6.2. Correlations

• Correlation Coefficients
• Pearson-Spearman-Kendall Correlations Matrix
• Partial Correlation Matrix
• Intraclass Correlation Coefficients

Correlation Coefficients measure the degree of association between two sets of data. They take on values ranging from -1 to +1 (inclusive), meaning complete negative and positive correlations respectively. A zero value means that the two data sets have no association. In this case they are said to be uncorrelated.

Two of the Correlation Coefficients in this group, Spearman and Kendall correlations are nonparametric. This means that it is the relative positions of data points in the sample that matters, rather than their nominal values. These routines involve highly demanding sorting and ranking phases, which may be time consuming with large data files.

Confidence intervals are reported for all Correlation Coefficients. Assuming the two samples have a joint bivariate normal distribution, the confidence interval for their correlation coefficient is computed after applying the Fisher’s z transformation:

     

     

     

where  is the critical value from the standard normal distribution.