Encyclopedia Entry

Coefficients of Correlation, Alienation, and Determination

Hervé Abdi

The coefficient of correlation evaluates the similarity of two sets of measurements (i.e., two dependent variables) obtained on the same observations. The coefficient of correlation indicates the amount of information common to two variables. This coefficient takes values between −1 and +1 (inclusive). A value of 0 indicates that the two series of measurement have nothing in common. A value of +1 says that the two series of measurements are measuring the same thing. A value of −1 says that the two measurements are measuring the same thing, but one measurement varies inversely with the other. The squared correlation gives the proportion of common variance between two variables and is also called the coefficient of determination . Subtracting the coefficient of determination from the unity gives the proportion of variance not shared between two variables, a quantity also called the coefficient of alienation . The coefficient of correlation measures only ...

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