In a recent post (https://irthoughts.wordpress.com/2010/04/23/beware-of-seo-statistical-studies/) we warned readers against SEO statistical studies. For those that want a second opinion, here is a collection correlation coefficient myths, taken from a reviewed manuscript written by top researchers from Sandia National Labs, Stony Brooks University, Iowa State University, Lewis and Clark College, and Applied Biomathematics. Enjoy it.
The authors provide applications to risk analysis while debunking the following widespreaded myths:
1. All variables are mutually independent.
2. If X and Y are independent and Y and Z are independent, then X and Z are too.
3. Variables X and Y are independent if and only if they are uncorrelated.
4. Zero correlation between X and Y means there’s no relationship between X and Y.
5. Small correlations imply weak dependence.
6. Small correlations can be “safely ignored” in risk assessments.
7. Different correlation coefficients are similar.
8. A correlation coefficient specifies the dependence between two random variables.
9. Correlation coefficients vary between −1 and +1.
10. Any correlation can be specified between inputs.
11. Perfect dependencies between X and Y and between X and Z imply perfect dependence between Y and Z.
12. Monte Carlo simulations can account for dependencies between variables.
13. Varying correlation coefficients constitutes a sensitivity analysis for uncertainty about dependence.
14. A model should be expressed in terms of independent variables only.
15. You have to know the dependence to model it.
16. The notion of independence generalizes to imprecise probabilities.
Read the article to understand in which context these are listed, before agreeing or disagreeing with these.
They also provide reference material to many correlation coefficients:
“There are many different measures of correlation that are in common use and many more that have been proposed. The most commonly used measures are Pearson’s product-moment correlation and Spearman’s (1904) rank correlation, but there are a host of other measures that also arise in various engineering contexts, including Kendall’s rank correlation, concordance of various kinds (e.g., Hoeffding 1947; Lehmann 1966; Scarsini 1984), Blomqvist’s (1950) coefficient, Gini’s coefficient (Nelsen 1999), etc. Hutchinson and Lai (1990) review many of these.”