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Let X be a standard normal variable (mean 0, variance 1). Let Y be equal to X*X. What would the correlation between X and Y be? Edit: point being that non-co

Let X be a standard normal variable (mean 0, variance 1). Let Y be equal to X*X. What would the correlation between X and Y be? Edit: point being that non-correlation doesn't mean independence.

whoisburbansky 6y ago
The correlation here averages out to zero because X can be negative but Y can't, right, what are you trying to show here?
- curiousgal 6y ago
  It's a standard example of why non-correlation doesn't mean independence.
- klmadfejno 6y ago
  Not only that, but while there's no LINEAR correlation, there's a perfect non linear function that any half-credible scientist would identify.
  - whoisburbansky 6y ago
    Agreed, but I still don't see how that's relevant to the Vitamin D/Covid severity correlation question. Presumably you aren't modeling either of the associated parameters with random variables that can be negative, and so even if one were a non linear function of the other, the linear correlation wouldn't be zero?
    - klmadfejno 6y ago
      shrug. You could imagine, for example, that too little Vitamin D is bad, and too much is bad, and arrive at a similarly (flipped) nonlinear fit with negligible linear correlation
legerdemain 6y ago
Sure, and another way to get a zero correlation is if you arrange all the data points evenly around a circle. Are you seriously suggesting that authors who took the energy to get a manuscript reviewed and published in a BMJ publication wouldn't examine a scatter plot or check the estimate of a quadratic trend that their analysis software almost certainly outputs?
- curiousgal 6y ago
  My point pertains to the conclusion the public might draw from the study. Just because Vitamin D is uncorrelated with Covid severity does not necessarily mean that they are not related. Same way Y depends on X but is uncorrelated with it.
  - legerdemain 6y ago
    Yes, and my point is that for your point to be relevant, the authors would have to exhibit a negligence that borders on the fantastical. No one would look at a significant quadratic trend in the data and say, "Nope, not gonna publish that juicy nugget!"

Let X be a standard normal variable (mean 0, variance 1). Let Y be equal to X*X. What would the correlation between X and Y be? Edit: point being that non-correlation doesn't mean independence.

whoisburbansky 6y ago

The correlation here averages out to zero because X can be negative but Y can't, right, what are you trying to show here?

curiousgal 6y ago
It's a standard example of why non-correlation doesn't mean independence.
klmadfejno 6y ago
Not only that, but while there's no LINEAR correlation, there's a perfect non linear function that any half-credible scientist would identify.
- whoisburbansky 6y ago
  Agreed, but I still don't see how that's relevant to the Vitamin D/Covid severity correlation question. Presumably you aren't modeling either of the associated parameters with random variables that can be negative, and so even if one were a non linear function of the other, the linear correlation wouldn't be zero?
  - klmadfejno 6y ago
    shrug. You could imagine, for example, that too little Vitamin D is bad, and too much is bad, and arrive at a similarly (flipped) nonlinear fit with negligible linear correlation

legerdemain 6y ago

Sure, and another way to get a zero correlation is if you arrange all the data points evenly around a circle. Are you seriously suggesting that authors who took the energy to get a manuscript reviewed and published in a BMJ publication wouldn't examine a scatter plot or check the estimate of a quadratic trend that their analysis software almost certainly outputs?

curiousgal 6y ago
My point pertains to the conclusion the public might draw from the study. Just because Vitamin D is uncorrelated with Covid severity does not necessarily mean that they are not related. Same way Y depends on X but is uncorrelated with it.
- legerdemain 6y ago
  Yes, and my point is that for your point to be relevant, the authors would have to exhibit a negligence that borders on the fantastical. No one would look at a significant quadratic trend in the data and say, "Nope, not gonna publish that juicy nugget!"