Independence

2 articles

Andres and marzos delta Autocorrelation technique Autoregressive fractionally integrated moving average Ball covariance Bangdiwalas b Basus theorem Bennett alpert and goldsteins's Biweight midcorrelation Ceiling effect Collider Comonotonicity Complex inverse wishart distribution Conditional dependence Cophenetic correlation Correlates of crime Correlation correction for attenuation Correlation does not imply causation Coskewness Covariance and correlation Cram rs v Cross covariance Ecological correlation Ecological regression Eddy covariance Factorial code Fkg inequality Fleisss kappa Functional correlation Gearys c Generalized canonical correlation Generalized naszodi mendonca method Generalized variance Getis ord statistics Gutenberg richter law Inter rater reliability Interclass correlation Item total correlation Iterative proportional fitting Join count statistic Kendalls w Krippendorffs alpha Lag windowing Law of total covariance Local independence Log linear analysis Long tail traffic Mat rn covariance function Maximal information coefficient Mean dependence Mediation Misconceptions about the normal distribution Morans i Negative relationship Neutral vector Nm method Quadrant count ratio Rational quadratic covariance function Rescaled range Rv coefficient Sample matrix inversion Scaled correlation Scotts pi Somers d Spatial weight matrix Spike triggered covariance Spurious correlation of ratios Spurious relationship Subindependence Super resolution optical fluctuation imaging Tail dependence Tj stheims coefficient Unbiased estimation of standard deviation Wartenbergs coefficient

Probability & Statistics LicenceAnalyse9 min

Five Numbers, Two Answers, and the Divisor Nobody Asks About

The standard deviation of 1, 2, 3, 4, 5 is either 1.4142 or 1.5811, and offering one of them without asking which question you are answering is the only wrong move. The sum of squared deviations is 10 either way, so everything turns on whether you divide it by 5 or by 4. Bessel's correction makes the variance unbiased and leaves the standard deviation biased low by about six percent at this sample size, and a third divisor beats both of them if you optimise for mean squared error instead.

Combinatorics & Discrete Math LycéeExplication9 min

One in Three, and the Card That Was Never in the Problem

Wind appears nowhere in the winning condition, so delete it: three cards in six equally likely orders, and you win in the two where fire comes last. One in four is the correct probability that fire is last of all four cards, a strictly smaller event, and the gap is exactly one twelfth.