches against the opposing goalie or pitcher.

The general idea of metagaming is to make choices that counter the likely choices of opponents. Against a learning opponent, this requires constant adaptation.

Consider fashion, where to win is to receive  attention, admiration as a consumer and sales as a designer. Fashion is played by wearing/creating an outfit that stands out from that of the existing crowd.

Consider the red queen hypothesis, a biological principle whereby a species succeeds by apadting to its prey predators and competitors. Specifically, the red queen hypothesis is that since all species are doing this, the best a species can hope for is to keep up in evolution, never get ahead.

Sabremetrics got so big as a statistical toolset not simply because it was interesting or novel, but because it was actionable. It provided information that could be converted in decisions, instead of just being elegant or produce a pretty graph.

If hitting in baseball is due for a comeback, might it make sense to load up your farm team with sluggers and curveball pitchers now? Do you reduce your emphasis on stolen bases in anticipation of fewer pitches per at bat?

Would a change from walks and strikeouts to hitting favour franchises that traditionally rely on high scores like Texas, or ones that rely on many small hits like Kansas City?

As always, comments welcome, including those stating I'm wrong about everything.

Teach the Controversy

What if we started including short (500 words, 2 pages double spaced) essay assignments into the stats curriculum?  Students could choose from various controversial topics in stats. They could be referred to a small amount of literature, such as a paper or a couple of book chapters on their chosen issue.

 

Essay questions could include:

- Take a side, or compare Bayesian vs Frequentist methods.

- Take a side, or compare parametric vs non parametric methods.

- ... or simulations vs real data.

- How important is parsimony vs accuracy?

- How valuable is null hypothesis testing, what does it mask?

- Should pvalues be the gold standard?

- How feasible are causality studies?

- Is multiple testing a valid remedy?

- Is imputation a valid remedy?

- Are the flexibility of ultra-complex methods like neural networks worth the fact that they can't be explained or described reasonably?

- Why do we use the mean as the basis for everything instead of the median?

 

In service courses, the essays could be more about social issues that statistics illuminate rather than the methodology itself.

 

- Discuss what multiple regression reveals about the wage gap between sexes. 

- Discuss publication bias and how asymmetric tests like funnel plots can expose it.

- Discuss the pros and cons of bar graphs and pie graphs.

- Consider [attached infographic]. Describe the author is trying to convey. Describe, as best you can from this graphic, what is really going on? How could the graphic more clearly convey this?

 

There are a lot of articles in chance magazine that a social studies ugrad could add their own perspective to while learning to incorporate statistical arguments into their own essays. Math background students benefit from the writing practice and wider perspective, and writing students will have an opportunity to use their strengths in an otherwise intimidating class.

 

The essay prompts above can be answered at multiple levels of depth, allowing them to be slotted into different courses. Finally, this gives the instructor license to remove other written questions from the remaining assignments, which can offset the change in marking load. The necessary material for writing would come at the cost of either some methods or some mathematical depth, but given the challenges in modern statistics, being able to consider questions like those above is worth that cost.