Struggle With Statistics? Your 'Fixed Mindset' Might Be To Blame (arstechnica.com)

A new study in Frontiers in Psychology examined why people struggle so much to solve statistical problems, particularly why we show a marked preference for complicated solutions over simpler, more intuitive ones. Chalk it up to our resistance to change. From a report: The study concluded that fixed mindsets are to blame: we tend to stick with the familiar methods we learned in school, blinding us to the existence of a simpler solution. Roughly 96 percent of the general population struggles with solving problems relating to statistics and probability. Yet being a well-informed citizen in the 21st century requires us to be able to engage competently with these kinds of tasks, even if we don't encounter them in a professional setting. "As soon as you pick up a newspaper, you're confronted with so many numbers and statistics that you need to interpret correctly," says co-author Patrick Weber, a graduate student in math education at the University of Regensburg in Germany. Most of us fall far short of the mark.

Part of the problem is the counterintuitive way in which such problems are typically presented. Meadows presented his evidence in the so-called "natural frequency format" (for example, 1 in 10 people), rather than in terms of a percentage (10 percent of the population). That was a smart decision, since 1-in-10 a more intuitive, jury-friendly approach. Recent studies have shown that performance rates on many statistical tasks increased from four percent to 24 percent when the problems were presented using the natural frequency format.

Comments

Huh?

[dtmos]

Part of the problem is the counterintuitive way in which such problems are typically presented. Meadows presented his evidence in the so-called "natural frequency format" (for example, 1 in 10 people), rather than in terms of a percentage (10 percent of the population). That was a smart decision, since 1-in-10 a more intuitive, jury-friendly approach. Recent studies have shown that performance rates on many statistical tasks increased from four percent to 24 percent when the problems were presented using the natural frequency format.

I've heard this argument before, and I just don't get it. "Percent" means per hundred, as the word is derived from the Latin "per centum," literally, "per hundred." It's a natural frequency format, just as much as saying "1 in 10 people." It's saying "10 per 100" people. What's so confusing?!?

Re:Huh?

[umafuckit]

I've heard this argument before, and I just don't get it. "Percent" means per hundred, as the word is derived from the Latin "per centum," literally, "per hundred." It's a natural frequency format, just as much as saying "1 in 10 people." It's saying "10 per 100" people. What's so confusing?!?

It's not confusing, it's just that many people don't do the conversion in their heads. Further, presenting the natural frequency is more useful for small percentages: e.g. 1 in 4,000 is definitely easier to digest than 0.025%

Re:Huh?

[dtmos]

It's not confusing, it's just that many people don't do the conversion in their heads. Further, presenting the natural frequency is more useful for small percentages: e.g. 1 in 4,000 is definitely easier to digest than 0.025%

1. What "conversion"?

2. What makes "1 in 4,000" easier to digest than "0.025%"?

Re:Huh?

[hey!]

Nobody is saying that 1-in-10 is mathematically different than 10%. It is heuristically more helpful to people with less mathematical competence.

When you're good at math, you naturally line up all the "givens" in a problem. You go over each one an interpret what it means, "So that means if I had 100 people, ten of them would prefer vanilla to chocolate..." It's like a wood carver examining a block of wood to find a good place to start cutting. You do this so automatically it seems intuitive to you, but it's actually the result of long training and practice.

To people who aren't as well trained in math, the "givens" look like an impenetrable wall of text, because the individual bricks in the wall don't instantly convey useful information to them. Well, of course they don't; you have to *think* about them, and the less accustomed you are to numbers, the more work it is for you for less certainty of reward.

But if you put a picture into peoples' heads, you give them an immediate handhold on the problem. It's not difficult for a mathematically fluent person to make his own handhold, but it is a stumbling block for a lot of people.

Re:Huh?

[Anonymous Coward]

"Percent" means per hundred

A lot of people don't even get that. The problem is innumeracy compounded by poor vocabulary.

Re: Huh?

[ahoffer0]

Exactly. Some people have no problem that kind of equivalency. A lot of people do. I'm glad this is getting some study by psychologists.

Re:Huh?

[gweihir]

2. What makes "1 in 4,000" easier to digest than "0.025%"?

Probably people being under the illusion they have an accurate image how many 4000 people are (for example). They do not.

Re:Huh?

[dtmos]

But if you put a picture into peoples' heads, you give them an immediate handhold on the problem.

So you're saying that the point is, if one replaces the term "10 percent" with "10 per hundred," people would understand the question better?

Re:Huh?

[Anonymous Coward]

Probably people being under the illusion they have an accurate image how many 4000 people are (for example). They do not.

Perhaps, but trying to imagine 4000 people is at least something I can attempt to do.

0.025% is just meaningless.

Re:Huh?

[hey!]

So you're saying that the point is, if one replaces the term "10 percent" with "10 per hundred," people would understand the question better?

Yes. I know it sounds weird, but it's really what you automatically do without planning when you approach a problem. But even if you're pretty good at math, having the problem stated in a slightly different way can help you when you're tackling problems that are hard for you. It's what a professor automatically does when a lot of students get stuck on a problem set question: he restates the problem in a way that enables the students to relate it to things they've already learned.

Re:Huh?

[Carrot007]

But if you put a picture into peoples' heads, you give them an immediate handhold on the problem. It's not difficult for a mathematically fluent person to make his own handhold, but it is a stumbling block for a lot of people.

Or in other words the usual people are all different and what one see/finds easy is not going to be what the next does. Apply this to everything and anything you won't go wrong!

If fact I find the opposite happens to me in this situation. Present some numbers to me and ask a question and I'm like fine. Tart it up with extra nonsence to help people form a picture (I'm looking at you stupid maths questions at school!) and I just stare blankly into the distance. I can usualy work it out (though I do find sometime removing the maths introduces ambiguity that other people do not see) but it takes me longer than if it were not there and longer than people that like it in that format.

Re:Huh?

[Calydor]

And then you boil it down to lowest common denominator, which is 1 in 10, yes.

Re:Huh?

[dtmos]

So you're saying that the point is, if one replaces the term "10 percent" with "10 per hundred," people would understand the question better?

Yes.

That's just sad.

What happens if you have a preamble to the question that defines "percent," e.g., "'Percent' means 'per hundred'"? Does that help?

Re:Huh?

[dtmos]

0.025% is just meaningless.

That's the kind of statement I don't understand. It's 25 out of 100,000 people. I mean, if moving the decimal point is such an advanced concept, how is it that the metric system is so successful?

Re:Huh?

[Anonymous Coward]

I used to draw colored ping pong balls from a box to demonstrate probability.

They're African-American ping pong balls, you insensitive clod!

Re:Huh?

[Anonymous Coward]

Have you heard the marketing story of a&w's 1/3 pounder versus mcdonald's 1/4 pounder?
Apparently many people thought they were getting ripped off and getting less meat with the 1/3 pound burger.

Re:Huh?

[Calydor]

You seem to be having trouble understanding that different people think in different ways.

Would it help with a preamble saying that other people are different from you?

Re:Huh?

[Anonymous Coward]

That way you give up one of the main purposes of the descriptive use of percentages, to compare them with other percentages in order to get an intuitively better understanding of the numbers involved. It's important to compare small probabilities of events to other small probabilities we take into account in our daily live, in order to get an intuitive grasp about how and whether we should act upon them.

Re:Huh?

[hey!]

Well, that's just another kind of "literacy" too. Everyone I think struggles with the fact that other people are different than they are; but I think quite a few people don't have any idea how different other people can be in their education and abilities.

Re:Huh?

[Kjella]

I think you vastly overestimate how well average people understand percentages and fractions.

"Alice's class has 30 pupils, where 10% prefer ice cream and 60% chocolate. How many have a different favorite?"
"Bob's class has 30 pupils, where 1/5th prefer ice cream and 1/3rd chocolate. How many have a different favorite?"

I think you'll be amazed to know how many can't find 9 and 14 without pen and paper. And a surprising number not even with pen and paper...

Re:Huh?

[mysidia]

I would rathter people just say "zero point 1" for 1 in 10, or "zero point zero zero zero two five" for 0.00025 (25 in 100,000).

When folks start spewing fractions like "1 / 4000" they cannot be compared mentally to other fractions like that have a different base, such as "276 in 4500".

Re:Huh?

