Back in the 70's I used to walk 20 miles as a child, and then go for farm work. As a mining engineer, I used to walk up 1.5 miles along a 1:3 incline (tunnel) everyday, sometimes during midnight, working 6-day week. Worked in dirtiest, noisy coal mines, near blast sites, soaked in black dust, with no place to sit during the shift. But never felt that it's something hard or bad, until some college kids, for who I was a tour guide, told me in horror that they wouldn't ever venture working in such place.
My boss laughs at that. He receives anonymous red-letter notes from the local extremist organization threatening him. He keeps a pile of those notes on a spike.
Nope. It's a true story. And how it relates to thread is given below in another of my comments. "Things change with time" should have given you some relation. Statistics is seen by the current generation as hard work, rightly so, due to availability of easier ways of dealing with it.
>> found that 62% of respondents reported no or limited statistical knowledge
The other 38% didn't understand the question...(my extrapolation)
I did a couple semesters of statistics at uni. And I can confidently say that the number of people who can answer 3 simple questions on statistics (like say mean versus medians, confidence levels or margins of error) is, well, a rounding error from 0.
Indeed, statistically, no-one has a clue how statistics work.
I did however learn enough to know that statistics can tell you absolutely anything you want them to say. Assuming you don't just make them up, they're trivial to manipulate to generate the headline you want.
When used to evaluate risk, the comprehension goes down further (a fact willfully exploited my any decent marketing.)
One of my favourite jokes: 93 % of statistics are made up on the spot, and 61 % of people believe them.
Bonus points for changing the figures every time you retell the joke.
I’d recommend reading “How to make the world count” instead of a work of a morally bankrupt guy who used the very same tricks he criticized to discredit the cancer studies of tobacco usage.
> the quote popularized by Mark Twain "Lies, damned lies, and statistics"
I’m increasingly convinced this is a thought-terminating cliche. Understanding the difference between a median, mean and mode is fundamentally empowering. Enough people, however, will stop themselves from trying to understand that by quoting such a joke.
Exactly 38% is way too high. Are we sure about that? Statistics is not some required learning in school. Even those who learned (me for example) cannot confidently claim what it actually means. I would say most of the people don't have a clue what statistics mean
Here in Norway, statistics has been introduced in 9th and 10th grade (15 and 16 year olds). Here[1] is what a 9th grader is supposed to know at the end of the school year. Some key points translated to English:
- Interpret and critically evaluate statistical representations from the media and the local community.
- Calculate measures of central tendency and measures of dispersion in custom and real datasets, and use the results to describe the data.
- Calculate and evaluate probability in statistics and games.
This came after my time, and our PIRSA score aren't the best so perhaps practice is lacking.
We are just as bad or worse with charts. I don’t know whether finding Tufte when I was still relatively young saved or harmed my sanity. Maybe both. Everyone’s charts are awful, including at least half of mine, and I was trying to be objective. Many people are just trying to prove a theory they had before the chart was made.
I started thinking about this percentage on decision makers around the world and got a chuckle.
I've been trying to talk about the median vs. mean with a bunch of politicians on themes around the zillionaires, wealth or consumption and for most parts they're clueless. Or the ones with degrees still go with the normal (mean that skews the normal) as they're afraid.
I just happened to get a copy of naked statistics yesterday, as I feel the human traits of poor comprehension of probabilities can be enhanced to at least some extent. And my degree from the social side didn't include statistics.
If there are better entry-level books on the matter I'm happy to take some recommendations.
> And my degree from the social side didn't include statistics.
In the university I went to, Department of Statistics used to be part of the Faculty of Social Sciences. It was impossible to graduate from social sciences without taking a few classes of statistics. Then in some reorganization, Department of Statistics merged with Department of Mathematics. Except that old-school statisticians didn't want to move to the Faculty of Science, and they somehow managed to keep their offices in the Faculty of Social Sciences.
Related, this result on statistics comprehension is another stepping stone on my path away from believing in technocracy - a journey I’ve been on for the past 10 years and have felt more passionately about over the past 2 years.
I was recently convinced by a rather compelling argument that technocracy (rule by the technically capable) often falls to a local minima where the people in power find the first scrap of evidence that supports their preconceived agenda. Wildly racist? Natural selection “proves” that all of your decisions are “technically” justified.
