Correlations

A correlation coefficient, denoted as r, is a number between -1 and 1 that indicates both the direction and strength of the relationship between two variables. The sign shows direction: positive means variables move together, negative means they move oppositely. The absolute value's closeness to 1 indicates strength; values near 1 show tight linear relationships, while values near zero indicate weak or nonexistent associations.

In a positive correlation, variables move in the same direction—as one increases, the other increases too. For example, vegetable consumption and sleep hours may correlate positively. In a negative correlation, variables move oppositely; as one increases, the other decreases. The strength of either type is determined by how closely data points cluster linearly around a trend line.

Correlation describes a relationship between variables but does not prove that one causes the other. A third variable may actually drive both observed changes. For instance, wealth correlates with intelligence, but education—a third variable—may be the true cause. Researchers must conduct follow-up studies to establish cause and effect relationships between variables.

When a correlation coefficient approaches zero, the relationship between two variables is weak or nonexistent. Data points scatter widely rather than clustering along a linear pattern, making it difficult to predict changes in one variable based on the other. For example, hours of sleep and shoe size would likely show a correlation near zero.

Correlations have predictive value when they are strong. For example, university admissions committees can correlate current students' college GPA with standardized test scores to predict success of applicants. The stronger the correlation observed in existing data, the more reliably researchers can forecast outcomes for new cases, though prediction accuracy decreases as correlation strength weakens.

A scatterplot is a graph that displays data points for each unit studied, with two variables placed on separate axes. It allows researchers to visually inspect the relationship between variables. When points cluster tightly along a line, correlation is strong; when scattered widely, correlation is weak. The scatterplot's pattern reveals both direction and strength at a glance.

Correlational research passively measures existing relationships between variables without manipulation, such as surveying vegetable consumption and sleep hours. Experimental research actively intervenes by manipulating variables to test cause and effect. Correlational designs are less invasive and useful for discovering associations, but cannot establish causation like experimental designs can.