[Anonymous Coward]

Because most people, especially now, have little physical grasp of numbers, beyond what they can count on their hands. Expressing numbers in ratios, rather than percentages, becomes much more meaningful when the percentage gets smaller and the numbers become indivisible by 2. 1 in 700 is much easier to grasp than 0.142%. To paraphrase George Carlin," think of how dumb the average person is, and remember that half of them are dumber than that."

Re:Huh?

[bzipitidoo]

Different views may sound trivial, but don't sell them short for that reason. There's the Linear Algebra concept of the Change of Basis, there's transforms such as the Laplace and Fourier, and more.

For a simple example, it is easy to multiply by ten in base ten. If we wanted to multiply by some other number, often, it could make sense to change the base. Easier to multiply by 2 if the numbers are represented in base 2.

Re:Huh?

[clovis]

It's not confusing, it's just that many people don't do the conversion in their heads. Further, presenting the natural frequency is more useful for small percentages: e.g. 1 in 4,000 is definitely easier to digest than 0.025%

1. What "conversion"?

2. What makes "1 in 4,000" easier to digest than "0.025%"?

I suppose it's because .025% is a poor choice of a way to express a value. Percent means parts of a hundred, and they make more sense when the values is between 1 and 100. When you're using percents that are far less than 1%, it is hard to get an intuitive feel for the relative size of whatever is being measured. Sure it's easy enough to do the conversion, but why not express it as a number that is scaled to the measurement in the first place.

It's sort of like when someone asked for the height of my son. I could say he is 0.0011 mile tall, and although you may have a good feeling for how long a mile is, you have no idea whether he is average, short, or tall until you've done the conversion.

Re: Huh?

[Anonymous Coward]

Yaeh, why say "one half" when you can say "50/100"? Anybody who doesn't must be terrible at math, so sad /s

Re:Huh?

[maglor_83]

And after you've done the conversion, you still have no idea because there are not enough significant digits.

Re:Huh?

[Anonymous Coward]

That's a huge problem. Some people never actually grok'ed percent, or division, or power, or exp, or e, or phi, or differential equations, or derivates of such.. Someone could actually be a good mathematician, but still have holes in their elementary understanding. Someone could be an excellent people person and make better estimates, but nobody ever knew why everything they touched turned to gold.

When you measure everything, you lose the value of everything.

Captcha: circus

Re:Huh?

[hey!]

In mathematics as an educational subject, learning each topic is to an unusual degree dependent on having a high degree of mastery of the prior topics. This means that in a mass educational system where students are put into a big room with a lot other students, missing a couple of topics can start an avalanche effect, the end result is the disaster of a person who "just can't do mathematics".

Any normally intelligent human being should be able to do math at a level which is quite rare in our society. The problem is that our educational system only produces mathematically literate adults as statistical outliers.

As for understanding and working with other people, it's only relatively recently that educators have figured out that teaching this should be on their agenda, and that remains controversial, so by in large student performance isn't measured and students aren't evaluated on their mastery of people skills.

Re:Huh?

[Anonymous Coward]

0.025% is just meaningless.

That's the kind of statement I don't understand. It's 25 out of 100,000 people. I mean, if moving the decimal point is such an advanced concept, how is it that the metric system is so successful?

0.025% carries a higher cognitive load than 10 in 4,000 or 25 out of 100,000 people. The latter two examples are easier to conceptualise as being very small numbers. What is 0.025% of anything? Difficult to visualise or conceptualise is the right answer for the majority of people.

Re:Huh?

[Anonymous Coward]

I would rathter people just say "zero point 1" for 1 in 10, or "zero point zero zero zero two five" for 0.00025 (25 in 100,000).

When folks start spewing fractions like "1 / 4000" they cannot be compared mentally to other fractions like that have a different base, such as "276 in 4500".

Yes, they can mentally compare 1/4000 and 276/4500 as (1 * 4500) / (4000 * 4500) versus (276 *4000) / (4000 * 4500). In each case the second ratio is larger than the first ratio but easier to compare mentally once transformed to a common denominator.

Re:Huh?

[Anonymous Coward]

I think you vastly overestimate how well average people understand percentages and fractions.

"Alice's class has 30 pupils, where 10% prefer ice cream and 60% chocolate. How many have a different favorite?"
"Bob's class has 30 pupils, where 1/5th prefer ice cream and 1/3rd chocolate. How many have a different favorite?"

I think you'll be amazed to know how many can't find 9 and 14 without pen and paper. And a surprising number not even with pen and paper...

In the examples the term favourite has two possible interpretations: 1. a favourite other than ice cream, or 2. a favourite flavour of ice cream other than chocolate. Therefore, the correct answer depends on interpretation of the question by the student and by the teacher; if their interpretations are not the same, then the student's response is marked wrong leaving the student confused.

Re:Huh?

[Ol Olsoc]

Any normally intelligent human being should be able to do math at a level which is quite rare in our society. The problem is that our educational system only produces mathematically literate adults as statistical outliers.

I think that it is just taught incorrectly. Back in Junior High, I seriously sucked at maths. Algebra was a struggle.

Then in High school, I had a teacher who insisted on us picking up and learning slide rules, even though they were rapidly becoming obsolete. The moment I finished my first lesson, it was like several locks in my mind opened - almost mentally painful. What was once a pain in the ass was now painfully but joyously obvious.

I don't know if it was just a fluke for how my particular brain operates, but the "mathemechanical" layout of a slide rule just changed everything. Now I can perfom a lot of stuff in my head with a sort of mental slide rule.

And when I see the outlandishly idiotic common core math, which would appear to be custom designed to make the subject as difficult as possible, I have to chuckle. Try giving the tykes a slide rule.

Re:Huh?

[preflex]

Yeah, so?

Mean, median, and mode are all types of averages.

Perhaps the "even dumber than that" segment of the population includes you.

Re:Huh?

[Anonymous Coward]

Because most people, especially now, have little physical grasp of numbers, beyond what they can count on their hands.

I don't know about you, but I can count to 1023 on mine.

Re:Huh?

[Anonymous Coward]

We do not learn logic along with the mathematics in schools. Natural language with deductive logic- from generalization to specificity, is used in arithmetic. There you go the steps one at a time and come back to the conclusion. Where as starting with Algebra, Calculus, Geometry, Statistics and higher mathematics involve inductive reasoning - from specificity to generalization is not explicitly taught but implied. Algebra does not say, that if you have two different homogeneous groups of things and there is a common name for the collection, such as pile of Bananas and pile of Apples , the common name is Fruits, thus you can only state bunch of Bananas + bunch of Apples and not say either bunch of all Bananas or all Apples. Thus, symbolically you can say for example, 5B + 6A and not 11Bs or 11As. So when we learn a natural language we learn about proper names and common names, but it is never brought back in the Algebra classes. It the same problems appears in Statistics too. Both the deductive logic such as, since all the items or objects or variables are of the same kind, we can and their coefficients or numerical adjectives and that is called counting. Arithmetic involves counting. Subtraction is complemented addition, multiplication is an abbreviation for successive addition, exponentiation is a shorthand (abbreviation) for self multiplication, factorial is decreasing multiplication. The mathematics research talks in his domain of language he or she may create using a subset of a natural language, but the teacher has no intuitive understanding of the underlying mathematician's knowledge. That we lean through “what and how” - the knowing part, but not the “why- the understanding part”. Mathematics text books are horrible because they have knowingly or unknowingly made the assumption which are not in general, stated explicitly. This study confirms this way of reasoning. For example, a natural language based single topic can be easily composed using deductive logic. But when you have to write an essay, you need to have composition course which involves inductive reasoning. That is not extended to teaching mathematics. This frightens the majority of people. Finally, a house wife is a mathematician – arithmetic she uses when she is buying things, algebra when she makes salad, or common noun based objects, calculus when she buys milk, oil, etc. and topology when she arranges her cooking pots, dresser, spices and so on. But what happens to them when they take mathematics courses?

Re:Huh?

[Anonymous Coward]

Nobody is saying that 1-in-10 is mathematically different than 10%. It is heuristically more helpful to people with less mathematical competence... To people who aren't as well trained in math, the "givens" look like an impenetrable wall of text...

“Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.”

Robert Heinlein

Re:Huh?

[Anonymous Coward]

Division is a non-trival operation and multiplying fraction is a non-trival consequence.

Re:Huh?

[Anonymous Coward]

In mathematics as an educational subject, learning each topic is to an unusual degree dependent on having a high degree of mastery of the prior topics. This means that in a mass educational system where students are put into a big room with a lot other students, missing a couple of topics can start an avalanche effect, the end result is the disaster of a person who "just can't do mathematics".

