Everything Is Correlated
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Everything Is Correlated
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Re: Everything Is Correlated
#2Like a background radiation, we have an "absolute background" correlation value...a value we might test against e.g. |+/- .02321|
Or we could drop the null
Re: Everything Is Correlated
#3[deleted]
Re: Everything Is Correlated
#4Agree that NHST using simple null hypothesis of the form
H0: μ = 0
However a composite hypothesis setup of the form
H0: μ ≤ 0
HA: μ > 0
Re: Everything Is Correlated
#5It is true that, as Fisher points out, with enough samples you are almost guaranteed to reject the null hypothesis. That's why we tell students to consider both p values (which you could think of as a form of quality control on the dataset) and variance explained. Loftus and Loftus make the point nicely: p tells you if you have enough samples and any effect to consider, variance explained tells you if it's worth pursuing. Both are useful guides to a thoughtful analysis. In addition, I'd make a case for thinking about the scientific significance and importance of the hypothesis and the Bayesian prior. And to put a positive spin on this, given how easy it is to get small p values, big ones are pretty much a red flag to stop the analysis and go and do something more productive instead.
Re: Everything Is Correlated
#6Agree that NHST using simple null hypothesis of the form H0: μ = 0 doesn't provide much value. H0 is never true, and the conclusion of "rejecting H0" based on a p-value is therefore not super profound. Also "rejecting H0" conclusion doesn't really tells anything about the alternative hypothesis HA (not even considered when computing p-value, since p-value is under H0). Dichotomies in general are bad, but NHST with po…
Couldn't you make an argument that the point H0 has use when you are testing whether two populations are identical? i.e. it's probably true that \mu is very close to 0 if it is the difference in heights of men from Nebraska vs men from Iowa.
Re: Everything Is Correlated
#7When the correlation is close to 0 it's often because of a feedback loop.
For example - in economy with central bank trying to hit inflation target - interest rates and inflation will have near 0 correlation (interest rates change but inflation remains constant). That's because central bank adjusts interest rates to counter other variables so that inflation remains near the target.
Other example (my favorite, it was mindblowing when my teacher showed it to us on econometrics as a warning :) ) - gas pedal and speed of a car driving on a hilly road. Driver wants to drive near the speed limit, so he adjusts the gas pedal to keep the speed constant. Simplistic conclusion would be - speed is constant despite the gas pedal position changing therefore they are unrelated :)
Re: Everything Is Correlated
#8When the correlation is close to 0 it's often because of a feedback loop. For example - in economy with central bank trying to hit inflation target - interest rates and inflation will have near 0 correlation (interest rates change but inflation remains constant). That's because central bank adjusts interest rates to counter other variables so that inflation remains near the target. Other example (my favorite, it was…
Good discussion. On the flip side, in my data mining class the professor keeps saying ~"you may be able to find clusters in a data set, but often no true correlation exists." However, that's an absolute statement I just don't swallow. In my mind what I see is that if an unexplained correlation or non-correlation appears, it may be random (or true) or it could be the result of an unmeasured (hidden) variable. In your two examples, your simply pointing out two respective hidden variables that weren't accounted for in the original analysis.
I think any data analysis should always be caveated with the understanding that there may be hidden variables shrouding or perhaps enhancing correlations - from economics to quantum mechanics. It's up to the reviewer of the results to determine, subjectively or by using a standard measure, whether the level of rigor involved in data collection & analysis sufficiently models reality.
Re: Everything Is Correlated
#9Cause, like, when you start learning about systems, everything is correlated, everything is connected, everything is linked, and you have to point it all out to everyone all the time.
Re: Everything Is Correlated
#10When the correlation is close to 0 it's often because of a feedback loop. For example - in economy with central bank trying to hit inflation target - interest rates and inflation will have near 0 correlation (interest rates change but inflation remains constant). That's because central bank adjusts interest rates to counter other variables so that inflation remains near the target. Other example (my favorite, it was…
Good discussion. On the flip side, in my data mining class the professor keeps saying ~"you may be able to find clusters in a data set, but often no true correlation exists." However, that's an absolute statement I just don't swallow. In my mind what I see is that if an unexplained correlation or non-correlation appears, it may be random (or true) or it could be the result of an unmeasured (hidden) variable. In your…
Perhaps they are trying to explain clustering illusion? The phenomenon that even random data will produce clusters. You can take that further and state random data WILL produce clusters. If you don't have clusters then your data is not random and some pattern is at play.
This really tricks up our mind as our mind tries to find patterns everywhere. If you try and plot random dots you will usually put dots without clusters. A true random plot will have clusters.
https://en.wikipedia.org/wiki/Clustering_illusion
Edit: Note your professor said "often" which means they did not make an absolute statement