Monday, March 19, 2007

Maths-statistics time!

Ok, enough with infinity, lets move onto something conceptually much easier. Statistics. You will, of course, remember the phrase "lies, damn lies, and statistics", which I'm pretty sure has been attributed to more than one person in it's time... Statistics don't really lie, but they can certainly be misinterpreted for someones gain. Statistics can sound impressive out of context, and without any kind of background, a statistic is fairly meaningless.

Generally, when someone says something like "57% of people hate you", they mean in a survey 57% hated you. It is very rare to talk about census data in statistics, although it of course occurs, and thats when you get your best results, because, well, you are talking about the whole population. The lies tend to occur on the lower level, but manipulation is everywhere.

The problem about statistics is that the results are not always obvious- they are sometimes counter intuitive. A nice example is tests. Lets suppose I have a great medical test that is correct 99% of the time. Awesome, you might think, lets use it!

That might not be such a good idea....

Suppose only 1 in 1000 people suffered from the illness. Then when I test the population if Britain (say) then there will be 60,000 with it- the test will catch 59,400. However there will be 59,940,000 people without it, and the test will think 599,400 of those have the disease! This is ridiculous, we have 10 times as many people who do not have the disease as do. This is why many tests that seem to be excellent are not used on a wide level, simply because you would end up scaring many many more people than you would save.

This is also worth baring in mind when you think about how strict the law should be. I suspect giving the police 99% accuracy is somewhat generous, but from this you can see that they would end up being wrong most of the time- this is partially why our legal system has to be so exacting, simply because we are not populated by criminals.



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