But more directly to your point about being effective communicators of statistics, I’ve found that it’s difficult to help someone form their own conclusion from statistical results. Most people want the conclusion fed to them, with the statistics supplied as evidence. It’s up to us (proper statisticians) to act ethically: provide analyses in good faith and challenge the poorly conceived analyses of amateurs and statisticians acting in bad faith.
When I have seen instances of this, it's usually because there is another variable. Example from wikipedia:
>A common example of Simpson's paradox involves the batting averages of players in professional baseball. It is possible for one player to have a higher batting average than another player each year for a number of years, but to have a lower batting average across all of those years. This phenomenon can occur when there are large differences in the number of at bats between the years.
The per-year values aren't weighted in the combined total average.
i mean, the headline statistic can be misleading, but you gotta dig in and wrestle with the details. just like anything, we cannot boil down complex things to single numbers and expect any sort of meaningful signal. we gotta roll up our sleeves, look at definitions, think about what our actual questions are, how we might answer those questions through measurements and observations, and what the confounders are. i think a common issue folks have with stats is that they expect a tidy answer, and it just doesn't do that: it's more of a way to prove the world...the results still need some interpretation.
> mean versus medians, confidence levels or margins of error
It's basic when you are attending an undergraduate course but most people can understand mean (as a dictionary might generically define it) and have a general feeling for margin of error (again, not in the mathematical way.)
Statistics has been the most difficult course in my CS course. For some reason when I start counting events to get a probability I find several perfectly plausible ways to count them, get five different probabilities and none of them is the correct answer.
And about being "trivial to manipulate [numbers] to generate the headline you want" a politician once told me that you can show the same numbers in any way you want, as in to demonstrate a thesis or its opposite.
In college, studying mathematics, probability was the course in did best in. The funny part is that I have a form of ilnumeria. Effectively I can’t count. As a result I have no desire to try to actually count things, and the easiest way for me to cope is by understanding the theory behind counting.
With large sets or sequences of numbers approaching almost infinity, counting as a method of determining how large things are ... doesn't work well as you found out. To determine if ginormous set A is larger than ginormous set B, you have to do things like matching-pairing. For every element in set A, pair it with an element of set B; if you exhaust all of the elements in B but still have elements in A... then set A is larger than set B.
To formulate the probability of B happening, for example, you have to make an educated guess. Create a functional equation that map A (all possibilities) to B (desired possibility). Then you make a ratio-fraction with the equation in the numerator and set A in the denominator. Using Algebra, try to eliminate references to A in both the numerator and denominator to give you an educated guess of what the probability is.
It seems like you are mostly talking about cardinality, or proofs of problems pertaining to them, and the person you are responding to is saying they struggle with combinatorics
I wish people had an intuitive understanding of probabilities. It seems the average person can only think in terms of "basically never happens", "fifty fifty" and "sure thing".
A probability that isn't computed (or reasonably computable) is just a personal feeling. Your 40% or 70% aren't probabilities if you didn't compute the probability of at least the key events involved to arrive at the number. People say a number as their confidence to meet the deadline on a scale from 0-100.
I'm not saying they're useless, they're an educated guess, a valuable means of communicating an expert opinion. It can be replaced with "I have high confidence of success".
The assessment is subjective, includes personal beliefs, assumptions, etc. not just measurable objective points. The measurement uncertainty at every step and the confidence interval are disappointing despite people using percentages, suggesting confidence to the percent. A scale from 1 to 5 is just as accurate.
2 people looking at the same situation could have very different degrees of belief, which is why 2 engineers could give very different estimates. But if I say I believe the likelihood of something is 73.8% I might be more credible to the listener. Looks like I calculated, not like the guy who said "3 out of 5 we get it done".
I'm not very familiar with how they work. Don't prediction markets give the individual gambler a boolean choice and this results in a picture of the split over the population? There's no granular option for the individual to bet 40% vs. 60% for something happening, the vote with 100% confidence that Spain wins the World Cup, they don't give 85% chance of winning.
The way to express a 85% confidence is to size your investment accordingly. For example, if the market is at 75%, then you buy yes-shares until the price is at 85%. If the market is at 90%, then buy no-shares instead until the price is down to 85%.
