Do you understand what a “95% confidence interval” means?

Friday, May 8th, 2020

Do you understand what a “95% confidence interval” means?, Peter Attia asks:

Distance from earth to nearest star (excluding sun), in light-years
95% confidence interval: [ _________ , _________ ]
GDP of Mongolia, in USD
95% confidence interval: [ _________ , _________ ]
Height of tallest man in recorded history, in inches
95% confidence interval: [ _________ , _________ ]
Depth of deepest part of Pacific Ocean, in meters
95% confidence interval: [ _________ , _________ ]
Average distance from earth to moon, in miles
95% confidence interval: [ _________ , _________ ]
Population of Russia in 2019
95% confidence interval: [ _________ , _________ ]
Maximum number of passengers carried on Emirates A380 aircraft (two-class layout)
95% confidence interval: [ _________ , _________ ]
Number of passengers who died on the Titanic
95% confidence interval: [ _________ , _________ ]
Market capitalization of Apple on the day Steve Jobs died, in USD
95% confidence interval: [ _________ , _________ ]
Fastest lap time in an F1 car around the Monaco circuit, in min:sec
95% confidence interval: [ _________ , _________ ]
Number of regular season goals scored by Wayne Gretzky in his NHL career
95% confidence interval: [ _________ , _________ ]
NASAs budget for the year 2019, in USD
95% confidence interval: [ _________ , _________ ]
Number of Big Macs sold globally in a year (on average) by McDonalds
95% confidence interval: [ _________ , _________ ]
Number of students from China attending U.S. colleges in the 2018-2019 academic year
95% confidence interval: [ _________ , _________ ]
Total number of passengers flying domestically on U.S. airlines in 2019
95% confidence interval: [ _________ , _________ ]
Amount of coal produced by U.S. mines in 2019, in pounds
95% confidence interval: [ _________ , _________ ]
Breeds eligible to compete at the 144th Westminster Kennel Dog Show
95% confidence interval: [ _________ , _________ ]
Number of total worldwide searches processed by Google each day
95% confidence interval: [ _________ , _________ ]
Full weight (including planes, ammunition, people) of a Nimitz-class aircraft carrier, in pounds
95% confidence interval: [ _________ , _________ ]
Number of times that the name “Jesus” appears in the King James bible
95% confidence interval: [ _________ , _________ ]

This is one of the key concepts in How to Measure Anything: Finding the Value of Intangibles in Business, by Douglas W. Hubbard.

Posted in Science | 5 Comments »

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John K. says:

May 8, 2020 at 7:00 pm

Regarding confidence intervals: in reality, the meaning of any confidence interval is undefined for any real-life result whatever. We cannot say whether our particular mean µ falls within the calculated confidence interval at all, let alone whether it falls within it “with 95% confidence.”

The mathematical meaning of the confidence interval is only defined in the case of doing the same experiment an infinite number of times, and then calculating each of those experiment’s confidence intervals. ALL the meaning is contained ONLY in the infinite set. There is NO mathematically-definable meaning even for the ‘infinity-minus-one’ confidence interval.

To repeat: We have no way of knowing whether or not any actual result we obtain falls within the calculated confidence interval. This is in fact admitted in comprehensive textbooks, though the implication is conveniently obfuscated. For example: “Therefore, we cannot say that there is a 95% chance that the parameter µ will fall within a particular 95% CI. However, we can say the following: Over the collection of all 95% confidence intervals that could be constructed from repeated random samples of size n, 95% will contain the parameter µ.” Rosner B. Fundamentals of Biostatistics. Fourth Edition, 1995. p. 162.

Dr. Rosner said it out loud: ALL the meaning in the term “confidence interval” is contained ONLY in the infinite set — and zero in any confidence interval we can actually calculate based on real data.
Bob Sykes says:

May 9, 2020 at 8:13 am

Wm. Briggs has a blog and a book and many refereed papers where he rants on about the stupidity of correlation coefficients, p-values, and confidence limits:

http://wmbriggs.com
Aretae says:

May 9, 2020 at 5:49 pm

I love Doug’s Book. I’ve been a huge fan since around the time we e-met.
Maxico says:

May 10, 2020 at 1:01 am

Sounds like a fallacy. If I’m 100% confident I don’t know the answer, how can I give a 95% estimate? Or the opposite, if I know something with 100% confidence, how can I scale it back to 95%? I got the point, but the video spent most of the time talking about nonsense and a very dumb exercise.
K.D. Kong says:

May 16, 2020 at 2:09 pm

Got 3 right (inside my range), was close on a couple more. Good exercise and very informative on swag’s and modeling.