Retired teacher's rant: this is a direct consequence of not allowing a student to repeat subjects in school because "everybody passes".

Re:Huh?

[Anonymous Coward]

In the examples the term favourite has two possible interpretations: 1. a favourite other than ice cream, or 2. a favourite flavour of ice cream other than chocolate. Therefore, the correct answer depends on interpretation of the question by the student and by the teacher; if their interpretations are not the same, then the student's response is marked wrong leaving the student confused.

(Ranting retired teacher AC again.)

Only if they don't show their working. If the way they get their answer is valid (eg they say "a favourite other than ice cream" or "a favourite flavour of ice cream other than chocolate") the student's response is marked correct (unless they slip up somewhere, eg 30/5=7, in which cast it's marked "mostly correct").

Re:Huh?

[Anonymous Coward]

We do not learn logic along with the mathematics in schools.

Nor apparently, how to use paragraphs and line breaks to render text readable.

Re:Huh?

[tlhIngan]

2. What makes "1 in 4,000" easier to digest than "0.025%"?

0.025% is not a "people friendly" number. It's a tiny fraction that most people will never see in their lives.

As an example, show me 0.025% of something. Anything. Perhaps 0.025% of a TV. Or a cup of water. Or your phone's storage. It's hard to visualize simply because it seems to imply "a portion of".

But 1 in 4000 is more "people friendly" because you're not asking a tiny part of something, but now one unit in a bunch of units. You don't show me 0.025% of a cup of water, but 1 cup of water in 4000 cups. I can't instinctively grasp 0.025% of a cup of water, but I can see a cup, and think I see 3,999 more.

Think of it this way - we are taught percentages as fractions of a whole. 50% of a cup of water is half a cup. But 1 in 2 cups is 1 cup full of water and 1 empty cup. When your percentages get smaller, it's harder to visualize the tiny part of the whole, but easier to recognize a whole as part of a bigger group.

And yes, "people friendly" units are very useful. It's why you see storage often measured in CDs and DVDs. And it's easy to confuse - even in the metric system. Take mass for example, it's measured in grams, But you can grasp 1,000 kilograms more readily than if it was stated as 1 Megagram, despite both being the same mass. "Kilogram" is a people unit - everyone's handled kilogram massed things in their lives.

Re:Huh?

[thegarbz]

1. What "conversion"?

Multiplication.

2. What makes "1 in 4,000" easier to digest than "0.025%"?

If you're asking this question then you don't understand the human mind in terms of it's ability to visualise and process numbers. That isn't a bad thing, it's probably that you are smart and surround yourself with smart people, but it always pays to understand how to talk with people who aren't so clever.
Simple tip: No decimals, base number of 1 as the lowest common denominator. Everything else should be stacked in terms of a 1. It is intuitively easier to understand for everyone than presenting something that needs to be multiplied from a factor of 1/100th.

Re:Huh?

[Anonymous Coward]

Partly this is due having no need to calculate percentages oo their "daily basis" and even scientists from hc side of stuff forget quickly how to do the maths...
among professions i've personally observed that people who work constantly on stuff that needs % is farmers when they mix feed and optimize growth... those are the ones that can actually "talk" with % and really understand... next from farmers is perhaps theoretical physics guys.... and yes i didnt account statisticians for a reason :D

Re:Huh?

[houghi]

Well, in non-metric it would be 25/100000th or 1/4000th. That is much better. /s

Re:Huh?

[houghi]

If you tell me somebody is 0.0011 km tall, the conversion is done pretty quick. You just move it 3 decimals and you have meters. The conversion is not instantly, but not a real issue either.

A better comparison would be 100 000 seconds is how long? Is that hours, or days?

Re:Huh?

[cascadingstylesheet]

But if you put a picture into peoples' heads, you give them an immediate handhold on the problem.

So you're saying that the point is, if one replaces the term "10 percent" with "10 per hundred," people would understand the question better?

Even better if you say it as "1 out of 10".

There is a certain (small) number of objects that people can sort of intuitively grasp. More than that, and it becomes an exercise in abstract thought, not concrete thought.

Above that small number, the numbers become symbols, and symbol manipulation capability is almost a synonym for IQ.

Re:Huh?

[GLMDesigns]

Well. We all know that there are 86,400 seconds in a day. So it's roughly 1 1/7 days.

Duh

Re:Huh?

[gotan]

That's not it.

It's easier to grasp what to do to those numbers. Presented with percentages it's often hard to see what mathematical operations are necessary to arrive at the desired answer in bayesian statistics problems.

E.g.
A medicinal test for disease X gives false positives in 0.1% of cases. It gives a false negative in 1% of the cases (i.e. correct positive in 99% of the cases). The disease afflicts 0.01%.
Of those tested positive, how many have disease X.

Of course one now could employ the statistics toolbox to solve that problem. OTOH one could compare the 10 in 10,000 false positives (with a slight error since only 9,999 are without disease), to the 1 in 10,000 diseased (noticing that the false negatives have negligible impact for the question at hand and we can work with 100% correct positives as well as 99% if we want an estimate).

So now we need to compare only small numbers, 10 false positives to 1 diseased positive or 1 in 11 which is about 9%.
(the correct result without the approximations is 10 in 111 or 9,009...%).

Also note the easy expansion of 1 in 1,000 to 10 in 10,000 to get to comparable numbers. It's not important to have an accurate image of those 10,000, what's of interest is to compare the 10 false positives to the 1 diseased.

Such medicinal tests help a lot to find candidates that should undergo more sophisticated (and much more expensive) tests, to see if they really have X (it'll reduce the expensive tests by a factor of 1,000), but patients need to be informed even with a "positive" result it's still unlikely that they have X, but advisable to do the more sophisticated test. One might think that the test is pretty useless if it delivers 91% false positives when in fact it is pretty accurate, only the occurence of disease X is so rare.

So such "frequencies" do not only help to get a (pretty) correct result without knowing any bayesian statistics tools, but also to understand how the information affects the result, and how the unintuitive (to someone not used to such statistics) result comes about.

Re:Huh?

[Anonymous Coward]

It's not confusing, it's just that many people don't do the conversion in their heads. Further, presenting the natural frequency is more useful for small percentages: e.g. 1 in 4,000 is definitely easier to digest than 0.025%

The problem here is that you use an edge case to support your comment. The percentage can be well represented between 1%~100%.

Percentage has its used. The problem is the education in the U.S. has been attempting to simplify the way mathematics is taught. As a result, the maths is taught in what "they think" is "make sense" but not what it is. To understand maths, the real challenge is to get kids to understand the fundamental of the subject. The education in the U.S. does the opposite -- teach to understand the result only. As a result, people don't understand maths when it gets to higher level. Just remember, percentage is under arithmetic which is the lowest level of mathematics.

Re:Huh?

[Anonymous Coward]

One of my biggest frustrations from my Jr High school days was when the teacher would give us a choice, either 10 word problems or 50 traditional ones.

I was always out-voted. I could finish 10 word problems before the class ended and would have no work to take home but deciphering those word problems was so difficult for many of the others that they preferred 5 times more work.

Re:Huh?

[Anonymous Coward]

Obviously 0.352 rods is about average.

Re:Huh?

[Anonymous Coward]

Yes, the mean, median and mode are all types of averages, they are not, however, what a typical layperson means when they say average. The typical layperson means mean when they say average.

In fact, most people don't even know what those other things are, let alone have any hope of calculating them.

Re:Huh?

[Anonymous Coward]

It's not any easier, Trying to imagine 4,000 people isn't as easy as you're making out. And it really misses the point, you shouldn't be visualizing these things. If you see a number like 0.025% you should be thinking that it's a relatively rare event. Similarly, if it's written as 1 in 4 000 it's still a relatively rare event.

Unless the event is so rare that you start having large numbers of zeros popping up between the decimal point and the non-zero numbers in the percentage, there just isn't any benefit to writing it the other way. Either way, you have to figure out how rare it is. This is just an example of rationalizing a lack of numerical literacy.

If you actually cared about the numbers, you probably wouldn't be representing them this way as they don't really do much for you without other information to help normalize the results.

Re:Huh?

[shaitand]

Okay, I see a lot of people missing the point here and a lot of people for who it is so obvious they can't explain it.

First, understanding how to move a decimal place does not mean doing so in tens with such frequency that it is automatic. Especially with large and small decimal numbers. It becomes very easy to be off by an order of magnitude as you get lost in a sea of zeros.