One of the first managers I had who studied management theory commented once that if estimates were accurate, we’d get them done earlier than expected as often as we got them done later than expected, which is not true and thus we are doing something wrong.
They do have an intuitive understanding! You just outlined it, and it works well enough for most things. Statistics is generally very useful, but for individuals it's not really important or useful to understand, because the data is rarely ever clear or trustworthy enough to use for making decisions about specific situations.
Probabilities might be more intuitive, statistics are intuitive only for the most straight forward topics. That's why it's so easy to present entirely correct but very misleading statistics.
And how people don’t get how probabilities work when run over repeated instances. Like it is only 0,1% risk that X happens everytime Y is done which sounds low but then it turns out Y is done Z number of times per day…
The word “most” is a mess. Strictly speaking the person with “the most” has the plurality, not even half. “Most people” can mean more than half, but is often used to mean or imply anything from a supermajority to “almost everyone”.
It would be interesting to probe the political orientation of the people who understand and those who don’t and see if there is some correlation there.
Rhetoric is persuasion under the presupposition that what you are trying to persuade someone of is true. Sophistry is indifferent to the truth and is merely concerned with results. Rhetoric respects the humanity of the interlocutor. Sophistry seeks to exploit him.
I would guess that 99% of Americans have a lower than average understanding of stats. Maybe you meant to use the median instead of the average? (Not every distribution is Normal)
the title, in respect to the content, is super lame "more than half"... dude what is "more" and how much more, and are we talking the upper bound or lower bound of the "more". perhaps we can conclude, the author demonstrates perfectly the principle that he tries to convene... few people are ready to work with statistics.
Statistics might be the most eye opening course I took in university. Like, I don't think I understood the concept of distribution before it and regarded an average of measurements as one measurement. I had a very strange concept of averages.
A side note - I blame that on our education. In my anecdotal n=1 case, the statistics were never taught in school (and I was in math class all the way and the school was higher tier locally, a "lyceum"). And in the local Polytechnic the only course which taught the subject was a Probability Theory and Math Statistics. It was one of those "intimidating" courses on my faculty, the ones which older students scare freshmen with. And it was indeed as crazy as they said, I remember nothing from it outside of the sheer horror of rote remembering hundreds of pages of, well, something. I scrapped by with a lowest passing mark and promptly cleared my brain cache of that.
Nowadays I often stumble upon this or that statistical topic, watch an educational video, read a wiki explanation and it makes sense. Plus I've picked up unstructured and chaotically a lot of terms just by reading IT articles and forums.
tl;dr - my point is, our education is severely lacking a simple, short and concise statistics course on ELI5 level, for middle schoolers. And it is a huge gap in skills people actually do need in common life, outside of STEM. And the skills I'm talking about aren't even hard, a core set of basic concepts, without any math, can likely fit in a tiny brochure written in simple literary English with a few illustrations. Or a set of YT videos along the same lines.
> The survey showed that 62% of U.S. adults self-report having little to no idea what statistics or statistical concepts like p-values are, but 90% of them would base decisions on reported statistics at least sometimes if they understood them better.
You're kidding, right? 38% self-report more than that? If their self-report were accurate it would imply an education system that has truly excelled.
Yeah I figure I'm "well educated" and I never took a real statistics class and so never learned the definition of a p-value. I also don't know about the Wars of the Roses or Millard Fillmore. I did learn about Hildegard von Bingen and Laguerre polynomials.
What does it really mean to properly understand p-value? What I remember is that if the p-value is less than 0.05, the research result is considered statistically significant. That's about as far as my memory goes. I know that's actually a misunderstanding, but that's how most people understand it. I'm not sure how much I need to know to say I truly understand it.
Agree. I think it's more important to understand statistical fallacies (selection bias, regression to the mean, survivorship bias, etc). Those are extremely common trip wires but to recognize them you don't need to memorize formal definitions.
It is mumbo jumbo (also people hearing “significant” treat this as “change is large and important” which is in no relation to the actual amount of change).
