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Pearson's correlation coefficient, when applied to a population, is commonly represented by the Greek letter ρ (rho) and may be referred to as the population correlation coefficient or the population Pearson correlation coefficient. Given a pair of random variables (for example, Height and Weight), the formula for ρ[10] is [11] where.
The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations. [4] This is the best-known and most commonly used type of ...
The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of Y is zero.
Intraclass correlation. In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), [ 1 ] is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other.
That is because Spearman's ρ limits the outlier to the value of its rank. In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman [ 1 ] and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables).
In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram. The correlogram is a commonly used tool for checking randomness in a ...
Formally, the partial correlation between X and Y given a set of n controlling variables Z = {Z1, Z2, ..., Zn}, written ρXY·Z, is the correlation between the residuals eX and eY resulting from the linear regression of X with Z and of Y with Z, respectively. The first-order partial correlation (i.e., when n = 1) is the difference between a ...
The classical measure of dependence, the Pearson correlation coefficient, [1] is mainly sensitive to a linear relationship between two variables. Distance correlation was introduced in 2005 by Gábor J. Székely in several lectures to address this deficiency of Pearson's correlation, namely that it can easily be zero for dependent variables.