Tag: Maths and Intuition

Prenatal Test False Positives: Bayes’ rule is still very, very important

January 14, 2022

Posted here are a NYT Article about genetic testing companies and the value of the results they provide along with an additional explanation of the math behind the issues.

Altogether, there are 415 positive tests: the 15 true positives, and 400 false positives. So if you get a positive test result, the chance that the fetus is actually affected is about 3.6%.

On its face, this sounds like a really good test! It detects 75% of cases, with only a 0.5% false positive rate. That seems like it should be helpful. 

https://emilyoster.substack.com/p/prenatal-test-false-positives

Further discussion from this author about Bayes’ rule

https://emilyoster.substack.com/p/bayes-rule-is-my-faves-rule

Data Analytics and Sports. Game 6 of the 2020 World Series

October 30, 2020
The conflict over the proper role of data analytics has been an ongoing story in modern sports for many years now. The controversy only intensified with the way the final game of the baseball World Series played out. Lots of angry sports talking heads sounded off about how much they hated the decision for the Rays to pull their starting pitcher and hate the role analytics play in sports. Interesting contrast between what the “data says” and what your gut says. 
 
This first link summarizes the situation and the videos at the top of the linked page are a few of the angry talk show hosts sounding off on their anger.
 
World Series 2020: Why the Tampa Bay Rays took Blake Snell out while he was mowing down the Los Angeles Dodgers
 
 
 
 
“Championships are not won by guidebooks”
 
Host Colin Cowherd makes some interesting points here about what he thinks are the appropriate times to approach the sport analytically.
 

 
 
Kevin Cash’s decision to pull Blake Snell, explained: How analytics overruled World Series context clues and cost the Rays
 
The long view of analytics points to reasons why pulling Snell was the right move, but it also ignores the individual context clues that Snell’s Game 6 domination provided.
 
 

Here are a few more resources on the topic. Depending on your students and their interests, 

Sports closer to art than science

CHANGING THE GAME- The Rise of Sports Analytics

Are super-nerds really ruining US sports? | Sport | The Guardian

 

Plane travel only feels like it’s dangerous

June 8, 2020

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Psychologists have long acknowledged that humans tend to “fear the rare”. Some 160,000 Americans die of heart disease each year, but few are paralyzed by the fear of clogged arteries. Instead, statistically unlikely events like earthquakes have an unreasonable grip on our imagination. While plane crash coverage may not give you a new phobia, experts regularly psotulate that extensive news coverage of plane crashes may play with our perception of risk.

https://www.popsci.com/plane-risk-safest-travel/

Here’s another great chart

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Covid-19, the Evil Genius, and How to Think about Societal Risks

March 28, 2020

Interesting article connecting ideas about how we assess risk, the language we use, and how we interpret data depending on how it is presented to us. This connects well to the conflict between emotion and reason in decision making but also our inability to think probabilistically.

If you ask someone if they would be willing to sacrifice 100K people to avoid this intervention, people will be inclined to say no, “I would never put a price tag on human life, much less 100K human lives.” But let’s say you ask the question differently: “Would you be willing to accept a one in three thousand chance of dying this year to avoid this public health intervention?”… Once you ask the question this way then instead of focusing on the raw number of deaths, we can focus on the tradeoffs,

https://reason.com/2020/03/26/covid-19-the-evil-genius-and-how-to-think-about-societal-risks/#comments

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Here are some additional materials related to how we think about numbers and risk, etc. from my Maths page

Here is the article that accompanies the handout above.

Some different questions that get at the same point.

Coronavirus ‘Hits All the Hot Buttons’ for How We Misjudge Risk

March 18, 2020

When you encounter a potential risk, your brain does a quick search for past experiences with it. If it can easily pull up multiple alarming memories, then your brain concludes the danger is high. But it often fails to assess whether those memories are truly representative.

A classic example is airplane crashes.

If two happen in quick succession, flying suddenly feels scarier — even if your conscious mind knows that those crashes are a statistical aberration with little bearing on the safety of your next flight.

Art and reality: How accurately does “Euphoria” portray real teens’ lives? Does it matter?

June 26, 2019

The central point here is that the show Euphoria inaccurately portrays teenagers’ lives which raises the question: Is there a responsibility that comes with creating artwork? Must it be accurate? Who decides?

The claim that the show is inaccurate is backup with statistics raises the question: How can math/statistics help us acquire knowledge? (or understand reality?)

People’s perceptions of teens’ behaviors seems to be generally inaccurate beyond what this show. If presented with this article and appropriate statistics would people change their mind or perceptions of these issues? I’m not sure that it would which leads us to the question: What is the role of intuition in acquiring knowledge? Can mathematical knowledge overcome intuitive beliefs?

This reminded me of an earlier article from the New York Times:

“The Kids Are More Than All Right”

https://well.blogs.nytimes.com/2012/02/02/the-kids-are-more-than-all-right/

The 12 Most Controversial Facts In Mathematics

December 10, 2017

Screen Shot 2017-12-09 at 7.52.49 PM.png“Mathematics has little surprises that are designed to test and push your mental limits The following 12 simple math problems prove outstandingly controversial among students of math, but are nonetheless facts.

“They’re paradoxes and idiosyncrasies of probability. And they’re guaranteed to start an argument or two. If you’re looking for a mathematical way to impress your friends and beguile your enemies, here’s a good place to start.”

https://www.businessinsider.com/the-most-controversial-math-problems-2013-3#-1

Why Do We Count?

March 20, 2017

“Numbers may feel instinctual. They may seem simple and precise. But Everett synthesizes the latest research from archaeology, anthropology, psychology and linguistics to argue that our counting systems are not just vital to human culture but also were invented by that culture. “Numbers are not concepts that come to people naturally and natively,” he writes. “Numbers are a creation of the human mind.””

https://fivethirtyeight.com/features/why-do-we-count/?ex_cid=538twitter

 

Gamblers, Scientists and the Mysterious Hot Hand

October 20, 2015

“The opposite of that is the hot-hand fallacy — the belief that winning streaks, whether in basketball or coin tossing, have a tendency to continue, as if propelled by their own momentum. Both misconceptions are reflections of the brain’s wired-in rejection of the power that randomness holds over our lives. Look deep enough, we instinctively believe, and we may uncover a hidden order.”

Planet Money Podcast: Episode 644: How Much Does This Cow Weigh?

August 9, 2015

An interesting phenomenon that has been proven true many times over but seems so counterintuitive it is hard to believe. When asked to guess the weight of a cow or the number of jelly beans in a jar, often the average of all the guesses is extremely close to the correct answer. Even more accurate than many “experts'” guesses. This is an interesting case in which we can prove something true mathematically but still have a hard time believing. Overall great podcast.

http://www.npr.org/sections/money/2015/08/07/430372183/episode-644-how-much-does-this-cow-weigh