>> 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 by 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.
You _have_ to change the numbers each time, because you're constantly measuring and these things have basic variation. It would be unrealistic if the fake statistics were the same every time!
> 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.
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".
Maybe people would have a better understanding of percentages if 20-sided dice were used more. "This has a 95% chance to succeed" -> roll a d20, anything but 1 is a success
Meanwhile 6-sided dice don't map to nice numbers, and having two dice makes the maths even harder to intuit
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.
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.
And I took some math in university before dropping out of CSC decades ago, so it isn't too hard, but my hunch is that with the BSs students the statistics in decent level would've been too much anyway.
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.
My thesis is that no-one understands. So there's no political orientation.
Your suggestion suggests that a little bit of technical education would change political allegiance. Alas that is incorrect. Politics is about worldview (me and mine versus you and yours) and a world view cannot be changed by something as mundane as education.
Each person has both a self-centered side, and a community-centered side. For some it's mostly self centered. For others mostly community centered. Politics is about finding out which side the population has swung to.
A bit of a tangent, but I don't think it's really fair to say it's about self vs community. I think the main reason that people start to lean in a different direction as they age is because you start to see cracks in the ideals you held when younger. The internet is a good example. Many of us lived through the birth of the mainstreaming of the internet. And our perspectives of what the future held at that moment was generally just exceptionally naive. For those who are a bit younger, a similar phenomena played out with the rise of social media as well.
And as you see how reality and society tend to 'really' work, wisdom in other words, it tends to result in a shifting perspective on the ideal way forward for society. I'm certainly much more socially minded than when I was younger now. And I also think that's fairly typical - like most young people I was completely self absorbed which makes 'real' social mindedness quite uncommon. Yet my political leaning is gradually shifting ever more towards the 'self centered' orientation, in your terminology.
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.
But definitions are very much important when discussing statistics. Being able to communicate using correct terminology is important. Part of knowledge is being able to ingest statistics produce by someone else.
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.
This is also a political problem. Most of the debates about racism for instance are between people who are illiterate in term of basic statistics, on both sides of the debate. They take extreme tails of distributions as benchmarks, think in term of stereotypes rather than distributions, infer rules from a handful of samples, etc. It makes the whole exercise sterile.
It is not just journalists and politicians that are guilty of that. I see that from many academics who should know better, particularly in humanities departments.
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. 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.
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.
And even the headline gets it wrong. They asked 1,000 people, over half of whom say they lacked basic statistical understanding.
The first question was:
“How much do you understand about statistics and p-values?”
not probability, p-values.
I had to look up p-values to check it meant what I thought it did to avoid making a fool of myself in this comment. I knew I was probably right, but possibly wrong.
The same goes for my assumption that this survey was engineered to deliver a bad result.
Why? because it makes it easier to get funding for a the author's solution to the problem. Again, probably right, possibly wrong.
Statistics, like math, is a language, first learn the vocabulary, then you can judge the meaning
Makes me wonder what the numbers are like in other countries. There's a lot of talk here about issues with the American education system and what not, but I suspect the numbers would be about the same in many other places too.
Like, if I asked the average person here in the UK what a p-value was, I suspect the majority either wouldn't know or would have barely heard of the idea. I suspect those numbers wouldn't change much in other countries, whether in Europe, Asia, Africa or South America.
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.
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.
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.
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.
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.
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.
> 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.
> 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”
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.
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!"
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!
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 “effect/change is large and important” which is in no relation to the actual amount of change).
Low p-value basically means how surprising your data would be if there were actually no effect (ie less than 5% of the time you’ll get this due to randomness if there is no change — which is rather impossible)
Sample size matters heavily. With more observations, estimates become more precise, so increasingly small differences can become statistically significant. With a large sample, you can therefore get a tiny, practically meaningless effect with a very small p-value.
Eg effect of $1 can be statistically significant (not random) which does not matter in practical terms if average is like $10000.
So the key point here is not only to look at the p-value but also at an actual change. If a drug gives you only 0.01% more hair, it doesn’t matter to you that it is guaranteed.
