Veni, Vidi, Validity – Blue Monday and Valid Arguments

(This post to the tune of…)

Professional statistics-mangler Professor Cliff Arnell is conquering the news again today, for his yearly profile-raiser about this being the most depressing day of the year. As Ben Goldacre has pointed out, he was paid to produce this research by Porter Novelli, a PR firm, who pitched the idea and date out to several academics back in 2005, to persuade people to buy holidays from a client of theirs. However, as any fule logician knos, merely because something has dodgy premises, that doesn’t mean it isn’t true – and vice versa, just because something is right, doesn’t mean that it was arrived at validly.

Admittedly, Arnall’s premises are totally flawed. His first assumption is, not only that depressive the  measurable, but that it’s the same for people all around the world; his statement is so all-encompassing that the ridiculousness of the equation he came up with isn’t really undermined by his self-deprecating honesty in saying “I’m only doing this for the money” – essentially he’s renting out his qualifications to the PR firm. The travel firm had chosen this date because it was the date they wanted people to start booking their holidays, and it was a cheap way of getting lots of national newspaper coverage (compared to advertising).
There’s an argument about validity here – arguments can be valid, but not true, and statements true, but not valid. Cliff Arnall’s argument is valid like so;
1: The day that maximises this equation is the most depressing day
2: January 18th maximises the equation.
C: Therefore January 18th is the most depressing day.
Sadly, his first premise is false, as his equation is utter bollocks, but there’s a second point – it’s possible to have a true conclusion even when all the premises are false.
1: Everything that has either Perpetual Yeast or Infundibulum Baking Soda in rises every day.
2: The sun is 90% Perpetual Yeast.
C: Therefore the sun rises every day.
So this could be the most depressing day, independent of his nonsense – and it has to be admitted that this _is_ a tremendously depressing day in Britain, the day when the glow of the holidays has completely gone and the grind of the next 11 months becomes apparent. Doing a quick straw poll of Facebook and Twitter, there’s significant number of people (above the normal monday whingers) complaining about this being a rubbish day/week. I’m not going to claim that this is statistically significant – just that my experience seems to bear up Arnall’s arbitrary claim. This could, of course, be because those people have seen the Blue Monday coverage in the news, and they’re highly impressionable.
There’s also the point that even if this is the most miserable day of any year, which I doubt considering the snowbound depression many people were in early in the year, or the Mumbai attacks of November 2008, or the tube attacks of 2007, even if it was for Britain, it’s not for the rest of the world. As Goldacre has said, seasonal suicide peaks vary from country to country and there’s been no consistent findings amongst studies. Of course, again, one shouldn’t link suicide peaks to depression peaks – though our intuition is that the two should be linked, the connection isn’t necessary, especially not when talking about the population at large. Many people were depressed when, say, England lost the cricket, or the Princess of our Hearts forgot to put her seatbelt on.
Cliff Arnall is wrong on so many levels; moral, factual, mathematical; that one should really just ignore him, but the total invalidity of his premises sadly doesn’t invalidate his conclusion.