ZapperZ said:
The statistics asking if a PhD recipient would do a PhD again is "naked data".
There's no such thing as naked data.
Do not confuse the two and undermining the statistics themselves.
Personally, I think that all data has to be treated critically, and you end up in a lot of trouble if you take any sort of data without thinking about what it means.
The reason I mention this is that I think that the OP ought to be encouraged in asking the question that he did. If it turns out that the statistics and the anecdotal data match up then you have more confidence in trying to figure out what is going on. If they don't then you dig some more and figure out what is going on.
But then, I can turn this around and tell you that without knowing the statistics, you might only hear about the tail ends of the Normal curve and miss the majority that is a more accurate representation of the situation!
Sure, you might get in trouble if you take anecdotal information and incorrectly assume that the data is representative, but you'll run into equally as much trouble if you assume the same thing about statistics. I'm not saying that you should ignore statistics, but it's *vital* that you cross check the stats with other data. Anecdotal information can get you into selection bias, but you have to be very careful with statistics, because they can be biased in the same way. If you are careful with your interviewing technique, you can often pick up selection bias with interviews more readily than you can with a survey.
The curve is almost never normal. What is often the situation is that you are trying to figure out the shape of the curve. One thing that you find in finance is that it is a bad, bad, bad, bad, bad thing to assume normality since extreme events happen far more frequently than the normal distribution.
Also, it really depends on what you care about. For example, if you are in risk management, you don't care about the 99.999% of days when the market doesn't crash. Most days you go to work, and the market doesn't crash, and you go home happy. What you do care about is that one day in 30 years in which the market does crash. The fact that Lehman Brothers only failed once is pretty irrelevant.
Now which one is more "accurate". It depends what you question are asking.
The extreme case? I don't get it. Norway had one major shooting incident in how many years that made the headlines around the world. So using that alone (the worst case situation), you are ready to make a conclusion on the crime rate in Norway? Is this rational?
Again it depends on what you are trying to figure out. You'll get into just as bad a situation if you assume because most days in Norway there are no major shootings that you shouldn't spend money on SWAT teams and police. Most days there are no hurricanes in New Orleans, but that doesn't mean that you shouldn't care about building dams and levees, or that you should ignore that possibility because it is a rare event. On the average, ships won't collide with icebergs, but you still want to have lifeboats ready.
If you work in risk management, you know financial crashes are rare but *YOU DON'T CARE*. You want to find out as much as you can about historical crashes and bulletproof your bank. To use your Norway example. If you are the head of the special anti-terrorist police, you don't care what the general crime rate is. You care that in the one situation when all hell breaks loose, you can survive.
A lot of this is influenced by my daily work. After the Lehman crash, you had a huge number of people getting hired in risk management and model control, and a lot of this work involves having a government official stare at you and ask, if this extreme, improbable event occurs, can you survive, and what will you do? They want to know that if you hit an iceberg, you have enough life rafts and have done the drills so that you don't take down the world economy (again). Telling them that in 99.99% of the days the world won't crash is irrelevant and will get you fired for incompetence. What you really what to do is to look for people that survived iceberg hits or didn't survive iceberg hits, and find out what they did.
Also relying on statistics can be dangerous. In physics and biology you can assume that the laws of physics and the human body don't radically change, but you can't assume this for economics. One thing that got people in trouble was that everyone looked at the numbers for mortgages in 2005 and they looked good. No one was defaulting. Everyone was happy. The loan statistics looked reasonable. What a lot of people didn't do was to just call people up and see what was going on. Forget about the numbers, who are you loaning to and what are the conditions of the loans. People that did that quickly figured out that massive loans were made out to people that couldn't possibly pay them back, and all of the statistics were being fudged, and we were heading to a blowup. The people that I work with managed to survive that part of the crisis because they didn't just trust the numbers and spent a lot of time questioning the statistics, which is why I'm glad that the OP is doing the same thing.