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.
Fair play to you for answering, but that’s not what a P value is! A p value is the chance of getting a result greater than the result you actually got, _assuming you are testing a hypothesis_.
I’m also pretty sure I would fall in the camp of saying “nope don’t understand P values” as I can’t remember anything else about them.
Same. I think it involves doing some other stuff very much properly... Like formulating whole thing... And even then you might luck out if you try enough of things...
So I admit I only know that P values are somewhat useful some of the time.
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.
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.
Stats is one of those subjects which displays the dunning kruger effect really well.
Sure on the surface stuffile averages, medians, standard deviations etc are quite easy but the moment you start going deeper you realize how difficult and un-intuitive things start to get.
I'm still in the valley of despair, and frankly it's probably the best place to be in for the average person. Understand the basics and know just enough to realize how easy it is to mislead people with it.
I think the average person is definitely intelligent. It's just that we are very prone to mixing intelligence with knowledge in addition to also forgetting how long it took us to learn things that are so automatic for us we see them as trivial.
Given that most measures of intelligence follow nearly normal distributions (as long as you stay away from the tails), I think it doesn’t matter that much.
>> 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 by any decent marketing.)
Statistically, most statistics are meaningless.
> Assuming you don't just make them up, they're trivial to manipulate to generate the headline you want.
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.
Well, if we're telling stats jokes...
A statistician is a man who with his head in the freezer and his feet in the oven can say "On the whole I feel perfectly normal."
Recommended reading: 'How to lie with statistics' - Huff, 1954
:)
The average body temperature of the people in a hospital is in the normal range. Many do have a slight fever, but some are in the fridge.
Our stat prof was a very special guy.
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.
After all the average human has one breast and one testicle.
Amd less than 2 legs.
If even one person has 1 leg, then the average is strictly less than 2.
You _have_ to change the numbers each time, because you're constantly measuring and these things have basic variation. It would be unrealistic if the fake statistics were the same every time!
> 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.
If you're not yet familiar with it, I present to you the Datasaurus Dozen: https://www.research.autodesk.com/publications/same-stats-di...
And the older Anscombe's Quartet: https://en.wikipedia.org/wiki/Anscombe%27s_quartet
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".
I think almost everyone threw a dice quite a few times while playing board games.
Maybe people would have a better understanding of percentages if 20-sided dice were used more. "This has a 95% chance to succeed" -> roll a d20, anything but 1 is a success
Meanwhile 6-sided dice don't map to nice numbers, and having two dice makes the maths even harder to intuit
XCOM should be added to the curriculum.
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.
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.
I'm a bachelor of social services and healthcare from applied side so if statistics we're mentioned they must've been in the small print.
And I took some math in university before dropping out of CSC decades ago, so it isn't too hard, but my hunch is that with the BSs students the statistics in decent level would've been too much anyway.
Dunno really.
> my degree from the social side didn't include statistics.
That's bonkers. Society is all about statistics, and the reverse. Without statistics any kind of social studies is only Just So stories.
It's the mathematical version of learning rhetoric.
Rhetoric teaches how to argue with words. Statistics is the same, but with numbers.
Half of all Americans have lower than average understanding of statistics (or at least, lower understanding than the average American)
Really?
Why not 5% of Americans having the same average level of understanding and only 47.5% having a lower than average understanding?
What assumptions are you making, and why should they be true?
You mean, the other 48% didn't understand the question. :)
> I did however learn enough to know that statistics can tell you absolutely anything you want them to say.
When told to a statistically illiterate person who isn't aware of Simpson's paradox and so on?
Being aware of Simpsons' paradox doesn't even help. There's no way of knowing what the right level of aggregation is without a theory.
> When told to a statistically illiterate person?
Which is a rounding error from 100% according to the GP.
That's obvious. I just hope the OP doesn't end up with the same expression as Anakin in the Anakin-and-Padme meme after this question.
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.
My thesis is that no-one understands. So there's no political orientation.
