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In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or r φ) is a measure of association for two binary variables.. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.
Phi is related to the point-biserial correlation coefficient and Cohen's d and estimates the extent of the relationship between two variables (2 × 2). [32] Cramér's V may be used with variables having more than two levels. Phi can be computed by finding the square root of the chi-squared statistic divided by the sample size.
In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ c) is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946.
Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y. Pearson/Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1).
T equals zero if and only if independence holds in the table, i.e., if and only if = + +. T equals one if and only there is perfect dependence in the table, i.e., if and only if for each i there is only one j such that > and vice versa.
Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X , we have the covariance of a variable with itself (i.e. σ X X {\displaystyle \sigma _{XX}} ), which is called the variance and is more commonly denoted as σ X 2 , {\displaystyle ...
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 .
Hi, sorry for the late reply. The Matthews correlation coefficient is a special case of the phi coefficient because it is the phi coefficient applied to a 2 × 2 table. All the Matthews correlation coefficients are also phi coefficients, but not all the phi coefficients are Matthews correlation coefficients.