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More than half of adults in U.S. say they lack basic statistical understanding
- ledoncool 2mo agowow, more than half..
- markdown 2mo ago99.99% actually.
- setopt 2mo ago"Think of how stupid the average person is, and realize half of them are stupider than that." — George Carlin
- gpt5 2mo agoI 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.
- BartShoot 2mo agoand who considers themselves to be in that lower half? Probably a lot less than half of the population
- isoprophlex 2mo agoShouldn't that be the median person for the quote to actually hold?
- setopt 2mo agoGiven 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.
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- floam 2mo agoThat’s surprisingly self-aware, and encouraging.
- simonw 2mo ago> 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.
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- ethersteeds 2mo agoWait... Your second paragraph is jarringly different from the first. How do they relate?
- sharkjacobs 2mo agoAnd how do either of them relate to statistical literacy in the United States?
- itake 2mo agoMy interpretation is how the risks (statistics) of those job functions are more known, people choose to avoid them. But the people that are-the-statistic don't necessarily agree with or understand those statistics. For example, if OP is a coal miner that hasn't had health issues yet, they may choose to discount statistics that declare x% of coal miners have negative health outcomes.
- adabovehuman 2mo agoThis feels correct. It's why they included the tidbit about their youth, they're saying their job was better than the life they grew with.
- zkmon 2mo agoStatistical literacy, or any literacy for that matter, requires hard work that is seen as a normal way of life. When machines do that hard work for us, it is no longer seen as a normal thing, but some unnecessary hard work (when we have cars, why walk 20 miles? And we have machines that do statistics). Just like how those college kids saw my work as horrifically weird hard work, while I saw it as a normal thing.
- itake 2mo agoI think they are saying as information (statistics) are known about the risks of those jobs, less people are interested in performing those jobs.
- sans_souse 2mo agoThat's like ⅐ of the US population..
- sixtyj 2mo ago“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 :)
- onion2k 2mo agoIt could be 1/14th. That's twice as many.
- BLKNSLVR 2mo agoI 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.
- mattvr 2mo agoThe 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 https://en.wikipedia.org/wiki/Misuse_of_p-values
- bruce511 2mo ago>> 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.
- kazinator 2mo agoYou mean, the other 48% didn't understand the question. :)
- salviati 2mo ago> 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_statistics 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.
- BLKNSLVR 2mo agoYou _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!
- dcminter 2mo agoWell, 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 :)
- arjie 2mo ago> 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.
- MathMonkeyMan 2mo agoYeah 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.
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- jdw64 2mo agoWhat 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.
- maccard 2mo agoFair 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.
- Ekaros 2mo agoSame. 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.
- ngruhn 2mo agoAgree. 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.
- jcgl 2mo agoAgreed. And throw in some Bayesian thinking too (like the Farmer and the Librarian).
- piskov 2mo agoIt 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.
- NitpickLawyer 2mo agoI'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.
- bbeonx 2mo agoyeah, 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.
- Karrot_Kream 2mo agoStatistical 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.
- maccard 2mo ago> 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”
- applfanboysbgon 2mo agoI 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?
- maccard 2mo agoYeah 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!
- izacus 2mo agoMost 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!"
- ViscountPenguin 2mo agoIn 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.
- blackbear_ 2mo agoThis 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.
- _joel 2mo agoWell, that's what happens when you use words like math and not maths. Although us Brits aren't that much better.
- idoubtit 2mo agoThe 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-creationism.aspx 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.
- sleepysloppy7 2mo ago[dead]
- duskdozer 2mo agoYour 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.
- dataflow 2mo agoEven 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.
- raincole 2mo agoA 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.
- applfanboysbgon 2mo ago38% 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.
- unsnap_biceps 2mo agoI 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.
- mcapodici 2mo agoThat has to be the most absurd but technically correct thing I have read.
- wafflemaker 2mo agoI 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.
- olsondv 2mo agoAnd 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.
- dr_dshiv 2mo ago“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/ https://worrydream.com/KillMath/
- frontfor 2mo agoThe 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.
- QuantumNomad_ 2mo agoBret 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://vimeo.com/906418692 https://worrydream.com/LadderOfAbstraction/ https://worrydream.com/LadderOfAbstraction/
- dgellow 2mo agoThat doesn’t make that Kill Math article better
- breezybottom 2mo agoI 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.
- dr_dshiv 2mo agoCan you give an example of a fundamentally unintuitive idea?
