2.4. Spearman's rho test

Spearman's rho test is also a non-parametric test and is one of the important tests widely used for studying a population that takes on ranked order values of the variables. If there is no trend and all observations are independent, then all rank ordering is equally likely (Shahid et al., 2012; Jaiswal et al., 2015). In this test, the difference between order and rank (d_i) for all observations x₁, x₂, x_3,…,x_n can be used to compute the Spearman's ρ, variance Var(ρ) and test statistic (Z) using the following equations:

The value of ρ is defined as −1≤ρ ≤ 1 in which ρ > 0 and ρ < 0 represent positive and negative correlations, respectively, where the significance is tested by the Z-statistic.