Statistics and Common Sense

[HydrogenBond]

One of the very useful tools of science is statistics. Unfortuneately, statistics also has a negative side that allows one to defy common sense. I would like to give an example.

 

If we gave everyone on the earth a ball and told them to throw it in the air, all the balls would fall to the earth due to gravity. Many people may not understand gravity but their common sense due to similar experiences, would tell them in advance what they should expect from this experiement. Very few people would expect the ball to levitate or keep going up unless they were out of touch with reality.

 

To make this experiment more scientific we next use a statistical study. Even though the data will be 100%, there is always a margin of uncertainty to statistics, due to theories like chaos. So the final results may look something like 99.99 +/- .01% to account for any unknown variables, lack of experimental control, etc.

 

Even the slightest honest statistical margin of error opens a new door, next to common sense, that leads to Disney World. If one is trying to formulate a theory for the falling ball, it is admirable to look at the variablity in the data so the theory can be made more inclusive. Possible things that would prevent 100% certainty may be the appearance of anti-gravity, influences of parallel universes, other dimensions, etc. One can see how common sense can be put aside in exchange for speculation into virtual reality due to focusing on the mathematical margin of uncertainty. I used Disney World because many of the rides are reality simulations that are quite good. But unlike leaving the vacation at disney world, one may takes these reality simulations back to their real world in total disregard to their original common sense. In the first experiment only those who lack common sense justify the ball not falling. While in the second statistical experiment some of the best minds begin to posulate the same thing due to shutting off their common sense in favor of speculation.

 

Another example is often used by the media to help sell soap. For example, if a new worm flu is discovered, the media might report that there has been a 50% increase in the worm flu over the past year. This would set off an alarm. What they don't provide is a common sense perspective which allows one to understand what the data really means. If there were only 2 cases last year and three this year, 50% doesn't mean quite the same thing, in the imagination. If one was to compare this new worm flu mortality rate to other things, it would not be considered even a minor threat. Yet science, politics, media, histeria often use math apart from common sense to drive culture to disney world. The experts have common sense but the voice of reason is often quiet.

[ronthepon]

Interesting.

 

But I must say that like many other things, statistics is a tool to be used with care, and in places where it is correctly useful.

 

I am sure that you are aware of the many different statistical methods of displaying data. (Not representations, methods) For most instances, there is a method that fits the scene correctly.

 

Further, for the gravity ball experiment you described, the margin of error would be expected, and usually ignored.

 

But the flu worm thing has a good lot of powerful reason. But again, there is another method of describing it scientifically and simultaneously with common sense. Take the method of absoute cases.

 

Using wrong statistical methods is also a powerful method of expressing the situation with maximum force. A good deal of social magazines use it here to over blow the situation.

[HydrogenBond]

The uncertainty in the gravity ball experiment is easy to ignor because one has common sense as a guide. But if one enters an arena where common sense has not yet been developed due to novalty, who knows where disney world begins or ends.

 

I believe commom sense is grounded in physical reality. If one looks at evolution, life evolved under the constraints of all the practical realities within the changing environment. If the environment gets colder, evolving animals will gain insulation value instead of lose it, i.e., common sense evolution. Instinct is a more advanced way to deal with reality, based on common sense behavior that has been averaged over time.

 

Statistic provides a way to separate ourselves from common sense. It is based on a black box, which is suppose to put blinders on our common sense, i.e., don't think, wait for the data to tell you what to think. Most people don't believe there are natural human instincts. This may be a sign of the times, indicative that human common sense, grounded on natural human instinct, is going the way of the dinosaur.

[TheBigDog]

Interesting thread HB. I always find it interesting how statistics are spun to push an agenda. One of my favorites is airbags in cars. While thousands of lives are being saved and injuries prevented by airbags, a twist of statistics is used to make the airbags themselves seem more dangerous than the crashes that are causing them to be deployed. We do not have an emidemic of spontanious airbag deployments. But from reading the warnings that are mandatory in every car you would think there was a loaded gun in the dashboard that might go off at any point in time. When in fact there is a safty device that will cushion you from harm in a violent crash, and you would CERTAINLY be at higher risk than if it were not there. This goes for both adults and children, thousands of whom have been saved by airbags, while some have been killed -many of whom would have dies anyway in the violent crash that deployed the bag to begin with.

 

Not trying to make this and airbag debate. I am using this as an example of statistics being used to drive an agenda.

 

Bill

[HydrogenBond]

Old Time science was based on observation of phenomena, forming a hypothesis, and then testing it with experiments. The hypothesis was either good or bad based on whether the experiments worked or not. Statistics makes the process half backwards; run the experiments in a black box, massage the results with statistics, and then form a hypothesis based on fuzzy data (halo of uncertanity). The problem with fuzzy data is that it allows more curves to be drawn through the points. If one had a zig-zag line with period side dots, if we connect the dots we will get a zig-zag line. If the dots are the size of pennies, I can connect the dots with a straight line, zig-zag line and everything in the middle. This gives us a range of mathematical correlations, with only one reflecting reality.

 

Statistical science assumes that one can not open the black box, allowing room for subjectivity. Whereas, old time science begins by opening the black box and draws conclusion on what is going on inside. This takes away the subjectivity because theores need to be made consistent with the inner working instead of an output product.

 

The black box approach does has an advantage. Because it does not require understanding the mechanism in the black box, but can provide a correlation for the data, it allows more people to participate in research. But science needs to stress than this is a secondary approach to be used if the blackbox is too difficult open. Unfortuneately, the former is starting to believe it is primary instead of secondary science.

