Once upon a time, goes the story, there was a Frenchman who travelled between country fairs. He said he could tell mothers-to-be whether they were expecting a little boy or a little girl. He asked only a modest fee and promised a full refund on his next visit if he turned out to be wrong.  As the years passed, his tally of successes grew alongside his reputation for honesty, as he paid out faithfully when his gift let him down. It was easy to be honest, as he earned a tidy living with no special skills beyond a pleasant face, an engaging line of patter -- and a better understanding of statistics than the average inhabitant of rural France. [Think carefully if you can't see the trick.]

It would seem that this wily Frenchman also understood statistics better than the members of New Zealand's Advertising Standards Authority. The NZASA recently rejected a complaint against Ken Ring, who claims that conventional meteorology is largely bunk and that the moon is the dominant driver of the weather. That by itself wouldn't earn him the attention of our Advertising watch-dog, but Ring also sells long-range weather forecasts based on his lunar meteorology: his website offers a range of subscriptions and one-off reports, and he makes strong statements about the quality of his services.

A key facet of the complaint was that "[Ring] is quite unable to make accurate long-range predictions", but in his rebuttal, Ring pointed to a number of apparently successful predictions. Like the itinerant Frenchman, Ring makes a lot of predictions, so luck alone ensures that some of them will be correct -- even a stopped clock is right twice a day. 

Beyond citing specific successful "predictions", Ring makes the stronger claim that his forecasts are "80 to 85% accurate", which the NZASA appears to have accepted without scrutiny.  It is not clear whether Ring submitted evidence in support of this number, but it is repeated several times on his website. On the face of it, 80-85% would be an impressive result, given that long-range weather forecasting is a notoriously challenging problem. However, this number is meaningless without a definition of "accurate" and a description of the methodology used to obtain it -- assessing the accuracy of weather forecasts is a complicated business. [Tip to any future complainants: ask how this figure was obtained and whether the result was independently verified.]

The NZASA decision dodges the real question, saying coyly that it is "not an arbiter of scientific fact". Strictly speaking this may be true. And yet, New Zealand advertising standards do require that claims for heath-related and therapeutic products be backed with evidence, and for these the NZASA does make a judgement call on the science. 

Statistical reasoning is a double-edged tool: it lets scientists sift useful knowledge from the noise of the world, but in other hands it becomes a device for separating the credulous from their cash.

Postscript: When I first heard the opening anecdote some time ago, it contained a Frenchman, although there is nothing explicitly French about the story. I searched for a source without success -- if anyone can point me to the origin of the story I would be very grateful. 

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