Skip to main content

Avoiding a Nightmare by Using Math

The answer lies in trigonometry. -Sherlock Holmes

Don't worry if you never learned trigonometry--the answers here lie in arithmetic.

Medical test results often come back positive or negative, as if the result were a certainty. Of course, there is the accuracy, but if the accuracy is 99% or so, what does that really mean? That you should get your affairs in order? Before you call your probate attorney, let's take an example from the book Calculated Risks by Gerd Gigerenzer.

Let's say you're a 40-something year old woman with no symptoms of breast cancer. You have a positive mammogram. What are the odds you have breast cancer?

Using some assumptions about test accuracy and rates of disease based on real data, the odds that you'd have breast cancer are one in eleven according to Gigerenzer. (If you were way off, don't feel bad--most of the physicians Gigerenzer tested were way off, too--and they had the data in front of them. Not that that's comforting in every way.)

A different example: what if you have no risk factors, but have a positive test for HIV? Your odds of actually having HIV are about 50%. But, if the experience of one of Gigerenzer's students who shopped around for good medical advice in Berlin is any indication, you're not likely to hear that from an AIDS counselor. In fact, one counselor--a physician--said, "With certainty, [false positives] do not occur; if there are false results, then only false negatives, occurring when the antibodies have not yet formed." Several of the counselors searched for information on false positives but couldn't find any.

Those with a positive test for a disease have reason to be cautiously optimistic. With a little data and some arithmetic, using a book on probability like Calculated Risks can help you decide how to proceed.

Comments

Popular posts from this blog

What $115 Buys--Junk Food vs. Real Food

A lady recently went off about how little food $115 buys, complaining that the pile of (mostly) junk food she bought wouldn't make a week's worth of lunches and snacks for her children. Sad to say, but this looks like what I see in a lot of grocery carts.  Fat pic.twitter.com/qbM23ydaOq — shellshock (@shellshockkk) March 7, 2025 Coincidentally, I paid almost exactly the same amount today on groceries that would make lots of healthy lunches. It's filling food that won't leave you hungry every few hours for snacks. If we want to make America healthy again, this is the way.  

Celebrities Shilling for Big Soda

There's a push in Washington and ten states to ban soda (and other junk food) from SNAP, a program for low-income people to buy groceries. This seems like a no-brainer: the N in SNAP stands for nutrition, and soda doesn't have nutrients. It's liquid sugar, the last thing we need in a country full of diabetics. People can drink water for virtually nothing and save their SNAP money for actual food. Yet a number of posts from otherwise sensible accounts have opposed this.  Reporter Nick Sorter says that a company called Influenceable has been paying influencers to post these opinions. (Click on the link for the full thread.) 🚨🧵 EXPOSED: “INFLUENCEABLE” — The company cutting Big Checks to “influencers” on behalf of Big Soda Over the past 48 hours, several large supposedly MAGA-aligned “influencers” posted almost identical talking points fed to them, convincing you MAHA was out of line for not… pic.twitter.com/PpPwH9lHGe — Nick Sortor (@nicksortor) March 22, 2025 Sorter adds...

$17/pound chips! Real food is cheaper

 My latest video on YouTube: Real food is generally cheaper than junk food--the pictures prove it. I took these at Kroger and from their website in March 2025. Prices are either straight from the tags or calculated based on product weight.  Music: On We Go (ClipChamp)  First photo by AS Photography: https://www.pexels.com/photo/vegetables-stall-868110/

1972: Carole King, M*A*S*H and...Food for 2014?

I feel well enough to try Atkins induction again. The palpitations are gone, even without taking potassium. My energy level is back to normal--no more trucking on the treadmill early in the morning  to burn off nervous energy or emergency meat, cheese and mineral water stops after yoga. It's back to lounging around to Chopin and Debussy in the morning and stopping at the wine bar for pleasure. I'm using the original Atkins book: Dr. Atkins' Diet Revolution from 1972. While looking in the book for a way to make gelatin (which is allowed on induction, but Jello(TM) and products like it have questionable ingredients), I felt the earth move under my feet : those recipes from 42 years ago look delicious and they're mostly real food. It makes sense, though: the cooks who wrote the recipes probably didn't have had a palette used to low-fat food full of added sugar or a bag of tricks to make low-fat food edible. Anyone who writes a recipe called "Cottage Cheese and...

What Is Atkins, Anyway? A Definition and Pitfalls

Over the years, I've read some strange ideas about what the Atkins diet is: All meat A crash diet Not low-carb, high fat High protein An eating plan where you gorge yourself Wrong on all counts. A friend of mine was curious a few weeks ago about what it really was. I described it to her, and she can't stop raving about it now: Friend: What do you eat? Me: Meat, eggs, cheese, non-starchy vegetables, and fats like olive oil, mayonnaise, lard and butter. Friend: How much do you eat? Me: You eat until you're full. Friend: When do you eat? Me: Whenever you're hungry. You should also take some vitamins. There are more details, of course, but that's it in a nutshell. How does such a simple diet get so convoluted in people's minds? I blame fads in eating and thought. A trend now is to eat vegetables by the pound --no exaggeration. Dr. Atkins' Diet Revolution specifically says not to fill yourself with vegetables--that's a tactic of tradi...