Second, percentages are used to express probability. They are not blind numbers on a page, to grasp them you must associate them with something. In the case of 4000 or 4500 the something can be just about anything you've interacted with that is a set of roughly 5000. Of course you can conceive of that, it's a small town. To say 1 in 4000 is comparable to one guy in a small town and 276 is comparable to a large church. How hard was that? 0.00025... ummm no, that isn't a number you actually encounter in life. All you can say about 0.00025 is that it is "really small" and out of context there is no definition or concept of how small. 25 in 100,000 is though, that is the change of a given dollar a middle class worker earns being the one he spent at the mexican place Friday or 25 people in a small city.

Re:Huh?

[Anonymous Coward]

This is why in some languages like Mandarin they give you the bottom first then the top. So, it's roughly translated as 4000 dividing 1. As I've just stated it is possible to do it in English, I have no idea why 4000 dividing 1 hasn't become a common way of expressing the idea as the size of the bottom number is essential to knowing what the result should be. 1 / 2 is a fairly large portion of the total, but 1 / 1 000 000 000 is frequently a rounding error.

Re:Huh?

[Anonymous Coward]

The problem is that we've been trying to math more girl friendly at the expense of making it more or less useless. That's where the focus on having things make sense without adequate consideration of consequences.

We fail to point out that there are numbers with and without units until quite a ways on and it makes the process of multiplication rather confusing, especially when the numbers have units which aren't being written while doing a problem. The result is that students don't really know when the units change or don't. This is a fairly big problem as the units are a part of what decides what numbers can be added together and which ones can't. Typically we'll talk about like terms in terms of the variable attached, but it's more than that.

Putting something in for the variable doesn't necessarily make it any better. You can still wind up with unlike terms even after putting the same type of number into the variable if you haven't been careful. This is a problem that crops up regularly in physics if you're trying to use the wrong equation and trying to use numbers that aren't appropriate.

Re:Huh?

[Anonymous Coward]

This is true. A lot of people with "learning disorders" don't have learning disorders, they received poor quality of education. Sometimes when you have a student that's not doing their work, failing to remember what to do, writing it poorly or staring off into space through the classes, that isn't a learning disorder it's a bad teacher or series of bad teachers. That can also be a learning disorder, but without being in the classroom it can be tough to tell.

The math covered through the first year of college, at bare minimum, is something that virtually every student can do provided they aren't suffering from profound learning disorders or cognitive disability. And yet the number who never get that far is a pretty large percentage of the US population at present.

A lot of that comes down to letting women teach so many of those early math classes without having had any of those later ones. If you don't take the later ones, then you can easily focus on making things comprehensible in a way that fucks the students over in the future. There should be a broad goal of moving students from the concrete to more and more abstract as time goes on. A typical student in elementary school can handle limited abstraction, which is why it's typical to first show algebra using something like 4x_=12 where the answer is 4x3=12. Putting an actual variable in rather than the blank can make it impossible for students of that developmental level to solve.

I've been doing math professionally for years now and I can handle very abstract concepts without much issue in most cases. If it's a new technique, I mostly need it spelled out step by step so that I can analyze it myself for the little gotchas and the practical domain of what I can use it for. And for composition of functions, I'm rather adept at looking at each nested bit as being a bit like it's own dimension on it's own coordinate systems so that I can slice it like that rather than just with respect to the original axes.

Re:Huh?

[Anonymous Coward]

No, that was even worse. This is a consequence of passing students without providing extra support to catch up. Having students repeat grades or topics accomplishes very little if you're not making changes to how it's being taught.

Unfortunately, as intuitive as it is to assume that students being retained to take the class again should lead to improvement, the research doesn't bear it out. The right thing to do is to pass the students and then offer whatever service is needed to get the students caught up.

Re:Huh?

[Ol Olsoc]

This is true. A lot of people with "learning disorders" don't have learning disorders, they received poor quality of education. Sometimes when you have a student that's not doing their work, failing to remember what to do, writing it poorly or staring off into space through the classes, that isn't a learning disorder it's a bad teacher or series of bad teachers.

And my algebra teacher was just that - bad. In addition to struggling, I was so bored that I wanted to scream. And the assholes in school and my parents were just "You're such a smart boy Ol, but you're lazy and don't apply yourself."

Dare I say that they were abysmally stupid assholes? A guy gets A's in everything else, and struggles with maths and anything beyond, and it is because he is lazy?

Then that slide rule epiphany .

And the aftermath was not all roses and honey either. I then understood that not only were they too stupid to allow me to learn, but that I was actually smarter than almost all teachers are. And I have not abandoned that fact - aside from the guy who found my problem, I developed an attitude against schoolteachers that continues to this day. My grades went up, my attitude shifted to getting all of my maths and above on my own, and virtually ignoring the assholes who should never have been teaching it in the first place. Took a while to develop a little humility to replace the low key anger.

Re:Huh?

[mysidia]

Especially with large and small decimal numbers. It becomes very easy to be off by an order of magnitude

You should be able to deal with zeros, but if you hate them, the solution is not to write things like 0.0025% for 1 fourty-thousandth --
you can write: that the fraction was 2.5E-4 and that's perfectly fine.

Second, percentages are used to express probability. They are not blind numbers on a page,

Probabilities Are by definition simple blind numbers on a page --- rational numbers no less than zero and no greater than unity or 1.
The symbols %, , and are merely shorthands for:
the fraction of 100, 1000, and 10000 respectively, with this number as the numerator.
Writing "10%," ".1," "1E-1," "1/10," "2/20," "1:10," "one tenth," or "1 in 10" each refer to exactly the same number, and have exactly the same meaning.
This is one of the first things schoolchildren are taught about the using %s, along with exercises in converting the shorthand into the represented fraction and to standard numerical notation.

All you can say about 0.00025 is that it is "really small"

That's not true... you can see the 25 in there and recognize that there is a 1/4th sitting in this number;
25 to 1/4 is one of the decimal to fraction conversions the schools drilled into students in the 3rd grade
to instantly recognize - (How else would you remember what 25% means or that a quarter equals 25 cents?).

Everybody knows what a fourth of an apple pie looks like. Now see those 3 zeros in front of it;
that means you should imagine sharing one fourth of a pie equally with 1000 people ---- like
all the people who came to the stadium to watch a football game, and .00025 is one person's share of that fourth of pie.

You're starting from an extreme bogus premise though --- the 1 in 4000 should not be associated with "one guy in a small town"; because
that's a misleading view of what the figure measures, etc, Besides it is extremely unlikely one person has ever seen all the people in
a small town --- that is in fact just as abstract an idea as 0.00025 is. Furthermore; the purpose of reading values from statistical data
is not to compare them to arbitrary quantities of things in the real world unrelated to what the statistics
are about, but to compare them to other statistical values within the same or other study.

When polling data is presented, for example --- the purpose of reading the numbers is for making
relative comparisons between the different options in that poll.

If you say 1 in 4000 chose option A, 1 in 3000 chose option B, 1 in 75 chose option C, and 1 in 2855 chose option D.
It becomes very obnoxious to try and compare these figures, because essentially: different units of measurement have been used each time.

It's like quoting the measurements of a building as 182 meters long by 300 pumpkins wide by one fourtieth of an eifel tower high.

That may sound like it makes it easier for someone to visualize the measurement, but it is sure as hell a majorly problematic way and imprecise way of describing things.

Re:Huh?

[shaitand]

"That's not true... you can see the 25 in there and recognize that there is a 1/4th sitting in this number;
25 to 1/4 is one of the decimal to fraction conversions the schools drilled into students in the 3rd grade
to instantly recognize - (How else would you remember what 25% means or that a quarter equals 25 cents?)."

Okay, yet again someone explaining the math as if anyone didn't understand it. Nobody is confused about the math. If nothing else at least acknowledge that it makes little to no sense to arbitrarily add an extra conversion to 100th's on every number instead of expressing the actual decimal place.

"Besides it is extremely unlikely one person has ever seen all the people in
a small town"

They don't need to, they need to know how likely they are to bump into someone picked out of a hat when they go to the store. Something they can get a sense of intuitively in an analog fashion because they experience and calculate those probabilities every single day, thousands of times a day. Present it in that way and they will immediately start thinking of the right questions like realizing the time period matters, things which can impact the result like events that would cause people to be more likely to head to store at the time, specific factors that could make one person more likely to go to the store, the understanding some of those factors could be short lived and skew the value in a smaller sample set, etc.

