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Comment by bruce511 | Hacker News Reader

>> 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.

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> 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.

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!

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

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.

I’ve heard this phrased as “the average person has an above average number of legs”.

Wouldn't "the typical person has above average number of legs" or some such be better?

Yes, but less pithy. Placing the "average person" next to the "average number of legs" makes it clear that the idiomatic and intuitive sense of "average" that most people have is wrong. The more precise "typical person" doesn't make that same point as well, though an intelligent reader would certainly be expected to be able to read the same from it.

Median person?

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.

I suppose you mean the book "How to Make the World Add Up" of Tim Harford?! :-)

Everyone should just read everything by Tim Harford and then the world would be a better place.

Busted! Yes indeed!

I'd recommend reading whichever book is better.

Bill Gates walked into a bar. Everyone was, on average, a multi millionaire.

Large bar.

Haha yes, should have said average billionaire!

> 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.

Its more a foreshadowing of Simpson's paradox and a cluster of similarly counterintuitive effects. Statistical evidence that is technically of high quality can cause decision makers to believe the exact opposite of what is true.

> Statistical evidence that is technically of high quality can cause decision makers to believe the exact opposite of what is true

High-quality statistics allow themselves to be inspected. When a statistic is being passed around unadorned, particularly with a call to action, that’s no different from an uncited fact being accepted at face value. (Most of the complexity of statistics is in sampling. Most of the errors in statistical judgment tend to come down to misunderstanding how a sample’s statistics translate to the population you actually care about.)

I think it is rather a healthy skepticism.

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.

Another good one: success in business is 40% people skills, 30% technical knowledge, 20% work ethic, and 15% basic math.

> 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

Yes, you're probably right.

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

I think 1/2 and 1/3 are quite nice as far as numbers go! Also 2/36 = 0.5555... is not that far from 5%

But (assuming two dice rolled at the same time) 2/36 is something like "roll a five and a six" or "roll either a pair of sixes or a pair of fives". Neither of which is quite as intuitive or commonly used in game design as "using one d20, roll a natural 20"

And yet they struggle with the abstract concept. They'll wonder why the candidate with a projected 20% chance of winning won. They won't know what to do with the information of a 70% chance of rain tomorrow. "Either it will rain or it won't, which is it!" Perhaps it's the frequentist approach that comes more natural than the Bayesian approach, who knows.

This isn't my original thought, by the way. Someone wrote more about it here: https://towardsdatascience.com/humans-are-bad-at-probability...

Nobody understands Bayesian approach. Look at Covid -- people FREAKED out when we updated guidance based on learning new information.

XCOM should be added to the curriculum.

XCOM probabilities are lies, just like Fire Emblem. Pretty much 0% of games that show you a "percent-to-hit" chance ever give an accurate number.

true for XCOM in all difficulties except the hardest iirc

1 tile in front of alient

96% chance of hit

miss. twice.

question sanity.

Fully agree. For example, I wish managers would be capable to handle the difference between a 40% and a 70% chance to meet the deadline.

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.

They're credences: https://en.wikipedia.org/wiki/Credence_(statistics)

Everybody has them, and they're not useless. Usually they're regularly updated when new information comes in.

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 most of the times 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".

Cue prediction markets etc. There are mechanisms to aggregate this and have a wisdom of crowd effect.

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…

I hate that I have to talk to so many people about Russian Roulette just with more chambers. But it’s the only analogy that hits.

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”.

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

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.

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.

> 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.

> 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.

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.

You mean, the other 48% didn't understand the question. :)

“I only believe in statistics that I doctored myself”

― Winston Churchill

It's the mathematical version of learning rhetoric.

Rhetoric teaches how to argue with words. Statistics is the same, but with numbers.

Not quite.

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.

No longer true. Rhetoric is now an epithet and when used as such means sophistry. Most people use it as an epithet.

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

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.

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...

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.

> statistics can tell you absolutely anything you want them to say

https://en.wikipedia.org/wiki/People_v._Collins

> 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?

> 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.

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.

speaking of theory, what exactly is the solution to this paradox?

what happens when data just russian-dolls in both directions the deeper you look?

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.

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?

It is the same as wealth, or any dataset that has large data outliers on one side.

Average and mean are the same: normal distribution. Average higher than mean: skewed by big outliers.

Professional statistician affects the distribution of statistics knowledge like billionaires affect wealth distribution.

Congrats for having a shot, sadly that doesn't answer the questions posed in the slightest.

Again, why does the GP assume that a full half are distinctly lower than "average understanding" ? Why the assumption that multiple numbers cannot share an average understanding?

It was a joke, you are, of course, technically correct, there’s no requirement for the mean and median to be the same.

Fair point, in my time zone it was late, I was crabby, and there was a surrounding context of "bad statistics" comments.

That said,

If the mean and median were the same your statement would still not be always true. For more than one reason.

No harm done :)

I’m interested, in what cases would it not be true if we assume “average” here to be “median”? I can only think of one: if we consider “understanding” to be discrete rather than continuous.

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.

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.

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.

I‘ve seen lots of people go the other way, moving towards a more self centered view of the world as they age.

The problem is that convincing yourself that you are smarter than your younger self with opposite views, means that you are right about the politics now, is just a fallacy.

The change doesn't come from thinking one is smarter or dumber, but you simply having much more information to work with. We form extensive opinions and views about the world relatively young, but it's largely based on things we have 0 personal knowledge or experience of.

Again I think the internet/social media are perfect examples. Predicting what would happen isn't about being smart or dumb. It's a matter of just not having enough real world experience to even begin to formulate meaningful views. And so the views and expectations we did form were quite out of touch with what really happened and indeed what we probably 'should' have expected to happen all along.

This is an universal experience which wouldn't explain the vast difference in worldviews.

I'd separate worldview from ideology. I think worldviews, for people who have all seen a comparable share of the world over a comparable time era, are going to fall quite close. But ideologies are something distinct from that. Worldviews should influence ideology, but in practice it's the other way around for many people - even as they age. In any case, without that world experience - the values we formulate when younger are going to be based on assumptions that will ultimately prove to be false.

>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.

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