What are the odds?

[peterbirks]

One of the millions of things which annoys me at work is when a journalist almost proudly proclaims that he is useless at maths (female journalists usually have the common sense to keep quiet about it).

This all harks back to the tradition in English schools that to learn anything practical that might be used "in trade" is undesirable. Read English Literature so that you can natter about Thomas Hardy over the differ table, but learn how numbers work? O h no dear. "I need to take off my shoes and socks if a number goes above 10!" (guffaw, guffaw).

So, anyhoo,

A while ago I laid into a certain "expert" witness ( I can't even bring myself to name this person, but I do hope that he is stripped of his knighthood and profesorship) who stated that the chance of there being two cot deaths in the same family was one in 73 million, thus completely misunderstanding the concept of conditional probability (it depends on your starting point mate), and contributing to the wrongful conviction (later merely deemed "unsafe") of solicitor Sally Clark. The calculation, by the way, was off by a factor of more than 300,000.

Did anyone in the court question the original mathematical statement? No. Not the judge, not the defense lawyers. Presumably, they too, were too busy at university learning a lot of useless stuff and not learning something that might have kept Sally Clark from three years' wrongful incarceration.

And now, she's dead. I wonder what odds our expert witness would like to come up with here. What are the chances of a woman having two children who died from cot deaths dying herself at the age of 42? Cor, if the first was 73m to 1, then this one must be out of the stratosphere.

Luckily, few readers of this blog will be innumerate. What continues to frighten me is that so many people "out there" are not only innumerate, but they embrace it. I mean, I might not understand engineering, but I don't go round saying that it's not worth knowing about. And I certainly don't look to take the stand to testify on the way a motor engine works, just because I drive a car.

Comments

[ribmeister.livejournal.com]

Math is wonderful, certainly as a poker player, I love statistical mathematics and it is remarkably useful to learn!
Lots of things in life didn't seem so useful, for example, if I was having a heart attack, I'd love that kid near me to able to do CPR, instead, well, he can tell you the largest bone in the body or what a leyline is.
I'd love to see more practical, useful, subjects being taught in school. Things that have a real value to the community.
History and Geography should take up no more than a year of the school life as mandatory.

As for the expert, I totally agree, the two babies were clearly not mutually exclusive as they came from the same womb. Just like that other poor bunch of kids who had the rare salt build up disease. God I'd hate to think what the parents were thinking, loving their children, watching them die, then seeing themselves locked away in jail for it.

[geoffchall.livejournal.com]

There are some expertises (?) in which I am resolutely boastful of my ignorance. What happens under the bonnet of a car is one of them, gardening is another. I'm content to know that when I turn the key, the engine works. But boastfulness is a sort of defence mechanism in most circs. If you have no ability at something when you feel you should be, then you feel better it you can be assertive about your ignorance than if you are shame-faced.

It works with other fields, like languages and sciences. The one field where there is no real boasting of ignorance is English Language. People display ignorance and poor use of English but no-one boasts about how they can't cope with irregular plurals.

I think Sally Clark's guy is a different kettle of fish. This was someone who was boasting of mathematical skills that they didn't have and a courtroom full of people with insufficient numerical knowledge to gainsay an expert witness. You have to fault the defence who should have had an expert rebuttal witness to say, "don't talk numerical bollocks."

[(Anonymous)]

This is only true if you accept Pete's contention that the defence didn't question the maths.

In fact, I would consider that barristers, as a profession, are in my experience among the most intelligent and multi-talented people.

Except that bloke who defended Gutshot, of course.

Titmus

Maths, History, Death...

[real-aardvark.livejournal.com]

My cousin's first son was a cot death, whatever that is. SIDS is a term coined by Dr Beckwith in 1969. The good doctor has recently stated that "If a prize were offered for the poorest definition of a disease or disorder in the scientific literature, this one would be a strong contender."

So, not just a mathematical howler of almost inconceivable stupidity -- and a lot of people go into medicine on almost tribal grounds, so it might be unfair to expect any competence in statistics -- but also a howler in Prof Meadows' chosen speciality. What a dickhead.

I'm still kicking myself that I didn't advise my cousin to get a vasectomy immediately, given the 1/1000 chance of being banged away for three years on the next child. (And god forbid him converting to Mormonism and breeding like a rabbit. You'd need a special gaol just to house those fuckers.) Still, he bullied my brother and me as a child, so it would have served him right.

My brother's second child died of a 1/5000 prenatal lung condition (ten days after birth). The same logic presumably applies. ("I'll just stick this tube down baby's throat and fill his lungs up with a pint or so of saline solution...)

In fact, there's no limit to the number of possible worms in Meadow's can.

(I'm assuming, btw, that the starting point of having one cot death in the family is what you mean by "conditional probability." Alternatively, you could be alluding to Ribmeister's point that there's only one womb involved -- and for that matter, in roughly 85% of cases, only two testicles.)

And at this point I could be snide and ask how much of Ribmeister's education is currently of "real value to the community." But that just wouldn't be me. As usual I take exception to the labelling of History as somehow without value; I'd argue that it's usually of far more value than O-Level French (which I also think should be mandatory for five years), or for that matter O-Level Physics, Chemistry, or just about anything. Up to and including an Honours degree in Mathematics from Nottingham, if the guy to whom I had to explain matrix multiplication was anything to go by.

I mean, what are we left with? The only things I learnt of direct possible value to the community were basic life-saving in the Cubs and a water safety proficiency certificate at school. Perhaps we should give up secondary education altogether and just send kids to the boy scouts for six years...

It never ceases to amaze me how many people outside the field of education believe that it's all about training. It isn't. That's why it's called education. Anything else is just 1984 without the capital letters.

For all those of us who hold both The Law and the British Medical Council in deservedly high esteem, nay, a shivery feeling of awe, may I recommend the following link:

http://www.bmj.com/cgi/content/full/332/7535/196-a

Oh, and as far as I recall, the defense didn't challenge the maths. I don't know who these paragon barristers might be, but none of my solicitor friends have met any of them.

RIP, Sally.

[(Anonymous)]

It's a general point that the expertise of any expert should be taken with a pinch of salt. For several reasons, such as:

1. All humans make mistakes from time to time.

2. All professions contain some dimwits; not all of them by any means are weeded out.

3. In most professions, I think, there are grey areas in which no-one really knows what he's talking about; but distinguished professionals don't like to admit this. For instance, in some areas of medicine doctors are reasonably expert; in other areas they're little better than witch doctors. But they assume an air of professional competence in all areas regardless.

-- Jonathan

Expert witness

[(Anonymous)]

I seem to recall hearing that a lawyer in the original OJ murder trial stated something like: "the probability of a wife whose husband beats her being murdered by her husband is over 10,000:1". Correct, perhaps, but there is a serious piece of statistical trickery going on in that sentence. And it didn't get commented on for a long time, certainly not in the trial.