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Spearman's correlation coefficient
Non-parametric measure assessing the strength and direction of the monotonic relationship between two variables based on their ranks rather than raw values. Particularly useful for detecting non-linear but monotonic relationships.
Kendall's tau
Non-parametric correlation coefficient measuring the concordance between ordered pairs of two variables. Calculates the difference between the number of concordant and discordant pairs normalized by the total number of pairs.
Partial correlation
Measure of association between two variables after controlling for the effect of one or more additional variables. Allows isolating the direct relationship between two variables by eliminating indirect influences.
Correlation significance test
Statistical test assessing whether the observed correlation coefficient differs significantly from zero in the population. Typically uses t-distribution or permutation methods to calculate the associated p-value.
Correlogram
Graphical visualization of the correlation matrix using colors, circles, or ellipses to represent correlation intensities. Facilitates quick identification of correlation patterns in multidimensional data.
Scatter plot
Bivariate graph plotting each observation as a point in Cartesian space with one variable on each axis. Allows visual inspection of the nature and intensity of the relationship between two continuous variables.
Coefficient of determination (R²)
Proportion of the variance of a dependent variable explained by independent variables in a regression model. Ranges from 0 to 1, where 1 indicates perfect prediction of the data by the model.
Point-biserial correlation
Coefficient measuring the relationship between a dichotomous variable and a continuous variable. Equivalent to Pearson's coefficient when one variable is coded binary (0/1).
Biserial correlation
Measure of association between a continuous variable and an underlying dichotomous variable assumed to be normally distributed. Differs from point-biserial correlation in its theoretical interpretation.
Phi correlation
Specialized correlation coefficient for measuring association between two dichotomous variables. Mathematically equivalent to Pearson's coefficient applied to binary variables.
Tetrachoric correlation
Estimation of correlation between two underlying continuous variables assumed to be normally distributed, observed only in dichotomous form. Particularly used in psychometrics and genetics.
Canonical correlation
Multivariate extension of simple correlation measuring the relationship between two sets of variables. Identifies optimal linear combinations of each set that maximize correlation between them.
Correlation bootstrap
Non-parametric resampling method for estimating the confidence interval of a correlation coefficient. Generates multiple bootstrap samples to construct an empirical distribution of the coefficient.
Variance Inflation Factor (VIF)
Indicator quantifying the amplification of a regression coefficient's variance due to multicollinearity. A VIF value greater than 10 generally suggests problematic multicollinearity.