Statistician Answers Stats Questions From Twitter - Tech Support
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Date: 2022-07-07
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Comments and reviews: 10
Isaac
Statistics are a measure of your best knowledge about reality. Every potential event, if you have no knowledge of it or premises necessary and sufficient for it, has either a 100% occurrence or a 0% occurrence, split as 50-50. However, we typically know -some- things about events in question, and the more true information we know, the more confident we can be that our statistical split is accurate.
If I correctly see the Ace of Space placed on top of a deck of cards, I can be 100% confident that the Ace of Spades will be first drawn; I am correct and the result obtains. If I believe that I see the Ace of Spades placed on top of a deck of cards, when it was in fact the Ace of Clubs, I can still be 100% confident that the Ace of Spade will be first drawn; while I am correct in expressing the probability as 100%, the result -does not- obtain. In both cases, drawing the Spade first is the correct prediction, but predictions by nature almost always have unaccounted for information. Known unknowns and unknown unknowns; whereas perfect knowledge would give us perfect predictions, which we would arguably just call observations.
It can be argued that 100% then is a superfluous probability; but perhaps it's better to say that 100% is best understood as approaching 100%, since we don't know how many unknowns there are in practical situations.
That said, we can arguably posit a model observer (a stand-in for ourselves) who has some good information but not perfect knowledge. A model observer might know that a fair deck shuffled well has a 1/52 chance of drawing the Ace of Spades first, and we typically just take that position, calling it -the- probability of an event's occurrence given the information. This seems to be the most useful way (as well as the first two examples) to use statistics to measure our confidence in areas of prediction.
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Statistics are a measure of your best knowledge about reality. Every potential event, if you have no knowledge of it or premises necessary and sufficient for it, has either a 100% occurrence or a 0% occurrence, split as 50-50. However, we typically know -some- things about events in question, and the more true information we know, the more confident we can be that our statistical split is accurate.
If I correctly see the Ace of Space placed on top of a deck of cards, I can be 100% confident that the Ace of Spades will be first drawn; I am correct and the result obtains. If I believe that I see the Ace of Spades placed on top of a deck of cards, when it was in fact the Ace of Clubs, I can still be 100% confident that the Ace of Spade will be first drawn; while I am correct in expressing the probability as 100%, the result -does not- obtain. In both cases, drawing the Spade first is the correct prediction, but predictions by nature almost always have unaccounted for information. Known unknowns and unknown unknowns; whereas perfect knowledge would give us perfect predictions, which we would arguably just call observations.
It can be argued that 100% then is a superfluous probability; but perhaps it's better to say that 100% is best understood as approaching 100%, since we don't know how many unknowns there are in practical situations.
That said, we can arguably posit a model observer (a stand-in for ourselves) who has some good information but not perfect knowledge. A model observer might know that a fair deck shuffled well has a 1/52 chance of drawing the Ace of Spades first, and we typically just take that position, calling it -the- probability of an event's occurrence given the information. This seems to be the most useful way (as well as the first two examples) to use statistics to measure our confidence in areas of prediction.
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PoMo
nice. I'd gone even further and gave examples of some of these numbers in relation to populations, e. g. population of the U. S.
Example a 1 in 100000 number of 3 generations being born on the same date: there's about 3000 people currently living in the U. S. that this happened to.
(warning: my number may be wrong by a factor of 3 or more, depends on if you count all 3 involved as one or as three, if they all must still be alive, etc.
or a nice IT example: -service uptime of 99. 995%-. well that means that on average that service is down 26 minutes per year.
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nice. I'd gone even further and gave examples of some of these numbers in relation to populations, e. g. population of the U. S.
Example a 1 in 100000 number of 3 generations being born on the same date: there's about 3000 people currently living in the U. S. that this happened to.
(warning: my number may be wrong by a factor of 3 or more, depends on if you count all 3 involved as one or as three, if they all must still be alive, etc.
or a nice IT example: -service uptime of 99. 995%-. well that means that on average that service is down 26 minutes per year.
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Caspar
Statistics are really just history, or projected history. It's very simple and the strongest tool of reason we people have come up with. A related concept to be aware of is extrapolation. This has to do with reading the history in such a way that you continue the trend given by past events out in the future. Very simple, very effective. The internet has trapped most people in the moment and we have become very vulnerable to distortions of proportions because everything is without context, without history.
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Statistics are really just history, or projected history. It's very simple and the strongest tool of reason we people have come up with. A related concept to be aware of is extrapolation. This has to do with reading the history in such a way that you continue the trend given by past events out in the future. Very simple, very effective. The internet has trapped most people in the moment and we have become very vulnerable to distortions of proportions because everything is without context, without history.