Low p-value basically means how sure we are the result is not a random variation (ie less than 5% probability of this change be a random thing — p=0.05)
Sample size matters heavily. With more observations, estimates become more precise, so increasingly small differences can become statistically significant. With a huge sample, you can therefore get a tiny, practically meaningless effect with a very small p-value.
One of the really awkward points of stats is that not only does sample size matter, but also model specification. Very small misspecifications can easily lead to infinitesimal P values over large sample sizes.
Similar things are true of Bayesian stats, leading to things like predictively oriented posteriors being studied nowadays.
P-values are almost always taught poorly, but it's not actually that difficult of a concept. I took statistics in high school, again in undergrad, and it wasn't until the third time in grad school that it actually made intuitive sense (thank you Julia Yang!). When you're testing a hypothesis in statistics, it's easier to formulate a "null hypothesis" which is the opposite of what you're testing, and then try to disprove that null hypothesis.
A p-value is the probability, assuming the null hypothesis is true, of obtaining a result at least as extreme as the one actually observed.
Put differently: if the null hypothesis were true, then for p=0.05 you'd see <things at least as far from the test statistic as what you just observed> at most 5% of the time.
Put differently again: If the null hypothesis you are testing is true, then for p=0.05 random sampling would not return an observation as far from the test statistic as you just observed, 95% of the time.
Say you go out and you see a sports bar and the FIFA world cup is on. France vs Sweden is playing on the TVs in the bar and the place is packed with fans of both countries. You look at a few people (wearing the national football colours) and you think to yourself "the French fans seem shorter than the Swedish fans". You decide to run an experiment to test this hypothesis. Lucky for you at half-time exactly n fans of each side agree to let you measure their height. You do this and of your sample of n fans, the French are 2cms shorter on average than the Swedish fans.
Now: the p-value is the probability of you getting a result at least this extreme assuming the null hypothesis (that there is no difference in average height between the general population of French and Swedish people).
> How much do you understand about statistics and p-values?
I suspect that it’s far far less than 38% of people who actually understand statistics to this level. I suspect if someone on HN went around and asked their co workers to explain what a P value is in 2 sentences, it would be less than 10% of a (presumably) highly educated workforce.
I suspect about 40% of adults are unable to tell the difference between mean/median/ mode, or could answer the Monty hall problem, or even “if I flip a coin 3 times are the chances I get heads 3 times in a row”
I mean, the Monty Hall problem is a literal gotcha that trips up literal professors, that's a horrendous example to use as the baseline for "basic understanding of statistics".
Other than that choice of example, I do agree in that I doubt anywhere near 40% of adults have basic statistical literacy. I've played in card game tournaments semi-professionally and just gambler's fallacy + results-oriented thinking alone make it so easy to take other people's money, and if you can't figure out such basic concepts as "getting tails once doesn't mean I'm due for a heads next flip" even when you're literally losing money, what are the chances of anyone else caring about understanding it when they're not even being given the hands-on reward-based reinforcement learning opportunity?
Yeah I maybe should have ignored the Monty hall problem - although I’d guess if you’ve studied enough stats to know what a P value is, and how to measure it, you’ve come up against the Monty hall problem!
Most HNers don't even understand what percentages are and throw out dumb statements like "mega corp can treat 1% of users like crap, it's a small number!"
In my experience, a not insignificant chunk of students actively in a stats class think that a p value is the probability of the null hypothesis. My money is on more like 3% of educated professionals.
If you asked me for the definition of p value I could give it to you but if you asked me what it meant before this thread I would have said the same thing as you’ve said here.
10% may be a magnitude too high at least if we expect the explanation to be correct. For example in a sample of statisticians/epidemiologists only 12.5% got two basic features of p-values correct [1]. And there are a lot of studies showing similar levels of misunderstanding among people using p-values professionally.
I use p-values daily. I can and do compute them using various methods, including by hand. But I'd still not be confident in my two sentence explanation. P-values are very unintuitive and very easy to get subtly wrong.
