You can prove anything with statistics

[ZERO]

I suspect it is a false claim. Statistics are raw data and should lead to one conclusion?
It is a common statement when stats are used as evidence. What is the truth?

[Cuddles]

The trouble is that statistics are not raw data. Statistics is a method for analysing large data sets, raw or otherwise. There are plenty of ways of getting the statistics to say what you want. To start with, you could just make up the data. If you don't want to go for quite such blantant fraud, cherry-picking the data (or the subjects giving the data) and leading questions are always good. Once you have the data, there are many, many different ways of looking at it, so there's bound to be one that will lead to the answer you want.

For example, take some of the surveys on the Twin Towers, since this is a popular topic for manipulating the statistics. Let's say you want to show that the majority of American citizens think the government was responsible for this. Assuming it's a real poll and not just made up, the easiest way to get the correct answer is to pick the people you ask. Instead of randomly phoning people, go to a truther rally and ask your questions there. You're virtually guaranteed to get 100% thinking it was the government.

If you can't quite bring yourself to get that close to them, just pick your questions carefully. A good leading question would be something like:
Do you think the government could have done more to prevent the attacks?
With hindsight the answer is of course they could, and most people will answer something to that effect. The important thing is to have multiple choice answers such as:
a) No, they did everything possible.
b) Yes, security could have been a bit tighter.
c) Yes, the government is hopelessly incompetent.
d) Yes, the government did it on purpose.
e) Not sure.
Hardly anyone will pick a), which means you can proudly announce to the world that 84% of Americans think 9/11 was the governments fault, even though that's not what most of them actually meant.

The important thing with all statistics is that unless you can see the raw data, the collection method and the workings, it is all extremely untrustworthy and shouldn't be taken too seriously. Even with respectable polling companies, the questions are usually written, at least partially, by the people commissioning the poll. Polls just asking questions in the street, write-ins or, horror of horrors, online polls are essentially worthless. Statistics published in peer reviewed journals are likely to be better, and are at least open about the methods, but even then there are often arguments about the validity of the analysis used and possible biases in the population.

As with anything, don't believe something just because someone has written about it. Look for peer review, openness, replication and so on. Can you actually prove anything with statistics? Well, obviously not, since you can't prove something that isn't true. However, it's relatively easy to make it look like you've proved something to people who aren't skeptical enough.

[ZERO]

Thank you for that comprehensive answer.

Yes, I see statistics are not raw data but the proccessed result. Quite obvious.
What you say about polls is interesting. When I was 18 I was questioned by the Morgan/Gallup poll. Some of the multiple answer questions I wouldn't answer because they just didn't fit my thinking. The interviewer was quite annoyed.>:D
Leading questions are ugly and I can see the contamination resulting.
So if stats are unreliable proof is difficult. However, If I understand you, similar results from independant sources can be viewed as accurate.

[Dr B]

Zero

You cannot say anything you want with statistics.....you can try, but if the populus is educated in statistics - they won't let you get away with it.

Idealistic I know - but it is true.

Also remember, facts never speak for themselves, they require someone to make cogent arguments for them.

Anyone who says to you, "ah well statistics are unreliable as you can say anything you like with them", does not really understand that it is the people who are unreliable - not necessarily the technique.

Also - keep in mind that stats do not prove anything, they merely give you a degree of confidence as to what the chances are on you accepting / rejecting the wrong idea. Stats themselves are based on assumptions - though these are not always unhelpful. O0

The point is - they are not concrete proof of anything - but this does not mean they are worthless.

[MRT]

Cuddles - strictly speaking, isn't your argument against biased data collection rather than statistics, as such? Properly applied, statistics will consistently answer whatever question you ask of it from the data you supply. As the old computing motto went 'rubbish in, rubbish out'.

The problem of biased data collection is a large part of skepticism is about, I would guess.

[bobdezon]

Statistics can be misrepresented though to alter the final conclusion. I remember a few years ago they purposely manipulated the unemployment figures (to much much lower). It turned out they had excluded a large percentage of the population because they didnt consider them to be unemployed. Remember those Y.T.S. Schemes? they never included the people in them in the unemployment data, and yet perversely included them in the employment figures. It also excluded under 18's from the unemployment figures, and then they could not claim any unemployment benefit etc.

[FarSideOfTheMoon]

Statistics can be misrepresented though to alter the final conclusion. I remember a few years ago they purposely manipulated the unemployment figures (to much much lower). It turned out they had excluded a large percentage of the population because they didnt consider them to be unemployed. Remember those Y.T.S. Schemes? they never included the people in them in the unemployment data, and yet perversely included them in the employment figures. It also excluded under 18's from the unemployment figures, and then they could not claim any unemployment benefit etc.

