Pearson correlation, which generates an r value or correlation coefficient, is one of the most common statistical procedures. Many academic papers that contain quantitative research also contain correlation analysis.
But what is correlation anyway? Think of it as the strength of linear association between two continuously measured variables, which, in this blog post, we’ll explore by building your visual intuition related to correlation. We can measure the strength of correlation as ranging between the r values of -1 (perfectly negative correlation) to 1 (perfectly positive correlation). In this spectrum, r = 0 is the complete absence of correlation. In the thee figures below, the first is r = 1, the second is r = -1, and the third is r = 0.
The pattern should be clear to you. The closer r is to 1, the more the two variables, x and y, are positively related. When x goes up, y goes up. The closer r is to -1, the more the two variables, x and y, are negatively related. When x goes up, y goes down. The closer r is to 0, the less the two variables, x and y, are related to each other.
When you conduct and report on correlation in an academic paper, you have to report the r value (which, as you’ve seen, can range from -1 to 1), but you also have to report on the significance of the r value. In keeping with standard recommendations, you will want to adopt p < .05 as your cutoff for statistical significance for correlation. Statistical programs (such as Stata, SPSS, R, etc.) that carry out correlation also report the p values for correlation. In other blog entries, we’ll show you how r is calculated, how to conduct ordinary least squares (OLS) regression with variable pairs for correlation, and what the coefficient of determination is.
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