Your suggestion suggests that a little bit of technical education would change political allegiance. Alas that is incorrect. Politics is about worldview (me and mine versus you and yours) and a world view cannot be changed by something as mundane as education.
Each person has both a self-centered side, and a community-centered side. For some it's mostly self centered. For others mostly community centered. Politics is about finding out which side the population has swung to.
A bit of a tangent, but I don't think it's really fair to say it's about self vs community. I think the main reason that people start to lean in a different direction as they age is because you start to see cracks in the ideals you held when younger. The internet is a good example. Many of us lived through the birth of the mainstreaming of the internet. And our perspectives of what the future held at that moment was generally just exceptionally naive. For those who are a bit younger, a similar phenomena played out with the rise of social media as well.
And as you see how reality and society tend to 'really' work, wisdom in other words, it tends to result in a shifting perspective on the ideal way forward for society. I'm certainly much more socially minded than when I was younger now. And I also think that's fairly typical - like most young people I was completely self absorbed which makes 'real' social mindedness quite uncommon. Yet my political leaning is gradually shifting ever more towards the 'self centered' orientation, in your terminology.
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.
[1]: https://www.udir.no/lk20/mat01-06/kompetansemaal-og-vurderin...
If you changed "most" to "all" you'd be well inside the margin or error.
There's a reason actuaries get paid the big bucks.
One can get paid the big bucks without a clue what they do, even some of the most brilliant statisticians do acknowledge the ambiguity of stats.
>mean versus medians
This is a tests of knowledge of definitions than actual statistical knowledge.
But definitions are very much important when discussing statistics. Being able to communicate using correct terminology is important. Part of knowledge is being able to ingest statistics produce by someone else.
>> found that 62% of respondents reported no or limited statistical knowledge
Combined with Dunning-Kruger, this means that the real number of people completely clueless about statistics is closer to 38%.
Funny that you mentioned an effect that may just have been a statistical artifact after all [0, 1]
(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...
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.
This is also a political problem. Most of the debates about racism for instance are between people who are illiterate in term of basic statistics, on both sides of the debate. They take extreme tails of distributions as benchmarks, think in term of stereotypes rather than distributions, infer rules from a handful of samples, etc. It makes the whole exercise sterile.
It is not just journalists and politicians that are guilty of that. I see that from many academics who should know better, particularly in humanities departments.
This isn't new. "Lies. Damned lies and Statistics" as a phrase is already quite old.
Many people selectively shop around statistics that match their prejudice or their social circles social etiquettes.
<https://en.wikipedia.org/wiki/Motivated_reasoning> affects us all. I'd like to believe education is an antidote, but really the only antidote is... not doing that.
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. 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.
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.
Are the materials for the class on complex system failure analysis you had available online? Thank you.
And even the headline gets it wrong. They asked 1,000 people, over half of whom say they lacked basic statistical understanding.
The first question was: “How much do you understand about statistics and p-values?”
not probability, p-values.
I had to look up p-values to check it meant what I thought it did to avoid making a fool of myself in this comment. I knew I was probably right, but possibly wrong.
The same goes for my assumption that this survey was engineered to deliver a bad result. Why? because it makes it easier to get funding for a the author's solution to the problem. Again, probably right, possibly wrong.
Statistics, like math, is a language, first learn the vocabulary, then you can judge the meaning
Makes me wonder what the numbers are like in other countries. There's a lot of talk here about issues with the American education system and what not, but I suspect the numbers would be about the same in many other places too.
Like, if I asked the average person here in the UK what a p-value was, I suspect the majority either wouldn't know or would have barely heard of the idea. I suspect those numbers wouldn't change much in other countries, whether in Europe, Asia, Africa or South America.
“Fortunately, concepts in statistics are grounded in intuition and rationality.“
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/
The article reads like work of a crackpot. There’s a reason why maths is done the way it is, and intimidating people is definitely not the motivation.
Bret Victor is awesome. I especially like his “Inventing on Principle” talk and his “Up and Down the Ladder of Abstraction” article.
https://vimeo.com/906418692
https://worrydream.com/LadderOfAbstraction/
I love how they include statistics in the headline of a story about the lack of understanding of statistics. Epic troll.
