Just Random?

Nine people have got breast cancer in an ABC newsroom in Toowong over the last 12 years. This is similar to the case of a spate of seven brain tumours in seven years at RMIT where the installation of a mobile phone tower was being investigated.

Obviously both these case look like there is a common link, but is it really? Are the chances of this occurring so low that we can rule out a coincidence?

Taking the breast cancer incidence we have the fact that just over 1 in 1000 women will get breast cancer each year. There are 60 women working at the studio in question. Thus over a period of 12 years we would expect around 1 woman to get breast cancer 60*12 = 720 woman-years. Using my rather simple binary model for 720 woman-years, gives something close to 1 in 1 million chance of this occurring. Long odds you would think…

Of course you also have to consider that this is happening all across the country and we don’t hear of it very often. There are some 4 million or so women working in Australia. If they all worked in workplaces with 60 employees per location we would have around 70,000 work places. So given this we would expect about a 7% chance for this to happen at least once. Still pretty long odds but no longer totally out of the question. The final point is that this is 7% per year. Across say 10 years, we are looking at getting to a figure of greater than 50%.

Now all these figures are approximations and fairly gross ones, but I’m pretty confident that they are in the right order of magnitude. Yes, some of the women were young and have a lower chance, than this, however some of them would have been older and have had a higher chance. The figure used is the average across all ages.

I would also stress of course there may well be an environmental factor. I sure can’t rule it out from my keyboard. The point is though that the chance of this happening somewhere, every so often, isn’t that unlikely, even if we just consider this one type of cancer. That something is unlikely to happen to me in particular is not the same as being unlikely to happen to someone somewhere. Randomness is not evenly distributed, and there would appear to be at least as much chance that these women have all had the bad luck to get cancer together, as there is of a common cause.

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5 Responses to Just Random?

  1. Rod Clarke says:

    this sound just like the Birthday paradox I was reading about in wiki the other day. After surfing around your links on Solid spheres

    http://en.wikipedia.org/wiki/Birthday_paradox

  2. Steve says:

    Its sort of similar. The point is that across a country of 20 million people you are going to get some long odds things occuring at times. In the same way that any one person has bugger all chance of winning Lotto, but the chance of someone winning it is actually very good.

    I certainly think the site should be well tested, but ultimately you have to realise that it may just be a random coincidence.

  3. Sacha says:

    It disappoints me when I see people not understanding probabilities and saying that “X must be causal” and not considering that it might just be random. This seems quite prevalent.

  4. Sacha says:

    Making causal leaps where they’re not warranted might be a result of how we evolved.

  5. Steve says:

    Sacha,

    I tkink its to be expected and fair enough that you would want the site investigated. The point is to realise that it might also be random, and if the site is cleared then it probably is.

    Its difficult to imagine what might be going on at this TV studio that doesn’t occur in thousands of places around the world. So once you’ve tested the site for radiation and toxic chemicals then you’ve got to figure its just bad luck.

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