And don't even start about the pointless surveys sponsored by corporate Britain which appear daily in the Newspapers....one shudders to think how targeted the questioning is for them to achieve the results they require.

[bobdezon]

I like the adverts for makeup/womens face creams etc. 90% of woman in britain are using this product. Then if you read the small print at the bottom of the screen it says

"based on a survey of 3 women, 2 trannys, a stray cat and a spanner"

The mind boggles.

[tkingdoll]

ZERO, if you're interested in trying to figure out what statistics to be skeptical of, a good place to look is the sample size. This is the actual number of people who were asked the question.

Now, if your sample is large enough and taken from the general population and not just one type of person, then you can say it's likely to be representative of the population as a whole. This is standard. When something tells you what a certain percentage of the population does, of course that survey hasn't asked everyone in the country. It's asked a representative sample and then weighted up the figures to the UK population.

For example, if the UK population is 55% male and 45% female, and I ask 2000 people "what is your favourite drink?", then I need make sure that my sample is roughly 55% male and 45% female if I want to make any claims about the UK population from my data. Let's say I claim "90% of UK women drink Baileys!". Quite a big claim. So if we examine my sample and discover that of the 2000 people I asked, only 10 of them were women, then we know that only 9 out of 2000 people actually claim to drink Baileys. My sample is not representative of the population as a whole so I can't make any claims about the UK as a whole.

The same goes for other demographics like age.

When you are analysing survey data, unless you are looking at something very niche and specific, then as a rough guide you shouldn't trust any data with a sample size of less than 50. That's because once you start to break it down into demographics, you're talking about very small numbers of people who actually answered the question.

Imagine you're looking at people who buy KitKats in the UK. You have a nice healthy sample taken from a nationwide internet survey of 3000 people. You want to break it down by geographic region. Your data tells you that 1000 of those surveyed live in London. That's fine, a random sample of 1000 Londonites will probably give you an accurate picture of Londonites in general. If 40% of your London survey respondents say they eat KitKats, you can safely claim that 40% of Londonites eat KitKats. But if you pull out the data for a tiny village in the Midlands, where only one person did the survey, is that one person representative of the whole village? Probably not.

Bobdezon touched on this, beauty companies are VERY fond of studies with tiny sample sizes. Buyer beware! What 18 women in controlled conditions say about Dove shampoo is not likely to be what most women think.

[ZERO]

ZERO, if you're interested in trying to figure out what statistics to be skeptical of, a good place to look is the sample size. This is the actual number of people who were asked the question.

Now, if your sample is large enough and taken from the general population and not just one type of person, then you can say it's likely to be representative of the population as a whole. This is standard. When something tells you what a certain percentage of the population does, of course that survey hasn't asked everyone in the country. It's asked a representative sample and then weighted up the figures to the UK population.

For example, if the UK population is 55% male and 45% female, and I ask 2000 people "what is your favourite drink?", then I need make sure that my sample is roughly 55% male and 45% female if I want to make any claims about the UK population from my data. Let's say I claim "90% of UK women drink Baileys!". Quite a big claim. So if we examine my sample and discover that of the 2000 people I asked, only 10 of them were women, then we know that only 9 out of 2000 people actually claim to drink Baileys. My sample is not representative of the population as a whole so I can't make any claims about the UK as a whole.

The same goes for other demographics like age.

When you are analysing survey data, unless you are looking at something very niche and specific, then as a rough guide you shouldn't trust any data with a sample size of less than 50. That's because once you start to break it down into demographics, you're talking about very small numbers of people who actually answered the question.

Imagine you're looking at people who buy KitKats in the UK. You have a nice healthy sample taken from a nationwide internet survey of 3000 people. You want to break it down by geographic region. Your data tells you that 1000 of those surveyed live in London. That's fine, a random sample of 1000 Londonites will probably give you an accurate picture of Londonites in general. If 40% of your London survey respondents say they eat KitKats, you can safely claim that 40% of Londonites eat KitKats. But if you pull out the data for a tiny village in the Midlands, where only one person did the survey, is that one person representative of the whole village? Probably not.

Bobdezon touched on this, beauty companies are VERY fond of studies with tiny sample sizes. Buyer beware! What 18 women in controlled conditions say about Dove shampoo is not likely to be what most women think.

So look for sample size and how widespread the participants are in society. This leads me to a new question.

Facts and evidence underpin a realistic opinion. How do you find this for yourself? Or a better way of putting it, what are some simple research methods for a layman like myself? Teach me to fish.:smiley:

[MRT]

Statistics can be misrepresented though to alter the final conclusion.

I agree. My argument is that the basic process of applying statistics in a standard way is a valid way of manipulating data. If it was not, much science would fall by the wayside. In proper statistics you start with valid data collection, then apply appropriate statistical tools and finally draw conclusions within the defined error limits.

