Correlation analysis

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 normally refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. [1]

Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation). [1]

Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of Y is zero. [1]

XLSTAT correlation tests allow one to compute different kinds of correlation coefficients, between two or more variables, and to determine if the correlations are significant or not. [2]

XLSTAT proposes three correlation coefficients to compute the correlation between a set of quantitative variables, whether continuous, discrete or ordinal: [2]

The following correlation coefficients are computable:

  • Pearson correlation coefficient

  • Spearman correlation coefficient (rho)

  • Kendall correlation coefficient (tau)

  • Polychoric correlation coefficient