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Nugboy
Horse racing odds used to always intrigue me as a kid my family used to always go and since they would only let us bring 20 bucks for 9 or 10 races, and they would let me and my sister place one 2 dollar bet per race. I always just picked the long shots and hoped. Rarely worked for me but won like 50 bucks one time. Gone a bunch of times to Saratoga cuz I live pretty much there. My wife hates feeling like the horses get -abused- so I have only gone like 2x since legally allowed to gamble
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Horse racing odds used to always intrigue me as a kid my family used to always go and since they would only let us bring 20 bucks for 9 or 10 races, and they would let me and my sister place one 2 dollar bet per race. I always just picked the long shots and hoped. Rarely worked for me but won like 50 bucks one time. Gone a bunch of times to Saratoga cuz I live pretty much there. My wife hates feeling like the horses get -abused- so I have only gone like 2x since legally allowed to gamble
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zero
Thanks, just about to do 1st yr stats course this trimester, was good to check and reinforce my own knowledge.
The basis for much of this is to assume the event is random, but also often the result(/s) fall within a normal bell curve.
I normally use red black in roulette to demonstrate independent events and some common fallacies. For example many will bet red if black has come up a lot, the chance of red/black is equal and for the next spin is always equal.
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Thanks, just about to do 1st yr stats course this trimester, was good to check and reinforce my own knowledge.
The basis for much of this is to assume the event is random, but also often the result(/s) fall within a normal bell curve.
I normally use red black in roulette to demonstrate independent events and some common fallacies. For example many will bet red if black has come up a lot, the chance of red/black is equal and for the next spin is always equal.
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Joel
When i was about 5 years old I flipped a 50c Australian coin (a very large dodecagonal coin) for a heads or tails to solve a disagreement. It landed on its edge. This was all the more amazing that such a coin can not roll, It has to actually land perfectly on that edge with almost no sideways force, otherwise it will fall.
That has always stuck with me since as evidence that anything is statistically possible. nothing is impossible.
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When i was about 5 years old I flipped a 50c Australian coin (a very large dodecagonal coin) for a heads or tails to solve a disagreement. It landed on its edge. This was all the more amazing that such a coin can not roll, It has to actually land perfectly on that edge with almost no sideways force, otherwise it will fall.
That has always stuck with me since as evidence that anything is statistically possible. nothing is impossible.
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Marcelo
I like the plane crash example and I think it relates to cassino and roulettes. A lot of people think that because the ball hit let-s say red 10 times in a row, the probability of it being on red again is extremely small and well, it isn-t. It-s true that the probability of hitting red 11 times in a row is really small. But as soon as it has already happened 10 times, the probability of the next one being red is roughly 50%.
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I like the plane crash example and I think it relates to cassino and roulettes. A lot of people think that because the ball hit let-s say red 10 times in a row, the probability of it being on red again is extremely small and well, it isn-t. It-s true that the probability of hitting red 11 times in a row is really small. But as soon as it has already happened 10 times, the probability of the next one being red is roughly 50%.
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Manjushri
We also measure crime rates or at least report them in weird ways, like nationally. IDC what happens nationally, at least in terms of my own daily life. What happens in my city or neighborhood, statistically or otherwise is far more important. Depending if you live in South Side Chicago or Topeka, Kansas or Nowhereville, Wyoming, those statistics will look much different locally.
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We also measure crime rates or at least report them in weird ways, like nationally. IDC what happens nationally, at least in terms of my own daily life. What happens in my city or neighborhood, statistically or otherwise is far more important. Depending if you live in South Side Chicago or Topeka, Kansas or Nowhereville, Wyoming, those statistics will look much different locally.
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Lovuschka
-No offense, but the answer to the three familiy members question is oversimplified. You will also have to take into account at which times people are more likely to mate statistically. Not on the chessboard, but in the sense of making children. So the chances of three family members being born on January 20 are not the same as three family members being born on July 4.
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-No offense, but the answer to the three familiy members question is oversimplified. You will also have to take into account at which times people are more likely to mate statistically. Not on the chessboard, but in the sense of making children. So the chances of three family members being born on January 20 are not the same as three family members being born on July 4.
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Scott
I disagree with the probability calculations for the family birthday. 1/365 - 1/365 assumes an even distribution of births across day of year (DOY, which we know isn't quite the case. We would expect the probability to change subtly by date. We could use birth record stats estimate the probabilities by DOY.
Good job on the video, by the way!
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I disagree with the probability calculations for the family birthday. 1/365 - 1/365 assumes an even distribution of births across day of year (DOY, which we know isn't quite the case. We would expect the probability to change subtly by date. We could use birth record stats estimate the probabilities by DOY.
Good job on the video, by the way!
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