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RichardKennaway comments on Should correlation coefficients be expressed as angles? - Less Wrong Discussion

43 Post author: Sniffnoy 28 November 2012 12:05AM

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Comment author: RichardKennaway 28 November 2012 10:18:00AM *  14 points [-]

It's interesting to compare these angles with those that come up in engineering.

  • One second of arc (the Ramsden theodolite): r = 0.99999999925

  • 1/5000 to 1/1000 inch per inch (accuracy of a try-square): r = 0.99999950 to 0.999999980

  • 1 minute of angle (the accuracy that a rifle should hold to) = 1 inch at 100 yards: r = 0.999999970

  • 1 degree: r = 0.99985

  • 1 compass point (1/32 of a revolution, limit of navigational accuracy in the days of sail): r = 0.981

And in contrast:

  • Correlation that implies 1 bit of mutual information (for a bivariate Gaussian): r = 0.866, angle = 30 degrees (exactly).

  • Correlation considered high in the softer disciplines: r = 0.8, angle = 36.9 degrees.

  • Correlation considered publishable: r = 0.2, angle = 78.5 degrees. This means that if the truth is due North, you're proceeding East by North (one compass point away from East).