Just as there is pseudoscience, there is pesudostatistics! In pseudostatistics, you can manipulate data collection to suit yourself, apply arbitrary innappropriate statistical tools and draw whatever conclusion you like from the results. This sort of thing is commonly done by lobby groups and others trying to influence opinion. It is amazing how surveys always seem to come up with a result that supports what a lobby group is lobbying about, isn't it? To spot pseudostatistics, always look at who is presenting the results and ask yourself what they would like them to be.

[FarSideOfTheMoon]

ZERO, if you're interested in trying to figure out what statistics to be skeptical of, a good place to look is the sample size. This is the actual number of people who were asked the question.

Now, if your sample is large enough and taken from the general population and not just one type of person, then you can say it's likely to be representative of the population as a whole. This is standard. When something tells you what a certain percentage of the population does, of course that survey hasn't asked everyone in the country. It's asked a representative sample and then weighted up the figures to the UK population.

For example, if the UK population is 55% male and 45% female, and I ask 2000 people "what is your favourite drink?", then I need make sure that my sample is roughly 55% male and 45% female if I want to make any claims about the UK population from my data. Let's say I claim "90% of UK women drink Baileys!". Quite a big claim. So if we examine my sample and discover that of the 2000 people I asked, only 10 of them were women, then we know that only 9 out of 2000 people actually claim to drink Baileys. My sample is not representative of the population as a whole so I can't make any claims about the UK as a whole.

The same goes for other demographics like age.

When you are analysing survey data, unless you are looking at something very niche and specific, then as a rough guide you shouldn't trust any data with a sample size of less than 50. That's because once you start to break it down into demographics, you're talking about very small numbers of people who actually answered the question.

Imagine you're looking at people who buy KitKats in the UK. You have a nice healthy sample taken from a nationwide internet survey of 3000 people. You want to break it down by geographic region. Your data tells you that 1000 of those surveyed live in London. That's fine, a random sample of 1000 Londonites will probably give you an accurate picture of Londonites in general. If 40% of your London survey respondents say they eat KitKats, you can safely claim that 40% of Londonites eat KitKats. But if you pull out the data for a tiny village in the Midlands, where only one person did the survey, is that one person representative of the whole village? Probably not.

Bobdezon touched on this, beauty companies are VERY fond of studies with tiny sample sizes. Buyer beware! What 18 women in controlled conditions say about Dove shampoo is not likely to be what most women think.

Those are good examples because they illustrate another pitfall to look out for - the quality of the sample beyond the simple demographics.

If you were interested in whether people drink Baileys or not, would your sample include people who don't drink alcohol, or people who don't go to pubs? What if you did your survey in the drinks aisle of a supermarket?

Similarly for KitKats, what if you did your survey in a corner shop? What about the part of the population who don't eat sugary snacks?

Advertisers use these tricks to introduce favourable bias to their results. How many times have you looked at a survey and thought those figures are just too high.

[Melanie]

Far Side... Cave ne ante ullas catapultas ambules

:smiley:

[median]

bobdezon wrote
Those are good examples because they illustrate another pitfall to look out for - the quality of the sample beyond the simple demographics.


Exactly, quality is important. What is also interesting is that you can have sample sizes too big as well as too small.O0
Variance is one to take into consideration as well.

[bobdezon]

That was farsideofthemoon's quote not mine, although its nice, I might claim it ;) possesion is 0.9% of the law ;D (and acorahs bread n butter)

[seren]

Posted on a another board I frequent.


Bread Kills!

1. More than 98 percent of convicted felons are bread users.

2. Fully HALF of all children who grow up in bread-consuming households score below average on standardized tests.

3. In the 18th century, when virtually all bread was baked in the home, the average life expectancy was less than 50 years; infant mortality rates were unacceptably high; many women died in childbirth; and diseases such as typhoid, yellow fever, and influenza ravaged whole nations.

4. Every piece of bread you eat brings you nearer to death.

5. Bread is associated with all the major diseases of the body. For example, nearly all sick people have eaten bread. The effects are obviously cumulative:
99.9% of all people who die from cancer have eaten bread.
100% of all soldiers have eaten bread.
96.9% of all Communist sympathizers have eaten bread.
99.7% of the people involved in air and auto accidents ate bread within 6 months preceding the accident.
93.1% of juvenile delinquents came from homes where bread is served frequently.
6. Evidence points to the long-term effects of bread eating: Of all people born before 1839 who later dined on bread, there has been a 100% mortality rate.

7. Bread is made from a substance called "dough." It has been proven that as little as a teaspoon of dough can be used to suffocate a lab rat. The average American eats more bread than that in one day!

