Almost every day you can find in media commentary that XYZ is causing stocks to fall (or rise). Such definitive statements are common—but what’s almost always missing is statistical proof. And if you ...

In the first case, there is a strong upward-sloping relationship between X and Y; in the second case, no apparent relationship; in the third case, a strong downward-sloping relationship. Note the ...

Elvis Picardo is a regular contributor to Investopedia and has 25+ years of experience as a portfolio manager with diverse capital markets experience. Yarilet Perez is an experienced multimedia ...

Depressed people send more email. They spend more time on Gchat. Researchers at the Missouri University of Science and Technology recently assessed some college students for signs of melancholia then ...

Statistical mechanics provides a fundamental framework for understanding how collective phenomena in many-body systems give rise to macroscopic changes in state, known as phase transitions. Research ...

Correlation doesn't imply causation. You've probably heard that before. It's a true statement that's important in statistical analysis—if more tall people own cats, that doesn't mean that cats cause ...

Given two jointly observed random vectors Y and Z of the same dimension, let Y be a reordered version of Y and Z the resulting vector of concomitants of order statistics. When X is a covariate of ...

Resampling procedures include hypothesis testing methods based on permutation procedures and interval estimation methods based on bootstrap procedures. The former are widely used in the analysis of ...