- zippyman55 2mo agoThere 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.
- nagi_builds 2mo agonot all U.S adults lack statistical understanding!
- wolfi1 2mo agothat's about 70%!
- sjhsj 2mo agoRatan
- mgaunard 2mo agoWe already know the pre-university US education system is bad (comparatively with other OECD countries), particularly in Mathematics. No surprise here.
- jyriand 2mo agoReminds 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."
- kleiba2 2mo agoAlthough by "average" you usually refer to the mean, not the median.
- lo_zamoyski 2mo agoIn common English, I would say that "average" as used in the quote is understood to be something closer to mode, hence why the joke works, because it trades on the ambiguity of "average" and the difference between mode and mean.
- hrideshmg 2mo agoStats 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.
- herbst 2mo agoThat's so obvious when the answer to "X per capita" is usually "but the US is so big"
- nxobject 2mo agoI was briefly excited that people were aware they lacked the understanding.
- notorandit 2mo agoBasic 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.
- ZeroDayDreamer 2mo ago[dead]
- 2d8a875f-39a2-4 2mo agoBeen saying it for years. Basic probability theory should be taught in schools, it's a strong tool for understanding the world around you.
- ninalanyon 2mo agoYou mean it isn't taught where you are? That's bizarre, it was part of the curriculum when I was in high school in England in the early 1970s!
- koonsolo 2mo agoMaybe 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.
- cm2187 2mo agoThis 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.
- MathMonkeyMan 2mo ago<https://en.wikipedia.org/wiki/Motivated_reasoning 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.
- apexalpha 2mo agoThis 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.
- dgellow 2mo agoAre 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
- clarionbell 2mo agoI would be surprised if a significant number of people anywhere had a basic statistical understanding. It is a difficult topic.
- CM30 2mo agoMakes 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.
- ANarrativeApe 2mo agoAnd 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
- dolmen 2mo ago> More than half of adults in U.S. say they lack basic statistical understanding So, when surveyed, they tell they are in the other half than they really are?
- LandR 2mo agoI was having a conversation with my dad about how if a virus had a 10% death rate it would be terrifying. His reply was that 10% was nothing, that means you've got 90% chance to survive. Then said you've probably got a 10% chance of being hit by a bus every time you cross the road. Just absolutely no idea what probabilities are at all or ability to extrapolate probabilities from real world lived experience.
- dgellow 2mo ago> His reply was that 10% was nothing Ask him how many times he would roll that dice
- beng-nl 2mo agoFittingly, he would be rolling that die
- OroPla 2mo agoIn my head he answered "in my day and age we had the black plague, with a 90% death rate". (It was 50%, but who checks these numbers anyway.) Guess we are so used to made up numbers and exaggerations that it's hard to take anything at face value.
- boogieknite 2mo agothe short story The Pill plays out a world full of people who reason similarly, among many other things. https://escapepod.org/2022/11/03/escape-pod-861-the-pill-part-1-of-2/ https://escapepod.org/2022/11/03/escape-pod-861-the-pill-par...
- Alien1Being 2mo agoI would estimate that 90% of software developers I have spoken to lack basic statistical understanding. Basic concepts like kurtosis, skewness, moments, the core Greeks all seem to be alien concepts to most.
- JumpCrisscross 2mo ago> 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.
- phendrenad2 2mo agoWhat's going on in Pennsylvania? Is it so highly educated a place that they don't understand that 50% of U.S. adults can't read at a 6th grade level, let alone understand "confidence intervals"?
- armcat 2mo agoBasic statistics and basic economics/finance are two subjects that are completely underdeveloped within the general population. Coincidentally those two effectively rule our entire lives. As an aside, STAT 200 looks like a solid stats course.
- amelius 2mo agoHow is that in China?
- drgo 2mo agothese are the self-aware ones. I worked with and trained hundreds of scientists; I would say 95% of them had at best a shaky understanding of basic probability and statistical concepts!!
- giantg2 2mo agoEveryone is hating on statistics, yet HN posts studies all the time. Yes, stats can be used deceptively or incompetently used, but they are generally useful. You just have to look at the full study to see what the starting data was and all the actions taken on it. Then you have to make a judgements call on if/how you want to apply that to your own choices, political policies, etc. A great example of a stats being used by two sides of an argument and political positions would be gun control. See Everytown Research and Crime Prevention Reseach Center. You can see what gets measured, included, excluded, etc by each side and how those results get fitted for support of political policy.