8. Primitive tribal societies that have no bread exhibit a low incidence of cancer, Alzheimer's, Parkinson's disease, and osteoporosis.

9. Bread has been proven to be addictive. Subjects deprived of bread and being fed only water begged for bread after as little as two days.

10. Bread is often a "gateway" food item, leading the user to "harder" items such as butter, jelly, peanut butter, and even cold cuts.

11. Bread has been proven to absorb water. Since the human body is more than 90 percent water, it follows that eating bread could lead to your body being taken over by this absorptive food product, turning you into a soggy, gooey bread-pudding person.

12. Newborn babies can choke on bread.

13. Bread is baked at temperatures as high as 400 degrees Fahrenheit! That kind of heat can kill an adult in less than one minute.

14. Most bread eaters are utterly unable to distinguish between significant scientific fact and meaningless statistical babbling.

In light of these frightening statistics, we propose the following bread restrictions:

1. No sale of bread to minors.
2. A nationwide "Just Say No To Toast" campaign, complete celebrity TV spots and bumper stickers.
3. A 300 percent federal tax on all bread to pay for all the societal ills we might associate with bread.
4. No animal or human images, nor any primary colors (which may appeal to children) may be used to promote bread usage.
5. The establishment of "Bread-free" zones around schools.

[Janot]

Posted on a another board I frequent.


Bread Kills!


Nice one - excellent examples of the confusion between correlation and cause/effect.

[Mulder]

If you can prove anything with statistics, prove spirits don't exist (using statistics, obviously).

[bobdezon]

In 100% of cases into the paranormal carried out by qualified professionals, it has never been shown that spirits exist or indeed any other paranormal phenomena exists.

[Mulder]

In 100% of cases into the paranormal carried out by qualified professionals, it has never been shown that spirits exist or indeed any other paranormal phenomena exists.

Who are these 'qualified professionals' and in what way are they qualified to judge?

[median]

I suspect, qualified experts in recognised fields of science. Areas that can actually help in providing answers to seemingly 'paranormal' events.
O0

[Mulder]

Experts like Robert Jahn, Rupert Sheldrake and Richard Broughton?

[Dr B]

errrrr no, real experts in science not pseudoscience.

[bobdezon]

Experts like Robert Jahn, Rupert Sheldrake and Richard Broughton?

Lol Yeah, Im sure the results will be a bit different if you used their data O0

[Mulder]

You said qualified professionals, so I gave you some examples (I could also add John Hasted, Archie Roy and many more). Do not these people all have qualifications from recognised academic institutions? I don't think they graduated from the 'online Minnessota University of Spiritual Development'.

If these are not 'qualified professionals' then please define the term as it is clearly different to the one I understand.

[bobdezon]

If archie roy was to give me astronomy data, I would be happy to check that. However if he gave me data on psychics and mediums, I would not be happy with that because I know his research is flawed based on prior work. I would still check the data out though because this time he might be onto something.

There are people with who have been awarded qualifications, it is however what they choose to do with them that counts. If a scientist produces solid verifable research consistantly then he is considered to be a good source of information. If however he gains his qualificaton and then loses the plot and announced undead fairies from ancient ireland were removing parts of the ISS in orbit, I would be sceptical of their information.

Qualfied professionals would be people I consider to have the correct qualifications and experience in their field speaking on a subject they understand and working wihin those parameters produce good results. Not the lunatics, who use psuedologic and make ridiculous claims without peer reviewed proof.

[Mulder]

So who are these qualified professionals who can pronounce on the existence of spirits? Priests?

[bobdezon]

Any scientist that can produce evidence of phenomena not known to exist or exist and behave in an unexpected way can claim (if they can prove) it could be paranomal. However once discovered and accepted it no longer becomes paranomal but perinormal as it is known to natural sciences.

It is anyone who can prove it to be real regardless of qualification, however if a bin man from chester announced it to be true rather than a qualfied professional they might have a harder time getting the press it needs to promote the idea as real.

[Mulder]

We seem to be going in circles. We started off with:

"In 100% of cases into the paranormal carried out by qualified professionals, it has never been shown that spirits exist or indeed any other paranormal phenomena exists."

Now it appears 'qualified professionals' do not include Prof Archie Roy but could include a bin man.

Sorry, but I'm confused!

Since your statement is in the past, I assume these 'qualified professionals' have already pronounced in '100% of cases'. So can you give me a few examples of who these people were and what their qualifications are? I think it might help me understand if I had concrete examples.

[bobdezon]

My point is you do not need a qualification to make a discovery. Anyone can make a discovery, however to fully understand the implications of that you would need to be qualified to assess it.

The people who test these phenomena like richard wiseman tony youens chris french etc have found no evidence to suggest the paranormal exists. There are many people who have reached the same conclusion and it is universally agreed by science to not exist. That is 100% effectively is it not?

