Death

How Statistics Turned a Harmless Nurse Into a Vicious Killer

Let’s do a thought experiment. Suppose you have 2 million coins at hand and a machine that will flip them all at the same time. After twenty flips, you evaluate and you come across one particular coin that showed heads twenty times in a row. Suspicious? Alarming? Is there something wrong with this coin? Let’s dig deeper. How likely is it that a coin shows heads twenty times in a row? Luckily, that’s not so hard to compute. For each flip there’s a 0.5 probability that the coin shows heads and the chance of seeing this twenty times in a row is just 0.5^20 = 0.000001 (rounded). So the odds of this happening are incredibly low. Indeed we stumbled across a very suspicious coin. Deep down I always knew there was something up with this coin. He just had this “crazy flip”, you know what I mean? Guilty as charged and end of story.

Not quite, you say? You are right. After all, we flipped 2 million coins. If the odds of twenty heads in a row are 0.000001, we should expect 0.000001 * 2,000,000 = 2 coins to show this unlikely string. It would be much more surprising not to find this string among the large number of trials. Suddenly, the coin with the supposedly “crazy flip” doesn’t seem so guilty anymore.

What’s the point of all this? Recently, I came across the case of Lucia De Berk, a dutch nurse who was accused of murdering patients in 2003. Over the course of one year, seven of her patients had died and a “sharp” medical expert concluded that there was only a 1 in 342 million chance of this happening. This number and some other pieces of “evidence” (among them, her “odd” diary entries and her “obsession” with Tarot cards) led the court in The Hague to conclude that she must be guilty as charged, end of story.

Not quite, you say? You are right. In 2010 came the not guilty verdict. Turns out (funny story), she never commited any murder, she was just a harmless nurse that was transformed into vicious killer by faulty statistics. Let’s go back to the thought experiment for a moment, imperfect for this case though it may be. Imagine that each coin represents a nurse and each flip a month of duty. It is estimated that there are around 300,000 hospitals worldwide, so we are talking about a lot of nurses/coins doing a lot of work/flips. Should we become suspicious when seeing a string of several deaths for a particular nurse? No, of course not. By pure chance, this will occur. It would be much more surprising not to find a nurse with a “suspicious” string of deaths among this large number of nurses. Focusing in on one nurse only blurs the big picture.

And, leaving statistics behind, the case also goes to show that you can always find something “odd” about a person if you want to. Faced with new information, even if not reliable, you interpret the present and past behavior in a “new light”. The “odd” diary entries, the “obsession” with Tarot cards … weren’t the signs always there?

Be careful to judge. Benjamin Franklin once said he should consider himself lucky if he’s right 50 % of the time. And that’s a genius talking, so I don’t even want to know my stats …

Advertisements

World Population – Is Mankind’s Explosive Growth Ending?

According to the World Population Clock there are currently about 7.191 billion people alive. This year there have been 118 million births (or 264 per minute) and 49 million deaths (or 110 per minute), resulting in a net growth of 69 million people. Where will this end? Nobody can say for sure. But what we can be certain about is that the explosive growth has been slowing down for the past 40 years. I’ll let the graphs tell the story.

Here is how the world population has developed since the year 1700. The numbers come from the United Nations Department of Economic and Social Affairs. From looking at the graph, no slowdown is visible:

Image

However, another graph reveals that there’s more to the story. I had the computer calculate the percentage changes from one decade to the next. From 1960 to 1970 the world population grew by 22 %. This was the peak so far. After that, the growth rate continuously declined. The percentage change from 2000 to 2010 was “only” 12 %.

Image

Of course it’s too early to conclude that this is the end of mankind’s explosive growth. There have been longer periods of slowing growth before (see around 1750 and 1850). But the data does raise this question.

Talk to me again when it’s 2020 or 2030.

Just by the way: according to estimates, about 108 billion people have been born since the beginning of mankind (see here). This implies that about 101 billion people have died so far and that of all those born, 6.5 % percent are alive today.

Did somebody say dust in the wind?

Smoking – Your (My) Chances of Dying Early from it

I admit that I smoke. And my first attempt to quit after 13 years of a pack a day only lasted one month. Here’s what convinced me to try:

  • 50 % of smokers will die early due to their habit (Source: WHO)
  • On average smokers die 10 years earlier (Source: CDC)
  • Every year about 6 million people die from smoking related diseases, that is more than one Jumbo Jet full of people every hour (Source: WHO)

Most sensible people wouldn’t play Russian Roulette, but some take even higher chances at early death with smoking.

http://www.who.int/mediacentre/factsheets/fs339/en/

http://www.cdc.gov/tobacco/data_statistics/fact_sheets/health_effects/tobacco_related_mortality/

 

The good news: If you start smoking in your teens, and quit at …

  • … the age of 30, you get all of the 10 years back; the damage done is almost completely reversible
  • … the age of 40, you get 9 of the 10 years back; the damage done is reversible for the most part
  • … the age of 50, you get 6 of the 10 years back; some of the damages are still reversible
  • … the age of 60, you get 3 of the 10 years back; most damages will remain, but life quality will improve

Since I just hit 30, I’ll be sure to give it another try once my vacation is over. Having too much time is a very bad idea if you want to quit, better do it when you’re busy.

http://www.netdoctor.co.uk/healthy-living/lung-cancer.htm

http://www.rauchfrei.de/raucherstatistik.htm