Correlations
Statistics

Pearson Product-Moment Correlation Coefficient

Pearson r is a measure of correlation between two variables. The associated tests evaluate whether the correlation coefficient for the underlying population is different from zero, i.e, whether there is a monotonous relationship between the two variables. Pearson's r varies from -1 to +1, with 0 indicating no relationship and 1 indicating perfect relationship.

This method assumes that the data is normally distributed, and the results being influenced by outliers, unequal variances, non-normality, and non-linearity.

  • The method requires one numeric data columns.
  • The test reports from Aabel include the correlation coefficient r, the critical two- and one-tailed r (0.05) and r (0.01) values, t statistic and p values (two-tailed and one-tailed).

Spearman's Rank-Order Correlation Coefficient (Spearman's ρ)

Spearman's ρ is the non-parametric analog of the Pearson product-moment correlation coefficient. The results or the former and latter are closely similar, as the Spearman correlation is calculated in a very similar manner as Pearson, except that Spearman first ranks the data.

    There are two different ways of calculating Spearman's ρ:

  • Converting each variable to ranks and calculating the Pearson correlation coefficient between the two sets of ranks
  • Converting each variable to ranks and for each observation pair, correcting the ties and calculating the difference between the ranks (this is the method used in Aabel)
  • The method requires two numeric variables.
  • The test results include the estimated Spearman's rank-order correlation coefficient (rs), the critical one-tailed and two-tailed rs (0.05) and rs (0.01), the t and z statistics and p values (two-tailed and one-tailed).

Kendall's Rank Correlation Coefficient (Kendall's τ)

Like Spearman's ρ, Kendall's τ is a non-parametric method of correlation between two variables, but has an advantage over Spearman's ρ: Kendall's τ also indicates the difference between the probability that the observed data are in the same order for the two variables vs. the probability that the observed data are in different orders for the two variables.

  • The method requires two numeric variables.
  • The test results include the estimated Kendall's τ, the critical one-tailed and two-tailed τ(0.05) and τ(0.01), z and p values (two-tailed and one-tailed).