Statistics · BEGINNER LESSON
Correlation
Correlation is a statistical measure of how strongly two or more quantitative variables move together, usually describing the strength of a linear relationship. It does not by itself prove that one variable causes the other.
What correlation is and what it measures
Correlation is a way to describe statistical dependence between variables. In the sources, it is used mainly for two quantitative variables, and it summarizes how strongly they are related, especially in a linear pattern. The Pearson correlation is the most common form for two quantitative variables, while other named forms exist for special data types. Correlation is based on groups of observations, not on a single person or single measurement.
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Best practices for moving from correlation to causation in ecological research
How it works
A correlation becomes large in magnitude when two variables change together in a consistent way. If the pattern is linear, Pearson correlation can capture it well. If the true pattern bends or curves, Pearson correlation may be small even when the relationship is clearly present. In regression language, the overall strength of explanation can also be summarized with R-squared, which represents the proportion of variation in the outcome explained by the variables in the model; in some mixed situations, eta-squared is used instead.
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [3] Translating treatment effects between correlated endpoints - PMC
What correlation can and cannot tell you
A correlation or association does not prove cause and effect. A third variable, called a confounder, may affect both variables and create a relationship that is not direct. The ecological source explains this with the Common Cause Principle: if two variables are statistically dependent, then one may cause the other, they may influence each other, or both may share a common cause. Correlation can suggest a causal question, but causal claims need extra assumptions and careful study design.
[2] Best practices for moving from correlation to causation in ecological research
Limits and interpretation
Correlation has important limits. The Pearson form mainly measures linear similarity, so it can miss curved patterns. Statistical dependence can exist without a visible correlation, because correlation is only one kind of dependence. Also, the sources stress that causal assumptions cannot be checked from data alone, even with very large data sets, and that missing or unmeasured confounding can distort interpretation.
[1] 6. The conundrum of regression, correlation, association, and ... - PMC [2] Best practices for moving from correlation to causation in ecological research [3] Translating treatment effects between correlated endpoints - PMC
SEE THE IDEA
From paired data to interpretation
Two or more variables are observed together in the same groups or studies.
A statistic summarizes how strongly the variables move together, often for a linear pattern.
Compare the data pattern with the statistic; a curved pattern can be missed by Pearson correlation.
Ask whether the link is descriptive only or whether confounding and causation need further study.
Paired data produce a correlation measure, and the pattern of the data determines how well that measure represents the relationship.
Correlation summarizes shared movement in data, but the statistic must be matched to the shape of the relationship and cannot prove causation.
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.