GlossaryStatistics and interpretation
Correlation
Correlation is a statistical relationship in which two measured variables tend to change together.
Correlation is a statistical relationship in which two measured variables tend to change together. It can describe a positive relationship, a negative relationship, or little measured relationship. Correlation does not, by itself, explain why the variables are related or establish that changing one will cause the other to change.
Reading a relationship
A correlation can be useful for exploring patterns, but it depends on what was measured and how observations were selected. The CDC's data-interpretation guidance emphasizes considering chance, bias, and other factors before interpreting an association as causal.
For public-safety comparisons, check the unit of observation. A relationship among neighborhoods does not automatically describe individuals within those neighborhoods. Totals can also move together simply because larger places have more residents and more recorded events of many kinds.
Example
Hypothetical example: Across ten cities, the number of fire stations rises with the number of annual emergency calls. The cities with the largest populations generally have more of both.
The relationship does not show that building stations creates emergencies. Population size is a plausible shared influence. Before drawing operational conclusions, an analyst would need an appropriate design and measures that address city size and other differences.
Common confusion
Two lines rising on a chart are not automatically a calculated correlation. A correlation coefficient summarizes a particular kind of relationship under a chosen method. For example, a method focused on straight-line relationships may miss a curved pattern.
Correlation is also different from agreement. Two sources can move together while consistently reporting different levels.
Limits and reporting
State the variables, time period, geography, and method. Check whether unusual observations drive the result and whether reporting changes affect both series. A correlation can identify a question for investigation; it cannot replace the evidence needed to attribute an effect to an intervention.