[Janot]

My point is you do not need a qualification to make a discovery. Anyone can make a discovery, however to fully understand the implications of that you would need to be qualified to assess it.More importantly, surely, that because there are so many crackpots with crazy theories, the chances of someone without qualifications being taken seriously is low. There is so much stuff out there to digest, an author with a qualification is more likely to be taken seriously.


The people who test these phenomena like richard wiseman tony youens chris french etc have found no evidence to suggest the paranormal exists. There are many people who have reached the same conclusion and it is universally agreed by science to not exist. That is 100% effectively is it not?I hope you meant to say it is universally agreed by science that there is no evidence that it exists. You never know...

[bobdezon]

one lives in hope.

[Mulder]

Can't agree. It seems to me that you are choosing your particular 'qualified professionals' according to the answer you want.

[bobdezon]

ok O0

[Admin]

Can't agree. It seems to me that you are choosing your particular 'qualified professionals' according to the answer you want.

If science is done properly it should make no difference as to who carries out the experiment/study.

Yes, there is something known as 'the experimenter effect' whereby researchers tend to find the answers they're looking for. This indicates either bad science and/or biased interpretation of the results.

Fortunately, science also requires replicability (is that a real word?). This means that if a finding is true then it should be able to be found by other independent researchers who replicate the study (they will replicate it if it's not obviously flawed).

The reason that paranormal phenomena are not considered real by science is that although they have produced many positive results in experiments (from precognition to psychic parrots) their findings just can't be replicated in follow up studies. This indicates experimenter effects rather than real, but transient, phenomena.

[Admin]

I left the house this morning with £10 in my pocket.

In the road I found £5 which I put in my other pocket - making me 50% richer.

When I got to work I found the £5 had fallen out through the hole in my pocket - making me 33% poorer.

Still, I didn't complain. After all, I was still 17% richer than when I left the house this morning. :cheesy:

Yip, you gotta be careful with statistics!

[Janot]

Let's say there are 2,000,000 men in Wales. 200 of them have only one leg.

Total number of male legs in Wales: 3,999,900

Average number of legs: 1.99995

Therefore: 99.995% of all men in Wales have a higher than average number of legs. :cheesy:

[Mulder]

My point - in case anyone hasn't yet got it - is that the '100% professionals...' statement is relying on the idea of trusting authority figures rather than on evidence. I'm always happy for matters to be decided by evidence. However, 'trust me, I'm a professional' is a bit too much like faith for my tastes.

[bobdezon]

I would trust an authority only if the data they provided was accurate, I wouldnt trust them simply because they were an authority, thats silly. Nowhere have I stated I would trust them soley because they were qualified. Nor would I trust them as an authority figure rather than on the evidence they produced.You made a good point before when you mentioned the scientists who are generally discredited not because their views do not conform with regular science, but because they insist they are correct despite evidence to the contrary. Their results are not repeatable by anyone performing the same experiments.

[Janot]

I left the house this morning with £10 in my pocket.

In the road I found £5 which I put in my other pocket - making me 50% richer.

When I got to work I found the £5 had fallen out through the hole in my pocket - making me 33% poorer.

Still, I didn't complain. After all, I was still 17% richer than when I left the house this morning. :cheesy:

Yip, you gotta be careful with statistics!Is this the same or a similar logical fallacy as the anecdote of the Scotsman (it has to be Scotsman) who always ran home behind a taxi, because that way he was saving more money than if he ran home behind a bus? :-[

[SKIRRID5]

I hope this is acceptable on this thread - it's certainly about statistics.
I've often come across the story of President Eisenhower being horrified to learn that 50% of Americans were below average intelligence, obviously meant to show how ignorant he was of mathematics. But was he?
It seems to me that the only way half the people involved would be below any average, would be if every single person was different.
Let's ignore the problems of measuring intelligence. Then let's ask how many IQs are available. I'm not well up on this so let's say 200 for argument's sake. That means 200 possible IQs have to be allotted to millions of Americans. Thus, each IQ value would relate, not to one but to a huge number of Americans. The commonest, or the average, or the mean, or whatever, would surely be the biggest group. So, even if the numbers of INDIVIDUALS above and below were equal (unlikely), those below would not be half the total number. Is there is statistician in the house? This has been annoying me for ages, and I'm dying to know the answer. Am I right or talking complete nonsense?