I'd say in reality it's way more than that. The first statistics course in uni was a very humbling experience. I realised that while I thought I understood a lot (and I was coming from a CS heavy background, olympiads and such) real statistics is way harder and a lot more counterintuitive than I thought. Granted, this talks about "basic" statistical understanding, but even that is way more complicated than most people assume.
yeah, i've studied a lot of math and a lot of cs, and stats is tough. part of the problem is the terminology, and just giving a ton of complex machinery without telling you what it's actually doing. i've never learned that way, and it is very easy to feel like you're doing some sort of dark magic.
also, probability theory vs statistics is an important distinction: prob theory is a nice clean mathematical subject, while statistics is almost the philosophy of applying probability theory to the world.
Statistical reasoning isn't really motivated when it's taught, at least in the US. My schooling (I did jump around a bunch) assumed the student to have picked it up through vague balls-and-bins style problems taught in various units in various grade levels.
By the time I took my statistics class in undergrad math, coming from a similar background to you, they just sort of assumed you had a head for combinatorics and used that to develop everything else. I was a really good student in undergrad and statistics was my hardest class, I spent like 2x time on that class than any other class.
In grad school I took a class on complex system failure analysis and was quite apprehensive. My hope was that I could team up with a classmate to help with the math while I could work on the systems levels analysis. Turns out that because I understood systems really well, system failure offered me the intuition I needed to really understand statistics. I aced the class, published a moderately popular paper in distributed systems using what I learned, then went and took our graduate level statistics class widely known to be very difficult and aced it.
I think tacking statistical thinking on as an afterthought in curriculum is a huge mistake in the school system, especially so in the age of machine learning. I think for the average student statistical thinking is even more important than a lot of trigonometry.
Ugh no. You and the sibling commenter pushed me to do some searching but it looks like that class isn't offered anymore. It was a special class anyway (which is kinda common in my head school.) I'll see if I can dig up some lecture notes from a long time ago.
Yeah. Like most people, my only experience of statistics is studying as part of maths in secondary school. I was really strong in maths generally and most of it came relatively easily to me, but I struggled with statistics. Examples like the Monty Hall problem show just how unintuitive the basic concepts are.
Given how effective stories and anecdotes are in convincing people, it really seems like the human brain is not wired to grasp these concepts easily.
This was abundantly clear when people, even on HN, were upset about the bureau of labor statistics revising their numbers tendentially downwards, probably confusing the notion of statistical bias for that of political bias.
If the figures are biased, just estimate the bias and correct for that, what is the big deal they said, as if the bias variance tradeoff was not a thing.
The fact that 62% of Americans have little or no understanding of statistics may be related to those 40% of Americans that believe in Creationism, i.e. human (and fossils) were created by God a few thousands of years ago, and not of randomness and evolution over millions of years. I think no other industrial country has that disbelief in science.
https://news.gallup.com/poll/261680/americans-believe-creati...
This problem with science is apparent in another survey: in 2009, a Pew Center publication showed that 33% of scientists in the USA believed in God (and 18% in a transient power), which is much lower than the 80% belief of the general American population at the time. Of course, this is not a proof of causality in either direction, but scientific knowledge is seemingly inversely correlated to religiosity. And the USA are still more religious than any other industrial more-or-less-democratic country.
Your link goes beyond your 40% figure as well if you add in the 33% who don't believe in strict Creationism but believe that Christian God guided the process of evolution.
Even leaving aside the quantitative stuff (p-values, medians, whatever) and can't crunch the math, IMHO at least you should have seen how statistics can lead you to the exact opposite conclusion from reality, so that you at least know whether to think twice about a conclusion drawn from statistics thrown at you. Yet I was recently quite surprised to learn that even many folks in tech had never encountered Simpson's paradox before. All it takes to start explaining that is a scatterplot and a few lines, and yet it doesn't seem to be taught widely. It's rather terrifying, given that most people (myself often included) will be happy to believe "obvious" conclusions drawn from seeing one percentage greatly exceed another.
A coarse understanding like "the smaller p-value is the more likely a headline is true" is worse than no understanding at all. I bet most people who believed they understood what p-value is are like that though.
I can beat a gorilla in a fist fight because it's gonna rip my body in half, but lose by disqualification due to rules violations. A posthumous win is still a win.
I would be more likely to believe the results if they tested these adults and not asked them.
There's a big ego hit in admitting you don't know something. And many people are brought up thinking that it's a shame not to know something and that someone is better for knowing something. Like, a better person, not just better in some field.
And then the second question was:
“How often would you base decisions on reported statistics if you understood it better?”
