Statistics · BEGINNER LESSON
Pearson correlation
Pearson correlation is a statistic for two quantitative variables that measures the strength of their linear relationship. Its value runs from -1 to 1, with values near the ends indicating stronger straight-line positive or negative association. [0,1]
What it is
Pearson correlation is used for two quantitative variables, meaning variables measured on a numerical scale. It summarizes the strength of their relationship, but specifically the strength of a linear relationship, not just any pattern. A value of 1 means perfect positive linear association, -1 means perfect negative linear association, and 0 means no linear trend is present. [0,1]
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Regression-based Modeling of Spearman's Rho for ... - PMC
How it works
The statistic is computed from paired observations and reflects whether high values of one variable tend to go with high values of the other, or low with high. Because it is based on a linear pattern, it can miss strong curved relationships. In one example, a scatterplot looked clearly related but the Pearson correlation was small because the true pattern was quadratic, not straight. [0,1]
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Regression-based Modeling of Spearman's Rho for ... - PMC
Mechanism and interpretation
A useful way to think about Pearson correlation is as a measure of straight-line co-movement. If the cloud of points bends, the statistic may understate the association even when the relationship is obvious in the plot. Another source notes that rank-based Spearman’s rho is an alternative when a non-linear monotonic relationship is present; it uses ranks rather than the original values. [0,1]
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Regression-based Modeling of Spearman's Rho for ... - PMC
Limitations
A major limitation is that Pearson correlation only captures linear relationships. It can be small for a strong curved pattern, so a low value does not always mean weak association. In genetics, one paper describes a specialized use for estimating recombination fraction in controlled biparental populations, but it also states this should not be used as linkage disequilibrium in random-mating populations and can be unreliable with segregation distortion or when markers are far apart. [0,1,2]
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Regression-based Modeling of Spearman's Rho for ... - PMC [3] Estimating recombination fraction via Pearson correlation
Related ideas
Correlation is about strength of association, while regression describes the structure of the relationship. R-squared, written R^2, is used for multiple independent variables and measures the proportion of variation in an outcome explained by the regressors together. [0]
[1] 6. The conundrum of regression, correlation, association, and ... - PMC
SEE THE IDEA
Pearson correlation in three steps
Start with paired quantitative measurements, such as x and y. [0,1]
Pearson correlation measures linear strength, not curved shape. [0,1]
Values near 1 or -1 show strong linear association; values near 0 show little linear trend. [0,1]
Each step depends on the previous one: numerical pairs are checked for linear co-movement, then summarized by a single number. [0,1]
Pearson correlation is a summary of linear association, so curved patterns may still be strongly related even when the value is small. [0,1]
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
Match each concept to its meaning
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.