[Janot]

I hope this is acceptable on this thread - it's certainly about statistics.
I've often come across the story of President Eisenhower being horrified to learn that 50% of Americans were below average intelligence, obviously meant to show how ignorant he was of mathematics. But was he?
It seems to me that the only way half the people involved would be below any average, would be if every single person was different.
Let's ignore the problems of measuring intelligence. Then let's ask how many IQs are available. I'm not well up on this so let's say 200 for argument's sake. That means 200 possible IQs have to be allotted to millions of Americans. Thus, each IQ value would relate, not to one but to a huge number of Americans. The commonest, or the average, or the mean, or whatever, would surely be the biggest group. So, even if the numbers of INDIVIDUALS above and below were equal (unlikely), those below would not be half the total number. Is there is statistician in the house? This has been annoying me for ages, and I'm dying to know the answer. Am I right or talking complete nonsense?
Well, I can't quite follow you reasoning. Supposing you were to be able to allocate people to (say) 200 different groups according to IQ. If you plotted a bar chart of the numbers in those groups, you would get something like a Gaussian distribution (i.e. a bell curve). You then say 'average' is nominally 100, and then you can allocate an IQ higher or lower to all the others. But the allocation to 200 groups is arbitrary - you could start again and define 200 groups, or 2000, or 2,000,000, until the actual number of people in the 'mean' group is very small. At that point, you can say that the number of people of lower IQ is the same as the number of higher IQ. By increasing the number of groups, the number of people in the 'mean' group can be reduced to one.

Yes, Eisenhower was ignorant of maths, if he really was horrified. But he is not the only one - recently an Italian fashion designer complained that all English women were below average height. Duh?

[Fiona]

Possibly a confusion between mean, median and mode?

[Janot]

Possibly a confusion between mean, median and mode?
Rats - if you had posted earlier, it would have saved me the trouble.:smiley:

[SKIRRID5]

Sorry, I still can't see it. My maths teacher at school did once say I'd be the death of him! How can you increase the number of groups without having more available values? Even if one agrees it is possible to measure intelligence with any accuracy, nobody would try to split an IQ. You wouldn't hear of someone with an IQ of 102.5.
Suppose it was peoples' heights. Say the smallest is about 3 feet and the tallest nearly 8 feet. That gives you a range of 60 inches (I got that right!). Now, it's not worth trying to deal in any closer accuracy than a tenth of an inch, since one's height diminishes during the day. So there would be no sense in trying to use more than 600 possible heights. There would be probably a few million folk about 5' 9", so I revert to my original point. You couldn't increase the number of groups unless you could usefully measure someone to about five decimal places.
How would this be different whether one used the term median or mode or average or mean or whatever? You'd never get down to one person who had a different height from everyone else in America. No doubt I'm innumerate.

[Fiona]

I am the innumerate's innumerate, actually.

But for what it is worth, there is no absolute measurement in practical situations so I do not think it matters how many groups you use. Each individual group will have a range within it anyway. So you draw a line down the middle of the middle group to get the average, and bob's your uncle :smiley:

Well I warned you ;D

[Janot]

Sorry, I still can't see it. My maths teacher at school did once say I'd be the death of him! How can you increase the number of groups without having more available values? Even if one agrees it is possible to measure intelligence with any accuracy, nobody would try to split an IQ. You wouldn't hear of someone with an IQ of 102.5.
Suppose it was peoples' heights. Say the smallest is about 3 feet and the tallest nearly 8 feet. That gives you a range of 60 inches (I got that right!). Now, it's not worth trying to deal in any closer accuracy than a tenth of an inch, since one's height diminishes during the day. So there would be no sense in trying to use more than 600 possible heights. There would be probably a few million folk about 5' 9", so I revert to my original point. You couldn't increase the number of groups unless you could usefully measure someone to about five decimal places.
How would this be different whether one used the term median or mode or average or mean or whatever? You'd never get down to one person who had a different height from everyone else in America. No doubt I'm innumerate.ok - you have your 60 groups of people in groups sorted to one inch. You will probably have 30 groups less than average height, and 30 groups of more than average heights. Half the population less, half more. Easy. Now if you take an odd number of groups, say 61, you will have 2 sets of 30 as above, and one set of 'exactly' average. If the number of people in this 'average' group is large enough, you can say that half of them belong to the lower half inch, the other to the higher half inch - below and above average. With nobody left over. :smiley:

[Cuddles]

You wouldn't hear of someone with an IQ of 102.5.

Why not?

The thing is, you're not talking about actual IQ or actual height, you're simply talking about how accurately we can measure, or how accurately it is useful to measure. Sure, if you limit your measurements so that you assign people to only 61 groups, there will be a significant number of people in the middle one, and so there won't truly be 50% above and below. But this does not describe reality. No matter how you choose to group people, none of them are actually the same height as any other (we're talking molecules here). It doesn't matter how you measure it, there will always be 50% above average and 50% below.

