Why ‘up to’ means nothing at all

The sale looked impressive – posters in the window guaranteed savings of “up to” 80%. Wow. We were about to go into the store when my friend asked: “But what does that mean?”

Sampling, probability and non-probability

Evaluating the significance of a survey used to be fairly straightforward – for any truly random sample, there is a well-defined margin of error which allows a critical reader to judge how valid any inferences are.

So for a survey of 1,000 respondents, the margin of error is around 3% at the 95% confidence level (this last figures indicates there is only a 5% probability that the findings were the result of chance). If a news story says Ed Miliband is leading David Cameron by 42% to 37% in the polls, we know this falls within the stated margin of error, since Ed Miliband’s true position may be 39% (42% – 3%) and David Cameron’s may be 40% (37% + 3%).

The difficulty from the pollster’s point of view is that creating a truly random sample is costly and time-consuming. So recently, non-probability sampling has enjoyed favour, particularly in the US and now increasingly in the UK.

Why the world has no place for ugly truths

If G. H. Hardy is much thought about these days (and beyond fellow mathematicians, he probably isn’t), it is as much for his dazzling aphorisms as his dizzying flights in the upper reaches of number theory.

“There is no permament place in the world,” he declared, “for ugly mathematics”. This has led to Hardy being characterised as an aesthete in the Wildean mould, compounded by C. P. Snow‘s dark references to his sexuality (in the foreward to Hardy’s autobiographical A Mathematician’s Apology, Snow alludes to “intense affections” for young men, “absorbing … exalted” but – to Snow’s no doubt immense relief – “non-physical”).

But the equivocation is doubly misplaced.

That’s magic! … not a lot

Numbers have always been associated with magic, from the Kabbalah to ‘unlucky’ numbers, such as 13 (down my street, the people next to house number 11 choose to live at 15A, much to the mailman’s bemusement).

The most recent version is exemplified in the online gaming shows, such as Jackpot247,  which tend to grace our airwaves in the unholy hours.

Watch the routlette shows (roulette having a negative chance of winning, so your optimal betting strategy here is to gather together all the money you ever, in your entire life, intend to gamble on routlette in a neat pile in front of you, and risk it all on one single, inglorious spin)

Goats, buses and the lottery

I can highly recommend Marcus du Sautoy‘s video on the Guardian’s new Newton channel, exploring the world of chance and probability.

The good professor shows how probabilities become counter-intuitive as soon as a modicum of complexity is introduced. We all know that the chance of guessing heads on a coin-flip is one-in-two, and it’s fairly straightforward to show the chance of scooping the National Lottery jackpot is just under one in 14m.