That is the point, just like geometry, algebra, trig, etc people are walking around with super computing power in their brains. Doing the math is easy in that they are already intuitively doing it, connecting our formalized system with the trained neural chains patterns which already exist in their brains in more efficient in formats that directly relate to natural group counts. It isn't that we don't know they are all just different ways of writing the same value.

Re:Huh?

[GuB-42]

Percentages outside the 0.1-1000 range can be very confusing, at least for westerners. We tend to group numbers by thousands, not hundreds, and percentages with a large number of digits are a mix of both. For example 10000% is x100, even though we spell it TEN thousand percent.
And 0.00025 is less confusing than 0.025%, at least for me, because I can almost see the 100000 in the 0.00025 as they are both around the same length.

What is Winter Sunlight?

[Anonymous Coward]

Your fixed mindset has led you to ignore it. It will soon appear in the northern latitudes; but what causes it, and what is it?

For this reason, God sends them a powerful delusion(operation of wandering)(planet) so that they will believe the lie.
IPFS

Re:What is Winter Sunlight?

[Anonymous Coward]

Your fixed mindset has led you to ignore it. It will soon appear in the northern latitudes; but what causes it, and what is it?

For this reason, God sends them a powerful delusion(operation of wandering)(planet) so that they will believe the lie.
IPFS

You're the guy with those videos. I remember you got me to watch one of the eclipse, and I was all like, "Yup, that's an eclipse."

I'm assuming you have some point, but are just really bad at getting it across. Something about God apparently. Talking about God is a lost cause unless the person you're talking to is already stupid enough to believe in God.

So you're not convincing anyone.

Re:What is Winter Sunlight?

[Anonymous Coward]

Watch the Winter Sunlight.

For those with eyes to see, let them see.

Who takes statistics?

[Anonymous Coward]

Statistics is typically a course for students in social and political sciences, psychology, communications, economics etc...

These are in general not the students with a strong interest or background in mathematics.

In reality, statistics is one of the most easy parts of mathematics, and in my experience as a statistics lecturer the main reason why so many students struggle with it is that those students who get to take it often have an aversion of everything mathematical and have (with the exception of the economics students) no other mathematics classes in their curriculum.

Re:Who takes statistics?

[Anonymous Coward]

Statistics is typically a course for students in social and political sciences, psychology, communications, economics etc...

And for students in maths, chemistry, physics, biology, engineering, geology, agriculturural science, environmental science... it seems you were unfortunate in your alloted classes.

Not people. *Robots*.

[Anonymous Coward]

This is a problem for a certain kind of ... people.
Those who are ideologistic instead of curious. Those who call everyone who changed his views because he learned something new a "flip-flopper" too. (And not just those who say whatever pleases the listener of the day.)

Those who are dumb enough that they don't know the constant stream of doubt that comes from constantly coming up with all the things that something could be wrong.

Which is, sadly, true for a much bigger part of the population than we'd like to admit.

But please don't act like it's a normal, human thing.
It's a thing of extreme stupidity. "Voter"-level stupidity. Opinionator-level stupidity. Believer-level stupidity. Triggered-passive-thinker-level stupidity.

It may be the norm where you live. It may even be the norm where I live. But unless we want to flop over, give up like losers, and act like the Idiocracy is a done deal, ... it's not what we should ever call normal.

I find it the other way round

[gweihir]

Percent is and its cousins are fine, but "natural frequency" is anything but "natural" to me. I have to convert it to make sense of it.

Also "jury friendly"? Does "success" here mean to get a conviction?

Re: I find it the other way round

[ahoffer0]

Success is a conviction or aquittal, depending on your interest in the trial. I know which one defendants is hoping for.

Re:I find it the other way round

[i.r.id10t]

"You've got to remember that these are just simple farmers. These are people of the land. The common clay of the new West. You know... morons."

Re:I find it the other way round

[gweihir]

Nice quote!

What century?

[Anonymous Coward]

the 21st century

As soon as you pick up a newspaper

These don't seem to go together at all.

Interesting stat

[Anonymous Coward]

OK. You know who you are. And so does President Trump--the pinkos, the beta males, the bull dykes, the sniveling femme boiz, the snowflakes, the amigos, and chocolate drops. He sees you. He tracks you. And he's coming for you. It is better that you flee the country and live out your life in a socialist paradise like Venezuela.

Make no mistake. President Trump is here, he chews up his enemies, and passes chunks of them in his stool. If you are his enemy, you may well be the next chunk in the porcelain bowl.

Was it natural frequency format,

[mark_reh]

or did they also avoid using words with more that 5 letters? #MAGA!

Re:Was it natural frequency format,

[Anonymous Coward]

#MUGA!

Re:Was it natural frequency format,

[Anonymous Coward]

or did they also avoid using words with more that 5 letters? #MAGA!

FWEE STUFZ!

Obama, 2015: Those jobs are never coming back

<Trump wins, jobs start coming back>

Obama, 2018: I built that!

Yeah, sure, JugEars. Sure you did. But YOU got to keep your doctor, didn't you? You lying sack of shit.

Re:Was it natural frequency format,

[Anonymous Coward]

We can do it in 3 letters:N, P and C

"Orange man bad", version 263

printf(get.statement(ReesistVariation(263)); //"Orange man bad" in one of the predefined forms in the console

Statistical weakness: people ignore the grave fact

[Anonymous Coward]

...that homosexuals are upwards of 10 times more pederastous than straights.

"The proportions of heterosexual and homosexual pedophiles among sex offenders against children: an exploratory study" by Freund K. & Watson RJ., https://www.ncbi.nlm.nih.gov/pubmed/1556756

Abstract:
Previous investigations have indicated that the ratio of sex offenders against female children vs. offenders against male children is approximately 2:1, while the ratio of gynephiles to androphiles among the general population is approximately 20:1. The present study investigated whether the etiology of preferred partner sex among pedophiles is related to the etiology of preferred partner sex among males preferring adult partners. Using phallometric test sensitivities to calculate the proportion of true pedophiles among various groups of sex offenders against children, and taking into consideration previously reported mean numbers of victims per offender group, the ratio of heterosexual to homosexual pedophiles was calculated to be approximately 11:1. This suggests that the resulting proportion of true pedophiles among persons with a homosexual erotic development is greater than that in persons who develop heterosexually. This, of course, would not indicate that androphilic males have a greater propensity to offend against children.

2 veils.
0: elementary fractions + lie
1: lie.

0: The homosexual is notoriously bad at math & logic, so you speak elementary fractions and introduce an inconsistency. He won't get what the fractions say and will be satisfied with "This, of course, would not indicate that androphilic males have a greater propensity to offend against children" for, after all, it's the last sentence in the abstract even though the one just preceding it is "This suggests that the resulting proportion of true pedophiles among persons with a homosexual erotic development is greater than that in persons who develop heterosexually"... This veil will allow the paper to get past homosexual censorship.

1: The second veil serves the purpose of arousing the suspicion of the heterosexual who overcame the first veil. For, the present study, owing to "the ratio of gynephiles to androphiles among the general population is approximately 20:1" and "the ratio of heterosexual to homosexual pedophiles was calculated to be approximately 11:1", pretends that *the ratio of homosexual pedophiles to homosexuals is but twice that of heterosexual pedophiles to heterosexuals*.

Proof:
F: faggots
S: straights

S/F = 20/1 = 20

FP: faggot pederasts
SP: straight pederasts

FP/SP = 1/11

We want an x such that FP/F = x * SP/S
x = (FP/F)/(SP/S) = (FP/F)*(S/SP) = (FP/SP)*(S/F) = (1/11)*20 = 20/11 ~ 2
Thus FP/F ~ 2 * SP/S
QED.

But the previous study reports "just" twice as many girls stabbed as boys. This can only raise the attentive reader's eyebrow for we are told in that paper that there are 20 times as many straights as there are faggots.

Let us compare the faggots' voraciousness* for children with that of straights.

"Previous investigations have indicated that the ratio of sex offenders against female children vs. offenders against male children is approximately 2:1"

X: girls stabbed
Y: boys destroyed

Y/X = 1/2
We want an y such that Y/F = y * X/S
y = (Y/F)/(X/S) = (Y/F)*(S/X) = (Y/X)*(S/F) = (1/2)*20 = 10
Thus Y/F = 10 * X/S i.e., *the faggots are 10 times more pederastous than straights!*

This is alarming for a paper from 1992. How much worse is it now...