100% of headlines of statistics-related articles must follow this rule.
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.
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.
I would be surprised if a significant number of people anywhere had a basic statistical understanding. It is a difficult topic.
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.
That’s surprisingly self-aware, and encouraging.
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.
We already know the pre-university US education system is bad (comparatively with other OECD countries), particularly in Mathematics.
No surprise here.
That's so obvious when the answer to "X per capita" is usually "but the US is so big"
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.
Been saying it for years. Basic probability theory should be taught in schools, it's a strong tool for understanding the world around you.
Basic statistical?
I have seen too many parents (i am a teacher) lacking basic mathematical and geometrical understanding.
Let alone, statistics.
Schooling is broken, society is rotting, culture is dead.
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.
That's like ⅐ of the US population..
It could be 1/14th. That's twice as many.
“More than half” may mean anything between 50 and 100 percent. :)
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 :)
Reminds me a joke by Robert Anton Wilson:
"You know how dumb an average American is. Well, mathematically speaking, half of them are even dumber than that."
Although by "average" you usually refer to the mean, not the median.
> 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.
I was briefly excited that people were aware they lacked the understanding.
Well, that's what happens when you use words like math and not maths. Although us Brits aren't that much better.
> 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”
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.
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!"
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!
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.
Agreed. And throw in some Bayesian thinking too (like the Farmer and the Librarian).
It is mumbo jumbo (also people hearing “significant” treat this as “effect/change is large and important” which is in no relation to the actual amount of change).
Low p-value basically means how surprising your data would be if there were actually no effect (ie less than 5% of the time you’ll get this due to randomness if there is no change — which is rather impossible)
Sample size matters heavily. With more observations, estimates become more precise, so increasingly small differences can become statistically significant. With a large sample, you can therefore get a tiny, practically meaningless effect with a very small p-value.
Eg effect of $1 can be statistically significant (not random) which does not matter in practical terms if average is like $10000.
So the key point here is not only to look at the p-value but also at an actual change. If a drug gives you only 0.01% more hair, it doesn’t matter to you that it is guaranteed.
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.
Fair play to you for answering, but that’s not what a P value is! A p value is the chance of getting a result greater than the result you actually got, _assuming you are testing a hypothesis_.
I’m also pretty sure I would fall in the camp of saying “nope don’t understand P values” as I can’t remember anything else about them.
Same. I think it involves doing some other stuff very much properly... Like formulating whole thing... And even then you might luck out if you try enough of things...
So I admit I only know that P values are somewhat useful some of the time.
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.
The question asked as part of the survey: “how well do you understand p-values?” Most scientists may not even be able to pass truthfully.
https://en.wikipedia.org/wiki/Misuse_of_p-values
38% of Americans say they have some familiarity with statistics.
On a somewhat related note, 8% of Americans say they can beat a gorilla in a fist-fight.
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.
> How much do you understand about statistics and p-values?
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.
not all U.S adults lack statistical understanding!
Maybe their survey should have asked one question: What is the difference between average and median?
More than half would not be able to answer this, and not only in US.
that's about 70%!
Stats is one of those subjects which displays the dunning kruger effect really well.
Sure on the surface stuffile averages, medians, standard deviations etc are quite easy but the moment you start going deeper you realize how difficult and un-intuitive things start to get.
I'm still in the valley of despair, and frankly it's probably the best place to be in for the average person. Understand the basics and know just enough to realize how easy it is to mislead people with it.
wow, more than half..
"Think of how stupid the average person is, and realize half of them are stupider than that." — George Carlin
I think the average person is definitely intelligent. It's just that we are very prone to mixing intelligence with knowledge in addition to also forgetting how long it took us to learn things that are so automatic for us we see them as trivial.
Shouldn't that be the median person for the quote to actually hold?
Given that most measures of intelligence follow nearly normal distributions (as long as you stay away from the tails), I think it doesn’t matter that much.
and who considers themselves to be in that lower half? Probably a lot less than half of the population
99.99% actually.
Ratan