Talk about a leading question. I get that they were tacking on their “study” to a larger question pool, but they could have put more effort in to the questions or done some actual testing.
I don't think it's a question of design. Some ideas in stats are just fundamentally unintuitive. Pedagogy can help mitigate this, but it would take a revolution to fit it into a neat and intuitive framework, like calculus.
There is the old joke that 87 percent of all statistics is made up on the spot. I’ve told it many times but a fair amount of people seemed to believe it hook, line, and sinker.
174 comments
[ 0.21 ms ] story [ 25.6 ms ] threadBack in the 70's I used to walk 20 miles as a child, and then go for farm work. As a mining engineer, I used to walk up 1.5 miles along a 1:3 incline (tunnel) everyday, sometimes during midnight, working 6-day week. Worked in dirtiest, noisy coal mines, near blast sites, soaked in black dust, with no place to sit during the shift. But never felt that it's something hard or bad, until some college kids, for who I was a tour guide, told me in horror that they wouldn't ever venture working in such place.
My boss laughs at that. He receives anonymous red-letter notes from the local extremist organization threatening him. He keeps a pile of those notes on a spike.
But if they release headline “62% of respondents” reported no or limited statistical knowledge while only 11% regularly use statistics in daily life…
…then they would loose more than half of readers who don’t know “per cent” or % symbol (?)
I thought that OP changed the original headline but no, psu.edu really published this :)
https://en.wikipedia.org/wiki/Misuse_of_p-values
The other 38% didn't understand the question...(my extrapolation)
I did a couple semesters of statistics at uni. And I can confidently say that the number of people who can answer 3 simple questions on statistics (like say mean versus medians, confidence levels or margins of error) is, well, a rounding error from 0.
Indeed, statistically, no-one has a clue how statistics work.
I did however learn enough to know that statistics can tell you absolutely anything you want them to say. Assuming you don't just make them up, they're trivial to manipulate to generate the headline you want.
When used to evaluate risk, the comprehension goes down further (a fact willfully exploited my any decent marketing.)
Statistically, most statistics are meaningless.
well encapsulated in the quote popularized by Mark Twain "Lies, damned lies, and statistics" [1]
[1] https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statist...
One of my favourite jokes: 93 % of statistics are made up on the spot, and 61 % of people believe them. Bonus points for changing the figures every time you retell the joke.
Our stat prof was a very special guy.
I’m increasingly convinced this is a thought-terminating cliche. Understanding the difference between a median, mean and mode is fundamentally empowering. Enough people, however, will stop themselves from trying to understand that by quoting such a joke.
Sure, a lot of people will not take their understanding any further, but most do not have the will or the time to do so.
Even knowing mean, mode and median is not enough. You really want standard deviation too. And that is just the basics.
There's a reason actuaries get paid the big bucks.
- Interpret and critically evaluate statistical representations from the media and the local community.
- Calculate measures of central tendency and measures of dispersion in custom and real datasets, and use the results to describe the data.
- Calculate and evaluate probability in statistics and games.
This came after my time, and our PIRSA score aren't the best so perhaps practice is lacking.
[1]: https://www.udir.no/lk20/mat01-06/kompetansemaal-og-vurderin...
I've been trying to talk about the median vs. mean with a bunch of politicians on themes around the zillionaires, wealth or consumption and for most parts they're clueless. Or the ones with degrees still go with the normal (mean that skews the normal) as they're afraid.
I just happened to get a copy of naked statistics yesterday, as I feel the human traits of poor comprehension of probabilities can be enhanced to at least some extent. And my degree from the social side didn't include statistics.
If there are better entry-level books on the matter I'm happy to take some recommendations.
That's bonkers. Society is all about statistics, and the reverse. Without statistics any kind of social studies is only Just So stories.
In the university I went to, Department of Statistics used to be part of the Faculty of Social Sciences. It was impossible to graduate from social sciences without taking a few classes of statistics. Then in some reorganization, Department of Statistics merged with Department of Mathematics. Except that old-school statisticians didn't want to move to the Faculty of Science, and they somehow managed to keep their offices in the Faculty of Social Sciences.
