Correlation Tests in R: Pearson Cor, Kendall’s Tau, and Spearman’s Rho

This chapter explains and practically illustrates to the readers how to conduct the three main types of correlational analysis in R, namely, The PearsonPearson, Kendall’s tauKendall’s tau, and Spearman’s rhoSpearman’s rho correlationCorrelation tests. These are the primary inferentialInferential (statistical) procedures or methods used by the researchers or the data analysts to evaluate the strength or degree (direction) of relationship between two variables (continuousContinuous or categoricalCategorical). The Pearson correlationCorrelation (also known as Pearson product–moment correlationCorrelation coefficient) measures the strength of linearLinear associationAssociation that exists between two continuousContinuous variables by drawing a “line of best fit” through the two datasets and establishing how far away the two data points are from the drawn line (model) of best fit. On the other hand, the Kendall’s tau and Spearman’s rho correlationCorrelation tests are considered alternatives (non-parametricNon-parametric equivalent) to the Pearson cor test mainly used by the researchers to measure the strength and degree of dependence between two categoricalCategorical or ordinal variables. The differences and similarities between the Kendall’s tau and Spearman’s rho correlationCorrelation tests are also discussed in this chapter. While the interpretations of the two methods (Kendall’s tau and Spearman’s rho) are very similar, and thus, appear to invariably lead to the same inferences or statistical results. The only difference between the Spearman’s rho versus Kendall’s tau method is that the Spearman’s rhoSpearman’s rho (ρ) statistics or results are calculated through the “ordinary least squaresOrdinary Least Squares (OLS)”, while the Kendall’s tau (τ) statistics is calculated through the “pairwise comparisonPairwise comparison” of all the data points. Thus, Kendall’s tau (τ) statistics are based on “concordant and discordant pairs”, while the Spearman’s rhoSpearman’s rho (ρ) statistics are based on “deviations”, respectively.