* I called it voraciousness for children of the respective classes. The harm caused against children isn't diminished, whether it be a recidivistic faggot or many faggots.

If you were to object that women may also be pedophiles...

"Pedophilia and heterosexuality vs. homosexuality" by Freund K., Heasman G., Racansky IG., Glancy G., https://www.ncbi.nlm.nih.gov/pubmed/6512871

Abstract:
In the context of a search for testable etiological theories of pedo

Radical shift in curriculum

[ahoffer0]

I've thought long and hard about this problem. After wrestling with it for a few years I'm ready to support a radical shift in public education.

Use the term "math" (or "maths", depending on your version of English) to refer to arithmatic, geometry, and algebra
"quantithinking classes".

Dump trigonometry and calculus from the curriculum. Replace with statistics, probability, design of experiments, and critical thinking. Call this new subject "quantitative thinking" (or whatever name you want) and give it equal billing as as language, math, science, literature, and physical education.

Re:Radical shift in curriculum

[Anonymous Coward]

Exactly this. Statistics and various things like it; Combinatorics basic logic and so forth - would be far more valuable to the average person than trig and calculus can ever be.

Re:Radical shift in curriculum

[Anonymous Coward]

...Dump trigonometry and calculus from the curriculum...

Science and engineering majors will burn you in effigy.

I'd like to add to your post w/ fact... apk

[Anonymous Coward]

See subject & as to WHO that enemy is? Take an INFORMATIVE fact-backed READ here https://it.slashdot.org/commen... & be further enlightened (the thing a devil or germ can't stand is being EXPOSED TO THE SUNLIGHT OF TRUTH/FACT he cannot defeat via his "babylonian money-magic deceits").

APK

P.S.=> I agree w/ MUCH of what you say (except for "amigos" & 'chocolate drops' parts - some may be criminals & WHY is in the post prior to that one's conclusions (bad upbringing, no guidance, POSSIBLY shit character to start w/ though & ENVIRONMENT that breeds criminals)) & on THAT note?

Quote StarWars: "Once you start down the dark path it will FOREVER DOMINATE YOUR DESTINY" & that's an INDIVIDUAL thing... apk

Intuitive And Jury Friendly

[tsqr]

Recent studies have shown that performance rates on many statistical tasks increased from four percent to 24 percent when the problems were presented using the natural frequency format.

Hmm, let me make that more intuitive and jury friendly for everyone: recent studies have shown that performance rates on many statistical tasks increased from 1 in 25 to about 1 in 4 when the problems were presented using the natural frequency format.

Re:Intuitive And Jury Friendly

[alvinrod]

Wouldn't it be even better (or at least more intuitive) to say it went from about 1 in 25 to about 6 in 25? If it hurts your head too much to deal with the percentages, I would imagine that converting the fractions would be just as confusing for a large subset of that group.

Re:Intuitive And Jury Friendly

[Anonymous Coward]

1 in 25 isn't a success rate, it's a measure of odds. Guess your stats knowledge isn't up to par either.

Re:Intuitive And Jury Friendly

[tsqr]

Actually, I'm just fine using percentages. "4 out of 5" is for dentist endorsement of toothpaste.

Re:Intuitive And Jury Friendly

[Anonymous Coward]

1 to 25 is an odds ratio, 1 in 25 is a success rate.

Re:Intuitive And Jury Friendly

[Anonymous Coward]

Chewing gum.

And I always heard that commercial to say that 4 out of 5 dentists were willing to admit that if the patient were going to chew gum, that sugarless gum was not as bad as sugared gum.

1 out of 5 dentists were willing to say "if they are going to ignore my advice not to chew gum, why do I care whether it has sugar or not?"

Re:Intuitive And Jury Friendly

[Anonymous Coward]

1 in 25 isn't a success rate, it's a measure of odds.

No, it's a measure of probability. Odds, by contrast, state success to failure. Thus a probability of 1 in 25 (1/25) expressed as odds that would be 1 to 24 (1:24).

Guess your stats knowledge isn't up to par either.

Posting as AC might have been the smartest thing you did today.

Re:Intuitive And Jury Friendly

[Anonymous Coward]

They could have just said that the number of correct responses to 25 questions increased from 1 to 6 and just left ratios out completely.

Further addendum... apk

[Anonymous Coward]

See subject: Many of the groups you point out are 'downtrodden' (many times due to their own doing - after all we cause 90% of our own problems in reality thru bad decisions or deceitful 'guidance') & EASY to recruit by those seeking power to use them for "strength in numbers" enmasse (gang mentality) but they're REALLY only cannon-fodder in the end - disposable assets NEVER INTENDED to be in the "upper echelons" etc. (just bullet-bags + sacrificial lambs (or should I say pigs instead by the viewpoint of their "masters" in the pyramid scheme who you NEVER SEE (they rely on that the MOST, hiding in the shadows "Wizard of OZ" pay no attention to the man behind the curtain style as cowards & weasels do)).

* ADDENDUM to my other post (good source in it) https://science.slashdot.org/c... DO READ IT!

(For your OWN sake & make your OWN determinations)

APK

P.S.=> It's a PITY they can't SEE IT FOR THEMSELVES though (but that's what the "devil" preys on the MOST - ignorance, he has ALL the cards & you don't so he runs the game & runs YOU into the GROUND (his goal))... apk

Presentation Bias?

[Anonymous Coward]

Article ignores presentation bias. Natural frequency format is oftwn a sign of cherry picking the sample that tells the desired story.

9 out of 10 people like the Cubs.
9 out of 10 [specific] people [we interviewed in Chicago] like the Cubs.

Re:Presentation Bias?

[Anonymous Coward]

Natural frequency format is oftwn a sign of cherry picking the sample that tells the desired story.

Reminds me of the old joke: "9 out of 10 physicians say smoking is good for your health ... mind you it too a really long time to find those 9 physicians."

But no, not really, you can do exactly the same with percentages, 90% of people like the Cubs (based in same sampling) ... I've seen recenty something along the lines of 80% of X report having experienced Y, in summing up the results of a voluntary on-line survey, when it should be 80% of X who were motivated to respond (where having experienced Y is among the main motivators) to the survey reported ...

More frequently still people (esp. politicians) mislead by not using statistics, but raw population figures, because those figures without context sound really frightening (but are essentially meaningless).

Re:Presentation Bias?

[jbengt]

9 out of 10 [specific] people [we interviewed in the north side of Chicago] like the Cubs.
FTFY

Do sports fans understand this any better?

[140Mandak262Jamuna]

Sports channels are obsessed with statistics. They constantly project before every field goal attempt, every extra point kick, the stats about the kicker. 28th attempt this season, 62% success rate, life time 433 attempts, 73% success, league average 75% ....

Being exposed to so much of this statistics, do sports fans use these in their real life? When they buy a car and they read a review, "10% chance of major repair in five years" do they think as often as "that kicker misses extra point"?

Re:Do sports fans understand this any better?

[Bert64]

You're more likely to learn something if the subject is interesting to you...
So for many people, "math" might be perceived as boring, while they like "sports"...

Re:Do sports fans understand this any better?

[Gilgaron]

Are there more sports nerds than math nerds, though? Mostly it gives the commentators something to say, probably just the Fantasy Football guys would be interested in keeping their spreadsheets up to date at home.

Polls are decided by who counts the votes.

[Anonymous Coward]

not by who casts the vote.

Even more jury-friendly ...

[fahrbot-bot]

... since 1-in-10 a more intuitive, jury-friendly approach.

Which would be 1-in-12.

alternatives

[supernova87a]

Maybe:

1) People who can't understand statistics shouldn't be put in charge of important decisions (un-democratic, I know), or

2) Statistics education needs to be made mandatory to qualify as high school educated in this country.

Re:alternatives

[yodleboy]

A semester of statistics and a semester of geometry would be much more beneficial than the typical full semester of geometry to the majority of high school students.

Re:alternatives

[Anonymous Coward]

stats help predict reality.. they don't define it. societies run by statisticians are tyrannical hellholes for individual initiative.

Psychology is bunk

[Anonymous Coward]

Less than half of their "experiments" can be reproduced, so it's not science, it's opinions.
Their ignorance is to blame.

Lies, Damn Lies and Statistics

[Anonymous Coward]

Pick up a newspaper and be inundated with: small sample sizes, biased sample selection, intentional elimination of contrary samples, samples fabricated from whole cloth, incorrect conclusions, bad controls handling, and about a million other sins against data accuracy.