I was recently convinced by a rather compelling argument that technocracy (rule by the technically capable) often falls to a local minima where the people in power find the first scrap of evidence that supports their preconceived agenda. Wildly racist? Natural selection “proves” that all of your decisions are “technically” justified.
But more directly to your point about being effective communicators of statistics, I’ve found that it’s difficult to help someone form their own conclusion from statistical results. Most people want the conclusion fed to them, with the statistics supplied as evidence. It’s up to us (proper statisticians) to act ethically: provide analyses in good faith and challenge the poorly conceived analyses of amateurs and statisticians acting in bad faith.
When told to a statistically illiterate person who isn't aware of Simpson's paradox and so on?
what happens when data just russian-dolls in both directions the deeper you look?
>A common example of Simpson's paradox involves the batting averages of players in professional baseball. It is possible for one player to have a higher batting average than another player each year for a number of years, but to have a lower batting average across all of those years. This phenomenon can occur when there are large differences in the number of at bats between the years.
The per-year values aren't weighted in the combined total average.
Combined with Dunning-Kruger, this means that the real number of people completely clueless about statistics is closer to 38%.
(Also, I assume you are joking in how you apply the effect here even assuming it is real)
[0] https://pmc.ncbi.nlm.nih.gov/articles/PMC8992690/
[1] https://www.sciencedirect.com/science/article/abs/pii/S01602...
It's basic when you are attending an undergraduate course but most people can understand mean (as a dictionary might generically define it) and have a general feeling for margin of error (again, not in the mathematical way.)
Statistics has been the most difficult course in my CS course. For some reason when I start counting events to get a probability I find several perfectly plausible ways to count them, get five different probabilities and none of them is the correct answer.
And about being "trivial to manipulate [numbers] to generate the headline you want" a politician once told me that you can show the same numbers in any way you want, as in to demonstrate a thesis or its opposite.
To formulate the probability of B happening, for example, you have to make an educated guess. Create a functional equation that map A (all possibilities) to B (desired possibility). Then you make a ratio-fraction with the equation in the numerator and set A in the denominator. Using Algebra, try to eliminate references to A in both the numerator and denominator to give you an educated guess of what the probability is.
96% chance of hit
miss. twice.
question sanity.
Everybody has them, and they're not useless. Usually they're regularly updated when new information comes in.
The assessment is subjective, includes personal beliefs, assumptions, etc. not just measurable objective points. The measurement uncertainty at every step and the confidence interval are disappointing despite people using percentages, suggesting confidence to the percent. A scale from 1 to 5 is just as accurate.
2 people looking at the same situation could have very different degrees of belief, which is why 2 engineers could give very different estimates. But if I say I believe the likelihood of something is 73.8% I might be more credible to the listener. Looks like I calculated, not like the guy who said "3 out of 5 we get it done".
Rhetoric teaches how to argue with words. Statistics is the same, but with numbers.
Rhetoric is persuasion under the presupposition that what you are trying to persuade someone of is true. Sophistry is indifferent to the truth and is merely concerned with results. Rhetoric respects the humanity of the interlocutor. Sophistry seeks to exploit him.
This is a tests of knowledge of definitions than actual statistical knowledge.
― Winston Churchill
Nowadays I often stumble upon this or that statistical topic, watch an educational video, read a wiki explanation and it makes sense. Plus I've picked up unstructured and chaotically a lot of terms just by reading IT articles and forums.
tl;dr - my point is, our education is severely lacking a simple, short and concise statistics course on ELI5 level, for middle schoolers. And it is a huge gap in skills people actually do need in common life, outside of STEM. And the skills I'm talking about aren't even hard, a core set of basic concepts, without any math, can likely fit in a tiny brochure written in simple literary English with a few illustrations. Or a set of YT videos along the same lines.
https://en.wikipedia.org/wiki/People_v._Collins
You're kidding, right? 38% self-report more than that? If their self-report were accurate it would imply an education system that has truly excelled.
Is that a well designed survey question?
I would expect the use of a specific jargon term in that question to affect the results in a significant way.
Low p-value basically means how sure we are the result is not a random variation (ie less than 5% probability of this change be a random thing — p=0.05)
Sample size matters heavily. With more observations, estimates become more precise, so increasingly small differences can become statistically significant. With a huge sample, you can therefore get a tiny, practically meaningless effect with a very small p-value.
