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In statistics, the correlation ratio is a measure of the curvilinear relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation.
In statistics, the Pearson correlation coefficient (PCC) [a] is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always ...
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related.
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 .
A typical "Business Statistics" course is intended for business majors, and covers [71] descriptive statistics (collection, description, analysis, and summary of data), probability (typically the binomial and normal distributions), test of hypotheses and confidence intervals, linear regression, and correlation; (follow-on) courses may include ...
Cluster data describes data where many observations per unit are observed. This could be observing many firms in many states or observing students in many classes. In such cases, the correlation structure is simplified, and one does usually make the assumption that data is correlated within a group/cluster, but independent between groups/clusters.
Correlation functions between the same random variable are autocorrelation functions. However, in statistical mechanics, not all correlation functions are autocorrelation functions. For example, in multicomponent condensed phases, the pair correlation function between different elements is often of interest.
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.