There's just too much money available to researchers being paid to deliver desired results (i.e. want us to prove sugar is healthy? No problem!). Whether it be for politics, product/drug research, agribusiness, whatever. The incentive to cheat is way too large, and there's no counter-balancing incentive (of similar significance) against cheating. Don't believe ANYTHING you read - someone was paid to make you believe it.

Bound for failure

[reanjr]

If you can't figure out 10% is 1-in-10, you have no hope of wading through the standard level of obfuscation added to any publication when discussing statistics.

Re:Bound for failure

[Anonymous Coward]

Especially since the goal of statistics, in many articles, is to lie and mask the truth.

Re:Bound for failure

[Anonymous Coward]

Statistics are great when you don't measure. Grades in school naturally tend to be pretty stable and follow standard distributions. When you measure it though, teachers start inventing and grading based on gaussian distribution. So the tail start wagging the dog.

Re:Bound for failure

[Anonymous Coward]

If you can't figure out 10% is 1-in-10 ...

... you probably won't be able to figure out that 96% is 24 out of every 25 either. ;)

Re:Bound for failure

[thegarbz]

If you can't figure out 10% is 1-in-10, you have no hope of wading through the standard level of obfuscation added to any publication when discussing statistics.

Sure. If you can't figure out the most simple case you're quite right. That doesn't change the fact that numbers can be presented in a more simple and intuitive way to aid the understanding of a wider audience.

Let's flip that argument:
There are some people who can't figure out that 10% is 1 in 10. However those that can, likely have no problem figuring out that 1 in 10 is 10%, so by expressing the number in its easiest to understand format you capture the understanding of the largest possible audience. The problem is always finding out what the easiest actually is.

Re: Bound for failure

[reanjr]

The problem is people don't know which is bigger, 7-in-10 or 13-in-25, so by using those ratios, you're guaranteeing those with numeric illiteracy have no chance of understanding the numbers. Everyone knows 52% is less than 70%, and has a good idea how big the difference is.

Re: Bound for failure

[thegarbz]

The problem is people don't know which is bigger, 7-in-10 or 13-in-25

Let me repeat myself: "The problem is always finding out what the easiest actually is.

Also 7 in 10 and 5 in 10 are also easy to understand. As are 70 out of 100 and 52 out of 100. Again, you target your lowest common denominator with the language they should understand. Your example effectively is the same as comparing numbers with non equal base units. If someone needs to convert something in their head then you've done something wrong in the way you've presented data.

Re: Bound for failure

[reanjr]

Percentages are a way of applying consistent base units, but you argue against it?

If you can't move a decimal point, you are not worth explaining statistics to.

Re: Bound for failure

[thegarbz]

Percentages are a way of applying consistent base units, but you argue against it?

I'm struggling to understand what it is you don't get when I say: "The problem is always finding out what the easiest actually is." You persist in talking about absolutes showing a fundamental lack of understanding of how to communicate with people. I never dismissed percentages, I only argued that you should explain something in its simplest terms, quite often that isn't in percentages.

If you can't move a decimal point, you are not worth explaining statistics to.

How elitist of you. That's a fast track way to get yourself killed by anti-vaxxers, or by a superbug thanks to the thinking that the uneducated are not worth speaking to.

Everyone is worth explaining statistics to.

Re: Bound for failure

[reanjr]

When someone is illiterate, you teach them to read. You don't just start writing everything at a kindergarten level.

The same applies to numeric literacy.

Re: Bound for failure

[thegarbz]

Indeed. So do you start by throwing the complete works of shakespere at them?

Also we're not teaching people, we're disseminating information. Or maybe you intend to start every post where you wish to use a percentage symbol with a 2 page primer of mathematics. In which case I tip my hat to you. That's more effort than most people will put in. The rest of us just find appropriate methods of communication.

Re: Bound for failure

[reanjr]

Correct. We're not teaching people. Education is orthogonal to the dissemination of information. Shakespeare doesn't teach you how to read his works, he expects you to become educated before the attempt. Don't try to tell Shakespeare to write like Dr. Seuss just because you find One Fish, Two Fish... more accessible than Hamlet. Learn to read. Then your opinion on the topic might begin to matter. Before then, you are an illiterate not worth taking the time for.

Re: Bound for failure

[thegarbz]

So we've gone full circle. Let me repeat and we'll see if we come with a different more sane outcome:

How elitist of you. That's a fast track way to get yourself killed by anti-vaxxers, or by a superbug thanks to the thinking that the uneducated are not worth speaking to.

Another whiny Republican faggot cries to herself.

[Anonymous Coward]

Giving away US treasury to the wealthiest corporations didn't create jobs, it enriched billionaires. The economy WAS in fact fixed by Obama, sorry retarded Republican trashmind traitor faggots. You don't matter, never did.

Since the authors of the study...

[LordHighExecutioner]

had to make some statistics about the collected data, I wonder if they had a fixed mindset...

Dear "SOROS loser": Newsflash

[Anonymous Coward]

See subject SOROS loser: Your side did what it ALWAYS does, lose - accept it (or can't you accept REALITY?)...

* Apparently not!

(ALL YOU DO is "HIDE" behind UNIDENTIFIABLE anonymous posts FURTHER making yourself out a FOOL you dimwitted little PAID OFF PUPPET thinking he can "fool" others with your BULLSHIT, lol!)

APK

P.S.=> Now hurry up & run back to your "masters" ROTHCHILD (for whom SOROS is even their "protege puppet") - crying "HELP ME MOMMY - I can't beat facts!" & NEITHER CAN THEY - they can only BUY UP NEWSCORP to feed the GOY CATTLE FAKE NEWS to mislead them https://www.infowars.com/trump... ? Good boy - now "SHOO" bitch!... apk

Comment removed

[account_deleted]

Comment removed based on user account deletion

Misleading answer to the Bayesian question

[Anonymous Coward]

The article mentions a Bayesian question that was used to evaluate peoples statistical ability:

"This involves giving subjects a base-rate statistic—say, the probably of a 40-year-old woman being diagnosed with breast cancer (1 percent)—along with a sensitivity element (a woman with breast cancer will get a positive result on her mammogram 80 percent of the time) and a false alarm rate (a woman without breast cancer still has a 9.6 percent chance of getting a positive result on her mammogram). So if a 40-year-old woman tests positive for breast cancer, what is the probability she actually has the disease (the "posterior" probability estimate)?"

They then give the answer as 5%, if (like me) you already did a rough calculation in your head and got "about 10%" you're not going mad. The actual answer is about 7.76%, so not that far off from the 10% you'd get with some heavy rounding.

I struggle with statistics

[Anonymous Coward]

Particularly with constantly-changing models which tell me that I need to change everything about how I live within X years or there's a Y% chance my quality of life will deteriorate rapidly. After X years pass I discover it was wrong; however "we have better computers and assumptions now" and "we can't take any chances" so I have X more years left.

Let's actually use statistics

[purplie]

As we're talking about statistics here, let call out any statement that was presented as a fact: "With 100% certainty, we report that the study concluded with that fixed mindsets are to blame with 100% certainty.... Roughly 96 percent of the general population (with 0% margin of error) struggles with solving problems relating to statistics and probability (with 100% certainty that our test problem is representative of most real problems). Yet being a well-informed citizen in the 21st century with requires us with 100% certainty to be able to engage competently with these kinds of tasks.... "As soon as you pick up a newspaper, with 100% certainty you're confronted with so many numbers and statistics that you need to interpret correctly," says co-author Patrick Weber, with 100% certainty a graduate student in math education at the University of Regensburg in Germany. With 100% certainty, most of us fall far short of the mark."

meatheads of planet Ostrich

[epine]

It's not confusing, it's just that many people don't do the conversion in their heads.

Okay, so you missed the first five minutes of the class where the concept of 'percent' is introduced in your grade six or grade seven math class.

Unintended consequence: dunderhead for life.

Bad five minutes to take two extra puffs after the recess bell rings.

Thereafter, it takes a SPECTACULAR level of blockheaded arrogance (I'm not going to learn, and you can't make me, but I sure can beat the living crap out of this giant 4x4) to sit in school for another five years, or ever read a newspaper, or ever watch a television news program, and never manage to fill in this small conceptual omission.

Re:meatheads of planet Ostrich

[DutchUncle]

Thereafter, it takes a SPECTACULAR level of blockheaded arrogance (I'm not going to learn, and you can't make me ...