- shmeeed 2mo agoThat headline is pretty generous... 62% is quite a bit more than half. It's actually more than 3/5. I'd even go so far to say it's nearly two thirds.
- seemaze 2mo agoEloquently embodied by the late misfit troubadour and grunge philosopher Todd Snider in Statistician's Blues https://www.youtube.com/watch?v=IUK6zjtUj00 https://www.youtube.com/watch?v=IUK6zjtUj00
- ghm2199 2mo agoOne of the simplest ways to measure risk in stocks, bonds, crypto, mfs etc for ordinary people is Maximum Drawdown. Once you understand how it works, it takes the stress out of making and managing your own portfolio P — espexially your non retirement account. The question you have to ask your self is: "Given some portfolio with returns of X%, am I ok with this asset being down by Z% over T years — i.e the _computed/inferred_ drawdown?" If the answer on one end is no I cannot afford P to have any drawdown at all, then just put your money in a cash/MMF and call it a day. Generally people are ok with some risk on some percent of P and stash the rest in cash, and you _risk adjust_ for Z and T. The portfolio choices are surprisingly simple. No other question matters. There are some risks but the key element is the understanding of the statistical variance because that allows me to say that "ok 50% of P can afford to be down for 3 years and I won't be homeless". Most people don't know this but most money managers(managing money for ordinary Americans) that you hire compute this number _once_ and make tiny adjustments to your portfolio(I am talking once a year maybe) and take 1-2%. I follow this guy called Dave Stein who has a B2C product called money for the rest of us that taught me this. I am not affiliated with them in any way.
- ghm2199 2mo agoI 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.
- tescreal 2mo agoHow correlated is the lack of understanding with anti-intellectual views? A lot of people aren't even curious in my experience.
- LatteLazy 2mo agoI actually think this is very good. People thinking they understand statistics is far more dangerous and causes far more issues that people honestly saying they don’t…
- egberts1 2mo agoLIES! We all know 20% more also means take 20% off gets us the exact same value. NEXT! No? Isn't that the beauty of gullibility?
- DataDive 2mo agoLOL, 62%? that seems low ... I would say the overwhelming majority of even university faculty members lack a basic understanding of statistics. In their heads, they’re doing something closer to informal Bayesian reasoning: they have prior beliefs based past observation, previous research, experience, etc., wich is then all baked into every choice and decision But when it comes time to write the paper, they translate that into frequentist statistics: p-values. As if all should be compared to random chance: significance thresholds, confidence intervals. They do this to give their conclusions formal credibility: oh look how compelling my result is, I found all this new surprising stuff. Close to 100% of life sciences research works that way.
- zug_zug 2mo agoI recommend every youth take a week to a month to try to read and internalize the book "Once upon a number." It's full of those odd statistical paradoxes that seem impossible but once you really wrap your head around them you realize how oversimplified your prior understanding of probability was.
- diogenes_atx 2mo agoAs a grad student at a public university in the USA, I worked as a teaching assistant for the sociology class "Introduction to Statistics." The course used SPSS software to enable the students to perform statistical analysis on data sets. Although we offered an excellent textbook (listed below), most of the undergraduate students struggled with the material, so my colleagues and I added a supplemental reading list to the syllabus for those students interested in studying the main concepts. The following books are the ones we recommended to the students. I have read all these texts, and they are pretty good at explaining statistics to anyone interested in learning the material at a conceptual level; anyone can read and understand these books, regardless of their educational background. Ian Ayres (2007) Super Crunchers: Why Thinking by Numbers is the New Way to Be Smart Joseph Healey (2020) Statistics: A Tool for Social Research [This is the textbook used in the class, which I highly recommend] Catherine Marsh and Jane Elliott (2008) Exploring Data: An Introduction to Data Analysis for Social Scientists, second edition John Allen Paulos (1988) Innumeracy: Mathematical Illiteracy and Its Consequences Nate Silver (2012) The Signal and the Noise: Why So Many Predictions Fail, but Some Don't Nassim Nicholas Taleb (2005) Fooled by Randomness, second edition; _______ (2010) The Black Swan: The Impact of the Highly Improbable, second edition
- duxup 2mo agoI’m at least happy they know…
- wajdym1960 2mo ago[flagged]
- PorterBHall 2mo agoNearly half of all US high school students are below average in reading.
- defrost 2mo agoWhat percentage are considered average?