<story><title>Everything Is Correlated</title><url>https://www.gwern.net/Everything</url></story><parent_chain></parent_chain><comment><author>ajuc</author><text>When the correlation is close to 0 it&amp;#x27;s often because of a feedback loop.&lt;p&gt;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&amp;#x27;s because central bank adjusts interest rates to counter other variables so that inflation remains near the target.&lt;p&gt;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 :)</text></comment>
<story><title>Everything Is Correlated</title><url>https://www.gwern.net/Everything</url></story><parent_chain></parent_chain><comment><author>limbicsystem</author><text>It is true that, as Fisher points out, with enough samples you are almost guaranteed to reject the null hypothesis. That&amp;#x27;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&amp;#x27;s worth pursuing. Both are useful guides to a thoughtful analysis. In addition, I&amp;#x27;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.</text></comment>