bob sykes: Calling Mohamed Farrah Aidid’s militia a mob is a bit much, but they were lightly armed and poorly trained. However, they defeated the US/UN mission to Somalia, or at least fought it to a draw. We’re still fighting Aidid’s grandchildren, and we still haven’t won. The war is now in its 4th decade, with no end in sight. Settling aside our Indian Wars (1607 to 1918). Somalia is the longest US war.
McChuck: Anybody who has ever played a wargame can tell you that your defenses can handle a certain amount of opposition, but when enemy numbers, regardless of quality, exceed that number, you get overrun. The mobs in Mogadishu back in 1993 weren’t well organized, weren’t well equipped, weren’t well trained, and weren’t well led. But there sure were a whole lot of them shooting at the Rangers.
Russell: New article about Thorp https://archive.ph/fq5JC
Phileas Frogg: The class divide in the US is as deep and wide as any as has existed in history, but instead of acknowledging the divide, much less trying to bridge it, we have chosen moralization and mutual animosity, which will be the death of us.
Freddo: https://www.zerohedge.co m/geopolitical/us-drones -are-expensive-and-error -prone-so-ukraine-turns- china
Jim: The principle applies whatever the source of the wall-penetrating radio waves in question.
Phileas Frogg: In conjunction with the Rob Henderson excerpt one can safely conclude that neither drug use, nor sexual immorality, can be meaningfully correlated with class. “But poverty causes crime!” Does it?
Bruce: Green energy is a patronage fraud, and Terraform Industries is working with it. But their tech isn’t a fraud.
Handle: What is Henderson taking about? I was under the impression that it was a broadly believed meme and one frequently portrayed in popular entertainment for several generations before Henderson was born that college kids got drunk and enjoyed / experimented with recreational drugs quite a lot. Maybe Rob’s poorer friends couldn’t afford to watch those episodes of South Park or didn’t hear about George W Bush’s “youthful indiscretions”? Man, the left really is...
Bob Sykes: How effing stupid are we supposed to be. The energy input to make the methane will be several times the energy of combustion when the methane is burned. And, of course, all the methane will become exactly the amount of carbon dioxide originally removed from the atmosphere. Net, no carbon dioxide removal. And considering all the carbon produced during the manufacture of the Terraform system and the solar/wind systems, this proposal actually increases atmospheric CO2. And the cost claims are...
Gaikokumaniakku: If it’s “synthetic,” they could just call it “synthetic methane,” right? Calling it “synthetic natural gas” makes my brain hurt because I like to think that natural things are not synthetic. I love methane tech because I was raised on Mad Max: Beyond Thunderdome. Typically I like to see it as a way of dealing with dung from agriculture, but I am a fan of methane tech regardless of how they make it.
Bruce: Very glad to see @TerraformIndies here. This could be really big. For example, why not put a Terrform Indies converter on every nuclear power plant in front of those electric heaters in the cooling towers? Closer to where people need natural gas than oil wells where they just burn the natural gas off because it’s not worth transport costs. And if CO2 is bad, like the climate change people say, it’s great to have a way to turn CO2 to something useful. And worse case, it’s a...
Namur: Well, it’s all about EROI (Energy Returned on Invested). Can this machine produce more energy in the form of natural gas than it consumes in the first place? Also, the energy to build and operate it also counts. Now, let’s say that it works: we are still far away for something like it that works for Diesel, the holy grail of our energy society.
Wawa: Misery causes drug abuse, whether rich or poor. Junkies and drunks are just self medicating in a self destructive way. When thousands of American soldiers, who were hooked on heroin, returned from Vietman the vast majority quickly kicked the habit. With the reason for their misery gone they stopped using. I noticed this first hand, when a buddy moved in with his girlfriend. Before she moved in he was a social drinker, after a few months with her he was an alcoholic. When she moved out he fully...
Bob Sykes: While the focus in Ukraine has been on the land war, and how drones have changed it, navies seem to be especially vulnerable. The Russian navy can’t seem to cope with them. I bet the US Navy will also be unable to cope. At 70 ton, $5M tank is easy prey to a cheap, small drone. US/NATO navies are unable to suppress Houthi drones and open the Red Sea. Are aircraft carriers viable? Some think that they would have been eliminated by the Soviet navy and air force in the 70′s.
Freddo: The armies of Ukraine and Russia are showing what can be done if it needs to be ready tomorrow and everything is expandable. Boeing is showing what happens when the procurement channel is filled with DEI hires.
Jim: Fun! https://www.youtube.com/ watch?v=bIVzK-h6qao
McChuck: Laser designators also use a coded pulse system. That avoids spoofing and also enables multiple projectiles to be inbound to separate targets simultaneously.
Lucklucky: Yes, one aircraft where that is clear is the Tornado. Under its chin it has the Laser Range Finder and Marked Target Seekers (LRMTS), a laser ranging device to help calculate distances, speed, etc. for the ballistic computer and navigation. If it wants to designate targets for laser guided weapons it needs an external pod like TIALD or LITENING put into a pylon.
Isegoria: The Black Cat Squadron Wikipedia entry explains: During the squadron’s 14 years of existence, five U-2s were shot down by PRC air defenses (using S-75 Dvina missiles), with three pilots killed and two captured. Another pilot was killed while performing an operational mission off the Chinese coast, while seven U-2s were lost during training missions, killing six pilots.

Isegoria

Do you understand what a “95% confidence interval” means?

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