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Here’s How Little I See Your Point

You may have seen an article linked to last week, written by Jordan Weissmann at The Atlantic. The article was titled ‘Here’s How Little Math Americans Actually Use At Work‘, although mysteriously this journalist makes use of some mathematical analysis of survey data, and not only that, the data appears to show that 94% of Americans claim to use mathematics as part of their daily job.

The article discusses people’s misconceptions about the future utility of what they were learning, as well as the divide between using ‘any math’ and ‘advanced math’, which includes calculus, algebra and statistics. The number of Americans who admitted to using this type of maths appears to drop off once you get to anything more complicated than fractions, and also presented is an analysis of this divide by job type.

A very well-written and thoughtful response to this has already been posted at mathematics professor Bret Benesh’s blog, which gives four reasons why the article annoyed him (and probably several other people too).

Investigative journalist attempts to test whether GCSE maths is ‘dumbed down’

Barnie Choudhury, principal lecturer at the University of Lincoln’s school of journalism with a background in investigative journalist, is taking the GCSE examinations in an attempt to “test whether or not the allegations made in recent years that exams had been ‘dumbed down’ were true”. An article in the Lincolnshire Echo says:

He sat his O-level in maths in 1981 and came out with a B grade.
If he does not match this when the GCSE grades are revealed in August, Mr Choudhury believes this will prove that exams today are harder.

Flaws in the experimental methodology left as an exercise for the reader, although Mr Choudhury hints at some when he is quoted saying:

A part of me is hoping that journalists are right – that exams are easier. But I see my daughter’s mathematics work now and I don’t know any of it. So I thought if she was going through the pain, then so would I and I’d see for myself how tough the exams are.
But now I’m wishing I hadn’t started. It has not been dumbed down at all – if anything, I’m finding it more difficult the second time around, even though I’m older and I’ve sat lots of exams in my life. Maybe my brain has slowed down but it really is difficult.

Source: University of Lincoln lecturer inspired to take maths GSCE by his children.

Visualising the wrong data on the Guardian data blog

This visualisation shows for each council or unitary authority how many hours a week you’d need to work, earning minimum wage, in order to pay the median rent for a one-bed flat. The minimum wage is a national constant.

No justification is given for using the median rent. In a fair world, the median rent should be paid by someone on the median income. Assuming that people earning the minimum wage are the lowest earners1 and make up X% of the population, then an upper bound for rent paid by people earning minimum wage should be the Xth percentile, if housing is provided fairly2.

Continue reading “Visualising the wrong data on the Guardian data blog” on cp’s mathem-o-blog

A Dismal Performance from the Dismal Science

Paul J. Ferraro and Laura O. Taylor ask, “Do Economists Recognize an Opportunity Cost When They See One? A Dismal Performance from the Dismal Science

One expects people with graduate training in economics to have a deeper understanding of economic processes and reasoning than people without such training. However, as others have noted over the past 25 years, modern graduate education may emphasize mathematics and technique to the detriment of economic reasoning. One of the most important contributions economics has to offer as a discipline is the understanding of opportunity cost and how to apply this concept to all forms of decision making. We examine how PhD economists answer an introductory economics textbook question that requires identifying the relevant opportunity cost of an action. The results are not consistent with our expectation that graduate training leads to a deeper understanding of the concept. We explore the implications of our results for the relevance of economists in policy, research, and teaching.

Importantly, given four options, only 21.6% of respondents chose the correct one. They performed worse than chance. Some feeble statistical analysis is performed by the authors.

This challenges none of my views about economists: none of them can do maths; none of them can do statistics; what they do has very little rational basis; they are terrible at designing questions for undergrads that don’t require you to make assumptions, often drawing heavily on cultural knowledge.

Found via MetaFilter, which compares the problem to the Monty Hall problem in probability. Nowhere near, in my opinion.

Pricing bot interactions

Carlos Bueno writes about a book “Computer Game Bot Turing Test”. This, he says, is:

one of over 100,000 “books” “written” by a Markov chain running over random Wikipedia articles, bundled up and sold online for a ridiculous price. The publisher, Betascript, is notorious for this kind of thing.

He writes that the pricing bots on Amazon Marketplace have got hold of this book and are “fight epic price wars” over it.

So with “Turing Test” we have a delightful futuristic absurdity: a computer program, pretending to be human, hawking a book about computers pretending to be human, while other computer programs pretend to have used copies of it. A book that was never actually written, much less printed and read.

He then talks about his own book (Lauren Ipsum; a children’s story about computer science) and how he saw pricing bots fighting over this. The book is print-on-demand, so a bot claiming to have a used copy could simply buy a new copy and resell it for a profit. Then the bots started to undercut the retail price! Finally, the Amazon pricing bot put his book on sale at 28% discount (and Amazon swallows the difference).

My reaction to this algorithmic whipsawing has settled down to a kind of helpless bemusement… After all, I no longer have a choice. The price is now determined by the complex interaction of several independent computer programs, most of which don’t actually have a copy to sell.

Read the whole story: How Bots Seized Control of My Pricing Strategy.

Why I like some bad maths stories

My two most recent posts here have been about a story reporting a coincidence as more exceptional that it is and ‘bad maths’ reported in the media. Both are examples of mathematical stories being reported in a way that is not desirable. Somehow, though, I like the whist story and dislike the PR equations. I have been thinking about why this might be the case.

The PR-driven, media-friendly but meaningless equations from the first article are annoying because they present an incorrect view of mathematics and how mathematics can be applied to the real world. Applications of mathematics are everywhere and compelling, yet the equations in these sorts of equations seem to present little more than vague algebra. The commissioned research with seemingly trivial aims I find more difficult because, as commenters on that article pointed out, it is really difficult to decide what is trivial. Still, reporting that a biscuit company has commissioned research into biscuit dunking is either meaningless PR or else a matter of internal interest, and certainly nothing like what I expect mathematicians do for a living.

Coming back to our Warwickshire whist drive: what do I like about this story? It too presents incorrect information about mathematics and the real world, claiming that the event, four perfect hands of cards dealt, is so unlikely that it is only likely to happen once in human history (and it happened in this village hall!).

I think the difference is that the mathematics used, combinatorics and probability, appear to be correctly applied. The odds quoted, 2,235,197,406,895,366,368,301,559,999 to 1, are widely reported and I see no reason to doubt them.

The problem, then, is one of modelling assumptions. Applying a piece of mathematics to the real world involves describing the scenario, or a simplified version of it, in mathematics, solving that mathematical model and translating the solution back to the real world scenario. In this case, the description of the scenario in mathematics assumes that the cards are randomly distributed in the pack. This modelling assumption, rather than the mathematics, is where the error lies.

The result is still a bad maths news story, presenting a mathematical story as something other than what it is, but while the PR formulae are of little consequence, this incorrect application of a correct combinatorial analysis is something we can learn from.

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