I've been wanting to post about this story for a while, but couldn't figure out what to say that hasn't already been said by many people before. So I'll just summarise and give one very interesting (if saddening) link. Google for more if you don't know the story already.
Joyce Hatto was a classical pianist who, after an unremarkable performing and recording career, retired in 1976, reportedly with inoperable ovarian cancer. Late in the 1980s, however, she began to release a series of CDs, produced by her husband on his own small independent label, that got rave reviews in the classical music press. When she died in 2006, she got flattering obituaries from pretty much every newspaper in the UK. But in February 2007, compelling evidence emerged that many of her highly-praised recordings were fakes: copies of earlier recordings by other, talented but semi-obscure pianists, sometimes sped up or down to alter the timing (and the pitch) slightly, but otherwise little modified from the originals. After some days of feigning ignorance, her husband, William Barrington-Coupe, came clean on the fraud; but it is still unknown how much of her repertoire was forged and how much may have been genuine.
Christopher Howell has a riveting article on his personal correspondence with Barrington-Coupe and Hatto. (Thanks to Pinaki for the link.) We rarely get to know what makes plagiarists tick; but the letters make fascinating reading for the detailed attention they pay to the deception. We don't know whether Hatto herself was party to the scam, but sadly, it appears she may not have been ignorant of it.
One other note: though the Hatto recordings lined up perfectly with previous recordings (nobody could have deliberately reproduced their own recordings to that accuracy, let alone someone else's, let alone accidentally), apparently that wasn't enough to totally convince some in the music press. Quoth Stereophile:
CHARM did timescape analyses of two different reissues of Jerzy Smidowicz's recording of Op.68 No.3. On a scale where precise agreement would be 1.0, the two reissues showed a correlation of 0.993. Comparing the Hatto and Indjic performances of the same mazurka resulted in a correlation of 0.996; comparing all 54 resulted in a correlation of 0.999.
Conclusive? Perhaps not, as there is still a one in 1000 possibility that Hatto made her own recordings, but certainly troubling.
Statistics 101 for Stereophile and friends: coefficients of correlation aren't probabilities. They can even be negative. In this case, the probability of getting such a correlation by chance is vanishingly small (just as the probability of two independent runs of 1000 coin-tosses being 99.9% identical is vanishingly small -- not one in a thousand, but more like one in 10^298). Perhaps, however, it was such ignorance of statistics that led Barrington-Coupe to initially try to bluff it out.
But music reviewers aren't the only ones confused by probability and statistics: a recent paper (that I mentioned two posts ago), purporting to link astrology and various diseases, made the point that standard methods used blindly by many medical researchers can suggest correlations when there are none. With a more careful treatment, the astrological effects vanished.
In medicine, of course, the consequences of such misunderstanding can be tragic. Among the worst examples was British paediatrician Sir Roy Meadow, whose flawed understanding of statistics led him to declare that multiple "cot deaths" are so vanishingly unlikely that the mother must be a murderer. Eventually skepticism arose, his ideas were discredited, and he was struck off by the General Medical Council, but not before his arrogant self-assurance had sent many mothers, who had already lost their children, to jail.
There are many more examples through the history of science and society. General understanding of statistics among the general public is abysmal -- it grates on me whenever a cricket expert says "by the law of averages, this team must lose soon". And therefore half-experts find it easy to hoodwink others, including other half-experts. Perhaps that will be the subject of another post...
was it by design that you started off a post about lies and wound up talking about statistics, after a detour through a mention of people who were (falsely) damned?
Wish I'd thought of that as a title...
We are of the same mind, I see. I tried to email the author of the Stereophile article about correlation/probability, but the message bounced.
On the blog:
I describe a similar analysis to yours (but being slightly more conservative):
Probability that a single Hatto recording is the same as the matching Indjic recording.
I use Mazurka in A minor Op. 17, No. 4 as an example in this case. I measured the beat timing locations in an independent manner. The accuracy of my timing measurement is 10 milliseconds. I then subtracted the difference between the two beat-time sets. There was a linear increase in the differences due to time shifting in one of the performances. This was removed. What resulted was a plot of timing differences between about 400 beats in the piece. There was a region of beat timing differences which was about 200 beats long, where the beat timing differences were all less than 11 milliseconds. If a human were to try to tap to a constant beat, they would be expected to get less than 1/2 of the taps within 25 milliseconds (note that mazurkas are not performed at a steady tempo, so it actually should be a larger deviation). Being able to hit the beat timings at less than a 25 millisecond deviation for 200 consecutive beats is equivalent to flipping a coin and having it come up heads 200 consecutive times. The probability of that occuring is one in 1^200 or 1 in 10^59. (Note that
I did not examine the timings of the notes which occured off of the beats, which would make that value even higher).
1 in 10^59 is approximately equivalent to one atom of hydrogen out of all others in a star...
Good analysis. I wasn't trying to calculate the probability for the music, just using the coin-tosses as an example for why probabilities for such highly correlated events would be vanishing low. (10^-59, 10^-298 are both 0 in practice...)
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