[HydrogenBond]

What sort of soured me to statistics was during a development project that was being scaled up. It was to be used for mercury water remediation and had political ramifications. I developed the process with old time science. There was no black box because the process was consistent with sound chemistry and worked like a charm.

 

Since others in upper management were not as familar with the technology, they gave me a full time statistician to make sure they could cover their political hinnies if something went astray. After pleading, they forced me to put the process into the black box. In the end, the black box was not needed because the mechanism worked exactly like predicted. Personally, I like to look in the black box and don't give much credibilty to black box science because it creates too much subjectivty. In my case, the politics required using statistics for its subjective fuzzy data value.

[someguy]

With the ball in the air scenario the 99% accuracy provides the statistical equaivalent of perfection. I think that 99% defines reality, maybe even 90%. The problem lies in satistics itself, or rather in percentages. When people see that there is a 99% chance they don't see 99 they see 1%. This is common in our society. People seem to look for the exception to the norm rather than point to the reality. Many superstitions (such as religius ones) support this kind of thinking. It seems to stem from an anti-science kind of thinking. That these are things that defy science itself or are unexplainable phenomena.

 

Common sense is something that simply doesn't exist. No two people will give you the same list that makes up common sense. So to defy common sense doesn't make any. What people are defying is plain old sense. They are defying what everyone else sees. They are saying that they think the unlikely is possible ad therefore probable. It is the Gambler's fallacy that you speak of.

 

In the other example, it is the missuse of statistics to sell soap and is disgusting. This is another reason why people deny their senses, it helps others make money.

Someguy

[HydrogenBond]

If someone was knowledgeable with statistics they may know that 99% is about as close to perfection as one may get with statistic. But like you said, that 1% opens the door to a bit of uncertainty that general sense would say should not exist. That uncertainty plays into the hands of all types of speculation.

 

That 1% is not just the realm of religion, marketing and the layman but is also used in areas of science. For example, it is assumed that the proton will decay. The odds are one in a zillion every million years (not exactly) Experiments were set up to look at this improbable trace chance to help prove theory based on these very slim odds. Physics is riddled with this. If we add Chaos theory, i.e., something is going to go wrong, than almost anything is possible leading to all types of speculation supported by math.

[TheBigDog]

In manufacturing 1% is totally unacceptable error. There is a well established set statistically based quality tools for standardizing processes and driving out variation. The goal of these is to acheive 6 sigma, or to have just 3.4 failures per 1,000,000 opportunities. But acheiving such high rates of success you take out of your cost structure the myriad of things you normally do in manufacturing to deal with less than perfect products. Six sigma is the holy grail, and very few industries actually acheive that level of performance. But in driving for it they remove all sorts of extrenuous costs and make a more reliable product.

 

But other industries need even more reliable performance than six sigma. Would you ride in an airplane if 3.4 of every million landings missed the runway?

 

Statistics are also useful when dealing with many complex systems that all need to all work perfectly. Take the space shuttle for example. If there are 100 systems on the shuttle that can cause it to have a misson failure, and each of those systems is 99.9997% reliable (six sigma), then the chances of a succussful mission is 99.966%. Sounds pretty good! Now you want to have 100 missions. What is the chance of a failure in 100 missions each with 100 critical components? 96.65% that nothing will go wrong. So any single mission is most likely to happen flawlessly. But in 100 missions have are likely to have serious problems with 3. So although each of the individual systems is nearly flawless, as you compound them together you get a less and less certain outcome.

 

So what does this have to do with common sense? It means that what we get in life is often exactly what we should expect. And statistics can help us to keep our expectations in line so we don't get disappointed too much by the inevitable.

 

Bill

[sebbysteiny]

You raise, from what I can see, two very interesting points and very different points.

 

Throwing ball experiment

People have said that whilst this is statistically true, most people would not have a problem with this type of situation because COMMON SENSE shows what is and is not a sensible thought. However, common sense is a very devious thing. It only applies to matters that have either been directly experienced by us or have been spoonfed into us at school. It therefore follows, that when making any kind of break into matters that we have not yet experienced, common sense will be a poor guide. For example, the idea that the world was round defied common sense for years. Further, the idea that the universe is actually a 4d universe of spacetime curved by matter also defies common sense, yet it is right to within the same margin of error. Even in politics, common sense often only reveals the first layer of a much deeper and unobvious problem. For example, common sense says if you increase the taxation on the rich, you get more money. However, labour (in UK) during the 60's (I think) tried that and discovered that when they reduced top rate taxation from 60% to 50%, they actually got more because the rich stopped funnelling their millions into tax havens.

 

I think that one must pick a %age certainty beyond which one is prepared to trust absolutely regardless of common sense. Sure you will be wrong once a year, but it's better than being wrong once a day.

 

worm flue

This seemed more about the way statistics can be distorted to create an argument that is unsupported by the facts for the purposes of hysteria or political advocacy.

 

Whist this is true, I am fundamentally uncomfortable with the alternative idea, that statistics are as easy to manipulate as molten steal and therefore cannot be trusted. I believe that one must treat them as one does with most propaganda and headlines. Try and ascertain the key facts and make up your own mind. With statistics, simply ask, yourself 'what are the real statistics that I would like to know to answer a point' and then find those facts. %age change, and absolute numbers will have a large effect on this. For example, in a news paper article today, the UK government will invest in speed cameras that take an average speed of people in residential roads. However, these will be expensive, and although it may reduce the number of road deaths by about something like 50%, England has the safest roads in the world and the money is probably best spent on hospitals where it will save far more lives. Again, it's just a question of finding the correct statistic and not allowing a politician or journalist with an agenda to do the work for you.