Similar things are true of Bayesian stats, leading to things like predictively oriented posteriors being studied nowadays.
A p-value is the probability, assuming the null hypothesis is true, of obtaining a result at least as extreme as the one actually observed.
Put differently: if the null hypothesis were true, then for p=0.05 you'd see <things at least as far from the test statistic as what you just observed> at most 5% of the time.
Put differently again: If the null hypothesis you are testing is true, then for p=0.05 random sampling would not return an observation as far from the test statistic as you just observed, 95% of the time.
Now: the p-value is the probability of you getting a result at least this extreme assuming the null hypothesis (that there is no difference in average height between the general population of French and Swedish people).
I suspect that it’s far far less than 38% of people who actually understand statistics to this level. I suspect if someone on HN went around and asked their co workers to explain what a P value is in 2 sentences, it would be less than 10% of a (presumably) highly educated workforce.
I suspect about 40% of adults are unable to tell the difference between mean/median/ mode, or could answer the Monty hall problem, or even “if I flip a coin 3 times are the chances I get heads 3 times in a row”
Other than that choice of example, I do agree in that I doubt anywhere near 40% of adults have basic statistical literacy. I've played in card game tournaments semi-professionally and just gambler's fallacy + results-oriented thinking alone make it so easy to take other people's money, and if you can't figure out such basic concepts as "getting tails once doesn't mean I'm due for a heads next flip" even when you're literally losing money, what are the chances of anyone else caring about understanding it when they're not even being given the hands-on reward-based reinforcement learning opportunity?
I use p-values daily. I can and do compute them using various methods, including by hand. But I'd still not be confident in my two sentence explanation. P-values are very unintuitive and very easy to get subtly wrong.
[1] https://pubmed.ncbi.nlm.nih.gov/35991465/
But statisticians not knowing the basics of the Null Hypothesis is absolutely terrifying!
also, probability theory vs statistics is an important distinction: prob theory is a nice clean mathematical subject, while statistics is almost the philosophy of applying probability theory to the world.
By the time I took my statistics class in undergrad math, coming from a similar background to you, they just sort of assumed you had a head for combinatorics and used that to develop everything else. I was a really good student in undergrad and statistics was my hardest class, I spent like 2x time on that class than any other class.
In grad school I took a class on complex system failure analysis and was quite apprehensive. My hope was that I could team up with a classmate to help with the math while I could work on the systems levels analysis. Turns out that because I understood systems really well, system failure offered me the intuition I needed to really understand statistics. I aced the class, published a moderately popular paper in distributed systems using what I learned, then went and took our graduate level statistics class widely known to be very difficult and aced it.
I think tacking statistical thinking on as an afterthought in curriculum is a huge mistake in the school system, especially so in the age of machine learning. I think for the average student statistical thinking is even more important than a lot of trigonometry.
Given how effective stories and anecdotes are in convincing people, it really seems like the human brain is not wired to grasp these concepts easily.
100% of headlines of statistics-related articles must follow this rule.
If the figures are biased, just estimate the bias and correct for that, what is the big deal they said, as if the bias variance tradeoff was not a thing.
This problem with science is apparent in another survey: in 2009, a Pew Center publication showed that 33% of scientists in the USA believed in God (and 18% in a transient power), which is much lower than the 80% belief of the general American population at the time. Of course, this is not a proof of causality in either direction, but scientific knowledge is seemingly inversely correlated to religiosity. And the USA are still more religious than any other industrial more-or-less-democratic country.
On a somewhat related note, 8% of Americans say they can beat a gorilla in a fist-fight.
There's a big ego hit in admitting you don't know something. And many people are brought up thinking that it's a shame not to know something and that someone is better for knowing something. Like, a better person, not just better in some field.
Talk about a leading question. I get that they were tacking on their “study” to a larger question pool, but they could have put more effort in to the questions or done some actual testing.
Yeaaah… let’s talk about that.
Seems like a fair bit of stats were designed to intimidate —so as to get people to stop asking questions. Or at least that is the effect!
Stats designed for intuition are few. See Kill Math for how it might be done: https://worrydream.com/KillMath/