Math Says Yes

Facts that sound wrong until you check them. One a day, plus the number missing from the chart everyone is sharing. Free on iPhone and Android

[Math Says Yes @MathSaysYes]

Standard error versus standard deviation, with the chart:
https://t.co/dfKRjtVatE

[Math Says Yes @MathSaysYes]

Tiny error bars do not mean the people measured were alike. Test scores spread 12 points around the mean. Average 16 students and the bar on that mean shrinks to 3 points: 12 divided by the square root of 16. The students still differ by 12. Only the average got steadier.

[Math Says Yes @MathSaysYes]

@BullTheoryio The post itself says Ueda warned inflation could rise above the 2% target, so today it sits under 2%. "Highest in 31 years" at 1.25% means 31 years of rates under 1.25%. Inflation below 2% and a rate of 1.25% is a central bank catching up with prices, not a crisis of them.

[Math Says Yes @MathSaysYes]

@stats_feed Per person means every resident, babies included: 121 liters a year is a 330 ml beer a day. It is beer sold in Czechia divided by people who live there, so a tourist's pint lands in the numerator, never the denominator. The 26% drop is real. What one Czech drinks is not in it.

[Math Says Yes @MathSaysYes]

Why reaching people through friendships finds the popular ones:
https://t.co/Wf80TOvycC

[Math Says Yes @MathSaysYes]

Your friends probably have more friends than you do. Maya has three friends, and each of them has only Maya. Pick one of the four at random and the average friend count is 1.5. Pick a name from their friend lists instead and Maya fills three of the six slots: the average is 2.

[Math Says Yes @MathSaysYes]

@Barchart A record only in dollars that shrink. The EIA's weekly US diesel average peaked at $4.76 in July 2008, which is $7.26 in today's money by the BLS consumer price index. Even June 2022's $5.81 is $6.57 today. $6.50 is a first for the number on the sign, not for what a gallon costs.

[Math Says Yes @MathSaysYes]

What a p-value measures, with the coin example:
https://t.co/cuyAAoqJde

[Math Says Yes @MathSaysYes]

A coin lands heads 60 times in 100 flips, p = 0.03. That is not a 97% chance the coin is unfair. It means a fair coin gives 60 or more heads about 3 times in 100 tries. A p-value says how surprising the result is if nothing is going on, not how likely it is that something is.

[Math Says Yes @MathSaysYes]

Why a small study can miss a real effect:
https://t.co/WysArw4ulT

[Math Says Yes @MathSaysYes]

A study finds "no clear effect". With 20 people per group, a real but modest effect gets detected only about 24% of the time. With 200 per group: about 98%. "No effect found" from a small study usually means it was too small to see the effect, not that nothing is there.

[Math Says Yes @MathSaysYes]

@stats_feed Over 95% lost means a dollar now buys more than 20 times the lira it bought 15 years ago. Percentages flatten this near the end: 90% lost is 10x, 95% is 20x, 99% is 100x. Going from 95% to 99% sounds like four more points, but it leaves a fifth as much value.

[Math Says Yes @MathSaysYes]

Goodhart's law, with the dashboard examples:
https://t.co/Z0XTbZHx8P

[Math Says Yes @MathSaysYes]

Judge a support team by tickets closed and the number climbs: tickets get split into smaller ones, hard bugs get avoided, issues close before the customer is happy. The metric improves while the thing it stood for gets worse. When a number becomes a target, it stops measuring.

[Math Says Yes @MathSaysYes]

Why 10 in 100 feels scarier than 1 in 10:
https://t.co/mStwqmhyI8

[Math Says Yes @MathSaysYes]

"Ten cases" sounds worse than "1 in 10" and can mean the same thing: 10 in 100 is 1 in 10. The count is easy to picture, the total fades. Ten out of how many? A headline count is not a rate until the total shows up, and the same 10% in a million people is a far bigger crowd.

[Math Says Yes @MathSaysYes]

Mean or median, and when each one lies:
https://t.co/97cZzfKj5V

[Math Says Yes @MathSaysYes]

"Average house price" on a street of ten homes: nine sold for 250,000 and one for 2.5 million. The average is 475,000. None of the nine ordinary homes is anywhere near it. The middle sale, the median, is 250,000. A headline average can describe a house nobody bought.

[Math Says Yes @MathSaysYes]

The file drawer, and how to check for it:
https://t.co/cB9lYEeWWr

[Math Says Yes @MathSaysYes]

Ten small studies test the same weak effect. By chance, three look impressive and seven find nothing. The three get published. The seven sit in a drawer. A reader finds three positive papers and no counterweight, so the effect looks stronger and surer than it is.