Measuring linear correlation of non-normally distributed variables - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-23T10:10:39Z https://stats.stackexchange.com/feeds/question/8063 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/8063 3 Measuring linear correlation of non-normally distributed variables Julian https://stats.stackexchange.com/users/3465 2011-03-09T09:43:14Z 2012-11-05T17:50:45Z <p>How can I measure linear correlation of non-normally distributed variables? Pearson coefficient is not valid for non-normally distributed data, and Spearman's rho does not capture linear correlation.</p> <p>Thank you</p> https://stats.stackexchange.com/questions/8063/-/8064#8064 3 Answer by Galit Shmueli for Measuring linear correlation of non-normally distributed variables Galit Shmueli https://stats.stackexchange.com/users/1945 2011-03-09T09:49:24Z 2011-03-09T09:49:24Z <p>Why do you require normality for computing a correlation? How about a simple scatterplot? As long as the data are continuous, ordinary (Pearson) correlation should be fine. All that it is measuring is the strength of the linear relationship between two variables (if indeed there is such a relationship).</p> https://stats.stackexchange.com/questions/8063/-/8066#8066 2 Answer by Peter Flom for Measuring linear correlation of non-normally distributed variables Peter Flom https://stats.stackexchange.com/users/686 2011-03-09T10:11:52Z 2011-03-09T10:11:52Z <p>What @galit said is absolutely right. You can find the linear correlation between any two continuously distributed variables.</p> <p>But perhaps you are thinking of the <em>meaning</em> of such a correlation? Indeed, <a href="http://en.wikipedia.org/wiki/Anscombe%27s_quartet" rel="nofollow">Anscombe's quartet</a> shows that while the correlation is <em>defined</em> for any pair of continuous variables, and its mathematical and statistical meaning is the same, its substantive meaningfulness may vary.</p> https://stats.stackexchange.com/questions/8063/-/8112#8112 3 Answer by Hong Ooi for Measuring linear correlation of non-normally distributed variables Hong Ooi https://stats.stackexchange.com/users/1569 2011-03-10T06:01:42Z 2011-03-10T06:07:40Z <p>In addition to Anscombe's quartet as mentioned by Peter Flom, <a href="http://ferrari.dmat.fct.unl.pt/personal/mle/GestaoRisco/Embrechts/risk.pdf" rel="nofollow" title="Correlation: pitfalls and alternatives">here</a> is a very nice paper in the risk-management context illustrating the problems of using linear correlation with non-normally distributed variables. In a nutshell, much of our intuition about how correlation behaves -- all values of $\rho \in [-1, 1]$ are possible; an exact monotonic relationship implies $|\rho | = 1$; $\rho = 0$ implies independence; etc, doesn't necessarily apply in the case of non-normality.</p>