An example my physics teacher used is the atmosphere. There are really quite a lot of molecules floating around in the air. However, if you draw sphere in the air and count all the molecules on its surface, the answer will be none. This is because while there are an awful lot of moelcules, there is much, much more space, and so a 2D surface is extrememly unlikely to actually intersect with any. The same is true for measurements. You can measure height as precisely as you like, the mean is extremely unlikely to actually be the same as any of them, and so you will always have 50% above and 50% below average.

[Dr B]

The bell curve theory anyone?????

More seriously, as Cuddles has pointed out so well, there are two issues (at least) here.

There is the issue of quantification itself - its scale and sampling method. Then there is the issue of statistical assessment of that variable. These are not the same thing.

If you alter how you define something quantitatively, you should not be surprised if your statistics are affected by it - but that does not validate the distinction you are now using for your variable.

[SKIRRID5]

Janot - you say my allocation of 200 groups is arbitrary. Not on my part! When statements are made about intelligence in the population, they are made in the context of the standard intelligence tests and IQs. As I said, I don't know how many possible IQs there are, but I'm pretty sure it's not more than 200. So I myself didn't allot the number of groups, and once again, the number of groups is limited by the precision with which the attribute in question can realistically be measured. Isn't that so?
I think it's best to think of this in terms of height, because some of you seem to be shifting from a discussion of statistics (my problem here) to a discussion of intelligence.
Someone (forget who) said we could draw a line down the middle of the "middle" group. But you can't, can you? When the original infamous statement was made which upset Eisenhower, it wasn't talking about groups, it was talking about individuals. I still think my original idea is correct, that half the population (OF INDIVIDUALS!) can be below any average or median or whatever, only if that average is represented SOLELY by one single person, whose IQ or height or whatever, is shared by nobody else. But of course there is no such person. The average is shared by a group of people, and in a whole population, a damn large group. This one can run and run!

[Janot]

Janot - you say my allocation of 200 groups is arbitrary. Not on my part! When statements are made about intelligence in the population, they are made in the context of the standard intelligence tests and IQs. As I said, I don't know how many possible IQs there are, but I'm pretty sure it's not more than 200. So I myself didn't allot the number of groups, and once again, the number of groups is limited by the precision with which the attribute in question can realistically be measured. Isn't that so?
I think it's best to think of this in terms of height, because some of you seem to be shifting from a discussion of statistics (my problem here) to a discussion of intelligence.
Someone (forget who) said we could draw a line down the middle of the "middle" group. But you can't, can you? When the original infamous statement was made which upset Eisenhower, it wasn't talking about groups, it was talking about individuals. I still think my original idea is correct, that half the population (OF INDIVIDUALS!) can be below any average or median or whatever, only if that average is represented SOLELY by one single person, whose IQ or height or whatever, is shared by nobody else. But of course there is no such person. The average is shared by a group of people, and in a whole population, a damn large group. This one can run and run!Your allocation into groups is theoretically arbitrary - the fact that in practice the measurement is not accurate enough to make them meaningful is irrelevant. It is a theoretical division.

If you want to use height, consider the argument that no two people are EXACTLY the same height. You can then order the people into a population from smallest to largest, having one person in each group. It does not actually matter if you get it wrong now and again, and that in one or two places you could swap the people round.
I'm not a statistician, just a mere physicist, so I can't explain any better than that. I don't really understand where you find a problem. ???

[Janot]

The above is valid for a normal population. For a different example, see my post #37 above.

[SKIRRID5]

This is much like the classic "Tortoise and the Hare" surely. To say that no two people are exactly the same height, is to take the position that the hare can never catch the tortoise. In the real world, the hare will do so. In the real world, vast numbers of people are the same height within, say a hundredth of an inch, and obviously for any particular height near average, there will be a hell of a lot. Of course the "groups" will shade imperceptibly into each other, but since a hundredth of an inch has no practical reality in the context of a person's height, it will still be the case that an awful lot of folk will be the same "average" height. I'm not a statistician or any kind of scientist, but it does seem to me unrealistic to claim that everyone in America has a different height, never mind IQ, which of course cannot be measured with any precision.
Maybe we should drop this before I irritate anyone!

[Janot]

This is much like the classic "Tortoise and the Hare" surely. To say that no two people are exactly the same height, is to take the position that the hare can never catch the tortoise. !Um - no, I can't see the remotest connection. The tortoise and Hare paradox is just an example of the inability to see that an infinite series of numbers can have a finite sum. Nothing to do with theoretical heights. :smiley:


Maybe we should drop this before I irritate anyone!Too late, but I agree :smiley:

[Cuddles]

but since a hundredth of an inch has no practical reality in the context of a person's height, it will still be the case that an awful lot of folk will be the same "average" height.

And this is the point you're missing. It is irrelevant whether a hundredth of an inch has any practical use, the fact is that people will be different heights. If one person is taller by even one molecule, they are a different height, end of story.

