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This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering. Compared to strain gauges and extensometers, digital image correlation methods provide finer details about deformation, due to the ability to provide both local and average data.
Again, a measure of distance between random variables may relate to the extent of dependence between them, rather than to their individual values. Many statistical distance measures are not metrics, and some are not symmetric. Some types of distance measures, which generalize squared distance, are referred to as (statistical) divergences.
A bivariate correlation is a measure of whether and how two variables covary linearly, that is, whether the variance of one changes in a linear fashion as the variance of the other changes. Covariance can be difficult to interpret across studies because it depends on the scale or level of measurement used.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. [citation needed]
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.
Similarly, when troughs (negative areas) align, they also make a positive contribution to the integral because the product of two negative numbers is positive. Animation of how cross-correlation is calculated. The left graph shows a green function G that is phase-shifted relative to function F by a time displacement of 𝜏.
Due to the fact that the mixed-design ANOVA uses both between-subject variables and within-subject variables (a.k.a. repeated measures), it is necessary to partition out (or separate) the between-subject effects and the within-subject effects. [5]
Bhattacharyya distance related, for measuring similarity between data sets (and not between a point and a data set) Hamming distance identifies the difference bit by bit of two strings; Hellinger distance, also a measure of distance between data sets; Similarity learning, for other approaches to learn a distance metric from examples.