A Very Interesting 'Wake Up' Call On Statistics

[Sukerkin]

I came across this on the BBC website and found it very interesting indeed. The number of times that scary sounding statistics are bandied about without context is growing all the time. This is an excellent example of why we should be very careful about what we take on face value.

http://news.bbc.co.uk/1/hi/magazine/7937382.stm

 

[CoryKS]

I'm to the point where if I see a percent sign I assume the writer has given up trying to make a valid point and is trying to baffle with ********.

This book is a classic: How to Lie With Statistics.

 

[Xue Sheng]

Without the formula to back up and explain the statistics and in some cases the size of the group sample and how they came to the conclusion that this particular group and the size of this particular group was a representative cross section I generally think of statistics as fairly useless.

 

[MBuzzy]

Statistics are very useful, you just have to know all of the details behind them. Always ask yourself: what/who was the sample group? what was the sample size? what statistical equation are they using? do I understand the context? etc....statistics are great...you just have to know how to read them and how to interpret them. ALWAYS look for the full study to get the details.

 

[Hagakure]

Statistically speaking, I tend not to believe them 80.4% of the time, especially when released by the British Government. When it rises to 100% of the time...

 

[Tez3]

Statistically speaking, I tend not to believe them 80.4% of the time, especially when released by the British Government. When it rises to 100% of the time...

Gosh, why ever not? ROFL!

Even when trying to be truthful I think government statistics get screwed up, it's just the nature of the beast I think. I know ours in the MOD get really mixed up, mistakes are made, people don't understand the figures and they get misinterpreted etc etc.

 

[exile]

From another point of view, though, statistics have *got* to work—if they didn't, insurance companies would be going broke all the time. Instead, they are probably better off than any other finance-based business. Their statisticians know exactly what inferences they can draw from actuarial tables, and how much they can lose on very off-chance events while still making a killing on the main chance. The problem isn't statistics itself as a mathematical method (again, thermodynamics and other very solid branches of science are built on a statistical base, where there are too many particles involved to carry out exact computations in less than the lifetime of the universe). The real villains of the piece are the models to which the statistics are applied, where crucial factors are either left out, or undervalued, or overvalued. And that's not part of statistics per se—it's really part of doing good (or not) science/economics/sociology/psychology/medicine/whatever. Statistics is just a way to make sure that you're drawing the right information and inferences from the numerical data you have. They can be done to perfection... but if the model sucks, so will the result. As the computational types say, garbage in, garbage out...

 

[Kreth]

I used to have a sig that said "41% of all statistics are made up." You can spin numbers to say whatever you want. It's worked well for both the anti-gun and anti-smoker crowds...

 

[Bill Mattocks]

Blaming statistics for their misuse is like blaming guns for their misuse. Statistics are a tool, like any other.

 

[MBuzzy]

An important thing to remember about statistics is that there are different kinds of statistics. For example, probability, such as "16.6% chance of rolling a 6 on a dice" is completely different than "42.3% of the population does ________" one is quantitative and discrete, the other, while discrete, is much more qualitative. How the statistical representative is derived makes a big difference. Statistics used by insurance companies and casinos....those are sure bets....given a large enough sample size and enough iterations. This is what people don't get.....statistics works over long periods of time and very seldom apply to a single person or a single iteration.

For example....if I have a 16.6% chance of rolling a 1 on a die, each time I toll, I have the same probability. Over 100 rolls, theoretically, 16.6 of those rolls will be the number 1. But as the number of rolls increases, the probability of rolling that 16.6% increases. Confusing....but you just have to understand how statistics work before you start questioning them. If it is in a news report or from an authoritative source, you can guarantee that the number is correct....it is just correct based on that individual study, sample, and instance....of which you may not be aware the details.

 

[Xue Sheng]

"Then there is the man who drowned crossing a stream with an average depth of six inches." ~ W.I.E. Gates

 

[Bill Mattocks]

For example....if I have a 16.6% chance of rolling a 1 on a die, each time I toll, I have the same probability. Over 100 rolls, theoretically, 16.6 of those rolls will be the number 1. But as the number of rolls increases, the probability of rolling that 16.6% increases.

No, it doesn't.

The die does not know how many times it has been rolled. Every time it is rolled, the chances of any given number coming up is exactly the same. The probability never changes.

If I flip a coin, there is a 50% chance it will land 'heads'. If I flip it a hundred times, there is still a 50% chance it will land 'heads'. If it lands heads 99 times in a row, there is still a 50% chance it will land 'heads' on the 100th flip.

That's why people who play the lottery for a long time think they have a 'better chance' of winning. They don't. They have the same chance as someone who just bought his first ticket ever.

 

[Sukerkin]

Bill, as part of my previous education I have been cursed with having to have a fairly detailed level of involvement with the science (art? ) statistcs.