And this differs from the state of affairs in America . . . how?

Stupid

[lorinc]

"As soon as you pick up a newspaper, you're confronted with so many numbers and statistics that you need to interpret correctly," says co-author Patrick Weber, a graduate student in math education at the University of Regensburg in Germany. Most of us fall far short of the mark.

Or maybe just acknowledge that the vast majority of humanity is just plain stupid, and that you are part of it...

Re:Stupid

[Anonymous Coward]

Or maybe just acknowledge that the vast majority of humanity is just plain stupid, and that you are part of it...

Yeah, that "math[s] education" gig? What a stupid waste of time.

If you can't make the numbers dance...

[Mal-2]

If you can't make the numbers dance like the Bistromathics drive on the Heart of Gold, you don't understand statistics.

10%. 9 to 1 against. 1 in 10. They all mean exactly the same thing. If you haven't grasped this yet, it's not because you have a "fixed mindset". It's because you don't understand statistics.

Really bad example

[Anonymous Coward]

I simply don't get the reasoning behind the drug addict example: I could easily do it in percentage, but I simply can't follow the arguments behind adding the numbers up using frequency. They have prepared the numbers to make it easy for the reader, but that is not the case in general, where you have to "prepare" the numbers yourself. Much easier to learn the general method with probability then.

Even the article gets it wrong...

[Guy Smiley]

> performance rates on many statistical tasks increased from four percent to 24 percent when the problems were presented using the natural frequency format

Shouldn't that be from 1-in-25 to 1-in-4?

Only in America

[Anonymous Coward]

since 1-in-10 a more intuitive, jury-friendly approach

Only American media use "1-in-X", most of the rest of the world has no problem with using percentages.

No, that's a millennial problem

[Anonymous Coward]

The rest of us actually do know how to think critically and weigh options. Speak for yourselves, children, and then have the long talk with the parents that thought it was in your best interest to be this way. Then have a talk with yourself and realize you are not a robot and do not have to be a slave to programming of *any* kind. Your mind is yours to use as you like, so is your lazy-ass body.

Yeah, I'll give the mindset problem some names

[evanh]

Marketing, lobbying, politics.

We are supposed to take this seriously?

[Anonymous Coward]

"Roughly 96 percent of the general population struggles with solving problems relating to statistics and probability. "

What the hell does "struggles" mean. And who are these 4 percent who don't ever "struggle" to solve any problem relating to statistics and probability?

I suspect the reason "students" would choose to use the tools they were taught to use is that they have no idea what the statistics actually mean, they only know how to calculate the answer they are being asked for. If they had been asked to give the answer in natural terms, i.e. not 5% but 1 in 20, they may have been completely unable to figure it out.

Re:We are supposed to take this seriously?

[Anonymous Coward]

"they only know how to calculate the answer they are being asked for"

This observation is more astute than you think. It is a problem of epidemic proportions in our failing education system, that students are being taught only rote memorization of formulas, rather than actual math or science. We are quickly going the way of east Asia with our approach to "education," and the result is that we have an entire generation of children (defined by "all those under the age of 27") who can't solve problems they have never seen before.

This approach which we are rapidly adopting so that we can continue to pay teachers $25K/year and administrators $250K/year, is going to destroy our country.

Re: Wooosh

[Anonymous Coward]

With 100% certainty, we report that the study concluded

Because "might be why" when translated into a percentage is 100%, of course, ...

Roughly 96 percent of the general population (with 0% margin of error)

... and "roughly" translates into exactly with 0% margin of error, etc.

If that was meant to be a joke, it's missing a vital ingredient.

You maths geeks are so clever (and sexy)

[Anonymous Coward]

That's the kind of statement I don't understand. It's 25 out of 100,000 people.

Ohh!!! Is that what 0.025% means? I get it now! ... I think 0.25% is bigger than 0.025% right? So it's like 25 out one million people. ;p

3 in 7 or 7 in 20...

[bidule]

... which is better?

I think that's enough to show that we need to normalize fractions into a common unit.
Lets use "ppm" for very low amount, and "percent" for higher quantities.

Ah, people can come up with statistics

[Anonymous Coward]

to prove anything. 40% of all people know that.

Statistics

[ledow]

I'm a mathematician.

The second someone digs out statistics, I can always pick 20 holes with their methodology used, presentation of, choice of, or analysis of their numbers. Usually, I could make things come out "oppositely" with only minor tweaking and use of the other statistics from the same dataset that they discarded out of hand, and usually I could provide much better justification for the numbers I used than the ones they did.

People use statistics to back up their claims. That's it. And if you go looking hard enough and present statistics to do that, you can ignore all the stuff that doesn't match your claims. It's really easy to do.

And because nobody understand statistics (I would posit this category even includes statisticians!), you can get away with it.

I like to shout at shampoo adverts when they say "Women agree*" where the * leads you to a footnote saying they tested 19 women and 67% of those agreed... so you're telling me that, actually, worldwide, 12.7 women agreed... What the hell kind of selection criteria did you use to get that, and what use is that if you don't specify that they were random women from the street in a controlled trial rather than, say, the people who work in the office?

The old saying is right - there are lies, damn lies and statistics. If someone quotes statistics are you, assume it's a lie. It almost always is. Even when it's not, it's merely the portion of the truth that can be spun positively if you don't mind looking through an n-dimensional kaleidoscope at the data.

And what are they trying to do by telling you this? They're trying to tell you "Hey, look, you're stupid and have no idea what's going on and actually everyone else is really onboard". Statistics are used as the worst kind of "peer pressure" - if they are trying to convince you of something, rather than inform you.

Statistics can be incredibly useful, very revealing, and can lead to a better understanding. If you get them from a professional. Who'll then tell you what the statistics *mean* and whether or not they have caveats.

If you get them from shampoo ads and random junk on the Internet, they are no better than any other "fact" spewed at you in such a manner... wrong.

(Interesting fact: There's a TV program called QI, in which all kinds of "you'll never believe" stuff is presented in what's supposed to be a highly intellectual quiz show. QI facts are heavily researched, almost always counter-intuitive or contrary to what everyone has been told, and they spend years with some of the cleverest people from the top universities doing research for each series. And in one episode they reveal that the portion of facts that they themselves got wrong, or which have changed since, was over 50%).

If someone quotes statistics at you, don't just nod and go "Oh really?" because you're then likely to repeat that statistic without every checking it. The correct response is to think "What's he trying to convince me of?". Because you don't use statistics for anything else.

And unless you understand, truly understand, statistics, you know that any kind of amateur data-gathering or analysis by even the most well-intentioned people is a bottomless pit of potential failure.

Hell, to be honest, 99% of the time, I can't even work out the right answer for some statistics so I make it up and say 99%.

Re:Statistics

[Anonymous Coward]

Roughly 96 percent of the general population struggles with solving problems relating to statistics and probability.

Why do I doubt that statistic? Are you sure the researchers who came up with that number didn't make a mistake? What fraction of the general population calculate any statistics or probabilties more than three times per year? Much less than 96 people out of 100, I guess.

Re:Statistics

[Anonymous Coward]

Whilst 99 % of the students in my year at university learned some sstatistics, around 0 % learned Bayes's theorem, though a handful may have heard about it since. The whole subject of Bayesian statistics is no part of tuniversity curricula in our country.

Re:Statistics

[Anonymous Coward]

If someone quotes statistics at you, don't just nod and go "Oh really?" because you're then likely to repeat that statistic without every checking it.

Good luck with that, because 60% of the time, it works EVERY time.

Now I feel better.

[Anonymous Coward]

It's nice to know I'm not alone, since I am one of the majority who "struggle" with statistics. I also struggle with the General Relativity text I'm reading (still struggling with tensors) and the Quantum Field Theory I'm also studying is challenging. Don't you think PhD statisticians also "struggle" with statistics? If they didn't, then would they (and their degrees) even be needed? I also struggle with English. This is compounded by the incompetence I observe in typical prose from journalists. For instance, what is the meaning in saying "110% effort" or in claiming r^2 values are a direct measures of correlation? Another example is a post which states that "people struggle so much to solve statistical problems" when what was meant was "when presented as a story problem, most people are unable to solve common everyday statistical problems". But that would require the writer to actually be able to articulate the actual point clearly.

"Natural frequency" loses consistent scale

[DutchUncle]

Maybe it feels "natural" for a single reference, but for a comparison it is useless, unless the group is exactly the same. And if the group is 100 . . . . we're done here.