Statistics · BEGINNER LESSON
Pearson correlation coefficient
The Pearson correlation coefficient is a statistical measure of how strongly two variables follow a straight-line relationship. It is written as r for a sample and ranges from -1 to 1, with no unit.
What it is and what it measures
The Pearson correlation coefficient is used to measure the strength and direction of a linear association between two variables. In a scatter plot, it summarizes how closely the points lie to one straight line. A value near +1 means the variables tend to increase together, a value near -1 means one tends to rise as the other falls, and a value near 0 means little straight-line association.
[1] The Non-Causality Of... [2] Limitations of Correlation Coefficients in Research on ... - PMC [3] OP-NDTP210085 1..6
How it is interpreted
The statistic is dimensionless, so it has no unit and does not change just because the measurement scale changes. The square of the correlation coefficient, called R squared, can be read as the proportion of variance in one variable that is explained by the other variable. The sources also note that the true population symbol is rho (ρ), while r usually refers to a sample estimate.
[1] The Non-Causality Of... [2] Limitations of Correlation Coefficients in Research on ... - PMC [3] OP-NDTP210085 1..6
How it works in practice
Pearson correlation is based on a linear model idea: it checks whether one straight line gives a good summary of the paired values. It does not tell you the full shape of the relationship if the real pattern is curved. The sources also note that the coefficient can still be estimated in some skewed distributions, but the main target remains a linear relationship.
[1] The Non-Causality Of... [2] Limitations of Correlation Coefficients in Research on ... - PMC [3] OP-NDTP210085 1..6
Limitations
Pearson correlation is sensitive to measurement error, outliers, and the range of observations. A narrow range can make the correlation look weaker, so values are not always easy to compare across studies or groups. It also does not prove causation: a correlation does not tell us whether one variable causes the other, or whether a third factor is involved.
[1] The Non-Causality Of... [2] Limitations of Correlation Coefficients in Research on ... - PMC [3] OP-NDTP210085 1..6
SEE THE IDEA
Pearson correlation coefficient in four steps
Two variables, X and Y, are measured on the same cases.
The pairs are plotted to see their pattern.
The statistic summarizes how well one line matches the points.
The result shows direction and strength of linear association.
Each step moves from raw paired values to a summary of straight-line association.
The coefficient compresses a cloud of points into a single number, but only for linear association.
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
Match each concept to its meaning
Drag a label onto its description, or select a label and then select a description. This also works with a keyboard.
4 pairs to match
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.