The aim of the correlation analysis is to characterize the existence, the nature and the strength of the relationship between two quantitative variables. The visual inspection of scatter plots is a prime instrument in a first step, when we have no idea about the form of the underlying relationship between the variables. But, in second step, we need statistical tools to measure the strength of the relationship and to assess its significance.
In these slides, we present the Pearson's product-moment correlation. We show how to estimate its value using a sample. We present the inferential tools which enable to realize hypothesis testing and confidence interval estimation.
But the Pearson correlation is appropriate only to characterize linear relationship. We study the possible solutions for problematic situations with, among others, the Spearman's rank correlation coefficient (Spearman's rho).
Last, the partial correlation coefficient and the related inferential tools are described.
Keywords: correlation, partial correlation, pearson, spearman, hypothesis testing, significance, confidence interval
Components (Tanagra): LINEAR CORRELATION
Slides: Correlation analysis
References:
M. Plonsky, “Correlation”, Psychological Statistics, 2014.