Probability is an area where people do seem to get particularly confused, even with what at first sight are straightforward 'problems'.

So, for any single die roll, the probability of getting a given number is fixed and unchanging, as you say. However, if the parameters are changed such that you are looking at the chance of a number coming up within a specified number of instances (rolls) then that probability is no longer fixed, as Buzzy said.

 

[Xue Sheng]

No, it doesn't.

The die does not know how many times it has been rolled. Every time it is rolled, the chances of any given number coming up is exactly the same. The probability never changes.

If I flip a coin, there is a 50% chance it will land 'heads'. If I flip it a hundred times, there is still a 50% chance it will land 'heads'. If it lands heads 99 times in a row, there is still a 50% chance it will land 'heads' on the 100th flip.

That's why people who play the lottery for a long time think they have a 'better chance' of winning. They don't. They have the same chance as someone who just bought his first ticket ever.

This is a great response to show why Statistics is not all it is cracked up to be there is a 50% chance every time you flip a coin of heads or tails but the probility is something different

Probability, or chance, is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

Chance however, in this case, to me is luck or fortune and yet probability can mean luck. But in Statistics it means

a. the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.

b. the relative frequency with which an event occurs or is likely to occur.

As to the lottery it is not so much how many tickets one has bought but how many tickets the lottery has sold that changes the likelyhood of a winner

 

[Bill Mattocks]

Bill, as part of my previous education I have been cursed with having to have a fairly detailed level of involvement with the science (art? ) statistcs.

Probability is an area where people do seem to get particularly confused, even with what at first sight are straightforward 'problems'.

So, for any single die roll, the probability of getting a given number is fixed and unchanging, as you say. However, if the parameters are changed such that you are looking at the chance of a number coming up within a specified number of instances (rolls) then that probability is no longer fixed, as Buzzy said.

Probability is always a prediction. The value will be determined, and for each individual roll of the die, the die is unaware and unaffected by the prediction probably places on it. "I'm due" is a fallacious statement, frequently repeated by people who mistake probability for statistical chance.

The probability that a given number on a die will come up as the number of rolls increases approaches 100%. The chance of any particular roll coming up a given number remains 1 in 6 regardless of what probability predicts for the mean average.

 

[Bill Mattocks]

As to the lottery it is not so much how many tickets one has bought but how many tickets the lottery has sold that changes the likelyhood of a winner

Correct. However, what people sometimes fail to grasp is that each lottery drawing is a new game. All odds are reset. A person who plays every lottery for ten years has the exact same chance to win as a person who plays the lottery for the first time ever, presuming that they each buy one ticket. If you want to increase your chances of winning, buy more tickets per game, not over time.

 

[Nomad]

I used to have a sig that said "41% of all statistics are made up."

Sorry, this is incorrect. I have it on good authority that 82% of statistics are made up on the spot.

 

[thardey]

Probability is always a prediction. The value will be determined, and for each individual roll of the die, the die is unaware and unaffected by the prediction probably places on it. "I'm due" is a fallacious statement, frequently repeated by people who mistake probability for statistical chance.

The probability that a given number on a die will come up as the number of rolls increases approaches 100%. The chance of any particular roll coming up a given number remains 1 in 6 regardless of what probability predicts for the mean average.

I think what they were referring to is the probability that the given number will be rolled anytime within that 100 rolls. Not each disparate roll.

If you rolled 100 dice, or one die 100 times, it is almost a 100% probability that at least one "six" would come up. As opposed to predicting each individual roll 100 times, in which case it would always be 1 in 6.

 

[Aniela13]

As part of my research training, a "statistics in psychology" course was required. What fascinated me (and very few other students...apparent I was one of the few that enjoyed the course!) was how many times our professor was careful to tell us things such as: "in this situation, make sure you show how big your sample was", "if a statistician or researcher doesn't have integrity, the numbers can become anything", and my personal favorite "a one-tailed test is almost always done to twist the facts" (if a test shows that something is initially not significant [probability less than .05 in most cases, sometimes under .01], the researcher can revise his hypothesis in retrospect to make it appear that he knew the direction of the data [this group was predicted *to do better/worse* rather than *to change* from this other group], thereby dividing the probability in half and making an insignificant change appear significant).

I have to agree with previous posts...when basing your opinion on statistics, make sure you know the sample size, characteristics of the sample, and (if possible) look at the entire study. It's a lot of reading, but when you've personally read through it all it makes it difficult for someone else to deceive you.

~Ani

 

[Bill Mattocks]

If you rolled 100 dice, or one die 100 times, it is almost a 100% probability that at least one "six" would come up. As opposed to predicting each individual roll 100 times, in which case it would always be 1 in 6.

That is correct.