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Statistics in a Nutshell, 2nd Edition by Sarah Boslaugh

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Chapter 7. The Pearson Correlation Coefficient

The Pearson correlation coefficient is a measure of linear association between two interval- or ratio-level variables. Although there are other types of correlation (several are discussed in Chapter 5, including the Spearman rank-order correlation coefficient), the Pearson correlation coefficient is the most common, and often the label “Pearson” is dropped, and we simply speak of “correlation” or “the correlation coefficient.” Unless otherwise specified in this book, “correlation” means the Pearson correlation coefficient. Correlations are often computed during the exploratory stage of a research project to see what kinds of relationships the different continuous variables have with each other, and often scatterplots (discussed in Chapter 4) are created to examine these relationships graphically. However, sometimes correlations are statistics of interest in their own right, and they can be tested for significance and reported as inferential statistics as well. Understanding the Pearson correlation coefficient is fundamental to understanding linear regression, so it’s worth taking the time to learn this statistic and understand well what it tells you about the relationship between two variables. A key point about correlation is that it is a measure of an observed relationship but cannot by itself prove causation. Many variables in the real world have a strong correlation with each other, yet these relationships can be due to chance, ...

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