> 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.

> 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.

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 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".

If you're not yet familiar with it, I present to you the Datasaurus Dozen: https://www.research.autodesk.com/publications/same-stats-di...

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

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

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.

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.

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.

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

It's the mathematical version of learning rhetoric.

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

> 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?

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.

Half of all Americans have lower than average understanding of statistics (or at least, lower understanding than the average American)

“I only believe in statistics that I doctored myself”

― Winston Churchill

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

>mean versus medians

This is a tests of knowledge of definitions than actual statistical knowledge.

>> 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%.

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.

> His reply was that 10% was nothing

Ask him how many times he would roll that dice

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.

<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.

Are you talking about actual academic work or the pop- version of it? Because most of the damage I see is in pop-psychology, pop-sociology. In my limited experience looking into the topic humanities researchers make specific balanced claims backed with some numbers and reasoning, and all the nuance gets lost when translated to news articles and pop-sci books or videos

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.

I think the posted article is also the description of America's labor market. Many people don't use it on a day today basis and most people cannot engage their system 2 to assess risks over a few weeks out, let alone 5-10 years.

But I found This is a real practical everyday example of why statistical uncertainty is important to know about. It teaches you how to compare — risk adjust — two vastly different investments e.g. BTC vs S&P or indexing vs value strategies. Then you sleep at night.

It is also not intuitive and many people are very anxious and FOMO driven when it comes to money. So you need to internalize the idea for it to sink.

The drawdowns are a statistical measure and you could be unlucky to catch a big depression style thing once in 30 years. And T is typically longer than 5 years, typically 10 or more.

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.

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.

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.

> Basic concepts like kurtosis, skewness

You can probably lead a decent life without understanding kurtosis and skewness. You probably can’t if you don’t understand when a normal distribution applies.

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.

[1] https://pubmed.ncbi.nlm.nih.gov/35991465/

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?

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.

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 :)

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.

Although by "average" you usually refer to the mean, not the median.

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).

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.

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.

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.

"Think of how stupid the average person is, and realize half of them are stupider than that." — George Carlin

99.99% actually.