järjekorrakorrelatsioon

Järjekorrakorrelatsioon is a statistical measure used to assess the strength and direction of association between two ranked variables. Unlike Pearson correlation, which assumes a linear relationship and interval or ratio data, rank correlation methods work with ordinal data or when the assumption of linearity is not met. This means it can be used when data is ranked from lowest to highest without necessarily having equal intervals between the ranks.

The most common types of rank correlation are Spearman's rank correlation coefficient (rho) and Kendall's rank correlation coefficient (tau). Spearman's rho, often denoted as $r_s$ or $\rho$, calculates the Pearson correlation coefficient on the ranks of the data. It essentially measures the strength of a monotonic relationship between two variables. A monotonic relationship is one where as one variable increases, the other variable tends to increase or decrease, but not necessarily at a constant rate.

Kendall's tau, denoted as $\tau$, measures the ordinal association between two measured quantities. It is based on comparing the number of concordant pairs to the number of discordant pairs. A pair of observations is concordant if their rankings for both variables agree, and discordant if they disagree. Kendall's tau is generally considered more robust than Spearman's rho when dealing with small sample sizes or data with many ties.

Rank correlation coefficients range from -1 to +1. A value of +1 indicates a perfect positive rank correlation, meaning that as one variable increases, the other variable consistently increases. A value of -1 indicates a perfect negative rank correlation, where as one variable increases, the other consistently decreases. A value of 0 suggests no rank correlation between the variables. These measures are valuable tools in non-parametric statistics, allowing for the analysis of relationships where parametric assumptions may not hold.