There is also the separate problem that the mean does not necessarily fall into any of your arbitrary categories. Say you group people so that they have a height of 1,2,3 or 4 arbitrary units. Instead of a normal distribution, these hypothetical people have an even distribution, so exactly the same number come under each category. The mean of this distribution is 2.5, so there isn't a single person who actually has the mean height. It is therefore entirely accurate to say that 50% are above and 50% are below.

[SKIRRID5]

No, no, I'm not going to be tempted, though I could answer the last two replies at some length. When I get my Nobel prize, you'll be sorry!

[Janot]

I think this comes under the heading of statistics, even though unconnected with the previous posts. I have just read an article in a Spanish newspaper about a dangerous stretch of road. The details are irrelevant, but a politician has just stated that it is a disgrace, because the road has the highest accident rate in the country, and nobody is doing anything about it.

Does this have any meaning? I mean, if they improved its safety, there would be another stretch of road taking over the title, and then that one would be the disgrace. They would then improve all roads until none of them were the most dangerous ....:sad:

[Cuddles]

I think this comes under the heading of statistics, even though unconnected with the previous posts. I have just read an article in a Spanish newspaper about a dangerous stretch of road. The details are irrelevant, but a politician has just stated that it is a disgrace, because the road has the highest accident rate in the country, and nobody is doing anything about it.

Does this have any meaning? I mean, if they improved its safety, there would be another stretch of road taking over the title, and then that one would be the disgrace. They would then improve all roads until none of them were the most dangerous ....:sad:

I suppose it depends exactly why it has the highest accident rate. Is it simply because, as you say, somewhere has to have the highest rate, or is there something particularly unsafe about it that could be fixed or improved. If the former, then it really doesn't mean anything, and presumably the place with the highest rate will change over time since it's basically due to chance. On the other hand, if there really is a problem but no-one has bothered doing anything about it, it is a disgrace. On the gripping hand, if there is a problem but no-one knew about it until now then something needs to be done, but it isn't a disgrace because they couldn't do anything until they knew there was a problem in the first place.

[Janot]

I suppose it depends exactly why it has the highest accident rate. I think the general conclusion for this highest accident rate was the amount of traffic, in particular, the number of HGVs ....Duh:-[

[Lord Muck oGentry]

On the gripping hand,

Aha, a Motie fan!

[tkingdoll]

I think this comes under the heading of statistics, even though unconnected with the previous posts. I have just read an article in a Spanish newspaper about a dangerous stretch of road. The details are irrelevant, but a politician has just stated that it is a disgrace, because the road has the highest accident rate in the country, and nobody is doing anything about it.

Does this have any meaning? I mean, if they improved its safety, there would be another stretch of road taking over the title, and then that one would be the disgrace. They would then improve all roads until none of them were the most dangerous ....:sad:

Yeah, it depends on how far above average it is. Say your average 'accident prone' stretch of road has four accidents a year. If the one you refer to has ten accidents per year, then something is more than averagely wrong. However, if it has five accidents per year, then it's as you say it's sort of meaningless to get hysterical about it.

[Janot]

Yeah, it depends on how far above average it is. Say your average 'accident prone' stretch of road has four accidents a year. If the one you refer to has ten accidents per year, then something is more than averagely wrong. However, if it has five accidents per year, then it's as you say it's sort of meaningless to get hysterical about it.Agreed. As ever, they gave no figures, so I couldn't make any judgement.

[SKIRRID5]

Well, here I am again. I dropped out of the discussion of the Eisenhower IQ anecdote, because nobody seemed to grasp my argument, and I didn't want to appear tiresome. However, I believe I have now been vindicated, and I hope some people will re-visit this thread.
I wrote to Mensa, and their supervisory psychologist had this to say (I have put the vital portions in bold type):
"The anecdote regarding President Eisenhower was, I believe, aimed to illustrate the fact that he did not understand, or was not aware of, the definition of an arithmetic average. The arithmetic average is defined as the point or value in a distribution which splits the distribution exactly into half. The average referred to does not relate to the people or objects measured to create the distribution, it refers simply to the value of the number at the point on the graph where the sample is exactly divided into two. To indicate the difference between the two concepts, it can be seen that the number which equates to the arithmetic mean may be a number which it is not actually possible for any given person to achieve on the measurement concerned (for example, it may be half way between two actual test scores. The Eisenhower anecdote involves an elision between the people in the distribution (50% of Americans) and the arithmetic mean (their average score - the score which splits the observed distribution in half). In a sense, the anecdote is an arithmetical joke or sleight of hand, rather than a real assertion about the number of actual Americans with a given IQ score."
I rest my case, m'lud. Most of you guys who thought I was out to lunch, were treating the "arithmetical sleight of hand" as a statement about the real world.