The correlation coefficient (r) is a statistic from -1 to +1 that describes the strength and direction of a linear relationship between two variables; the sign shows direction (positive or negative), the absolute value shows strength, and r never proves that one variable causes the other.
The correlation coefficient, written as r, is a single number that summarizes the linear relationship you'd see on a scatterplot. It runs from -1 to +1. A positive r means the variables move together (more study time, higher grades). A negative r means they move in opposite directions (more screen time before bed, less sleep). An r of 0 means there's no linear relationship between the two variables.
Here's the part that trips people up. The sign tells you the direction of the relationship, and the distance from zero tells you the strength. So r = -0.8 is a stronger correlation than r = +0.5, even though it's negative. Think of r as a two-part message in one number. And the most tested fact of all is what r can't do. A correlation coefficient describes how two measured variables relate, but it can never tell you that one causes the other. Only an experiment with manipulation and a control group can do that.
The correlation coefficient lives in Topic 1.5 (Statistical Analysis in Psychology) and supports the research design content in Topic 1.2 (Research Methods in Psychology). Correlational research is what psychologists use when an experiment would be impossible or unethical, like studying sleep deprivation and depression. You can't randomly assign people to be sleep deprived for months, so you measure both variables and compute r. Because the AP Psych exam includes a research-based free response (the Evidence-Based Question and Article Analysis Question both lean on research methods), being able to interpret an r value, name its limits, and explain the third-variable problem is a skill you'll use across every unit, not just Unit 1.
Keep studying AP Psychology Unit 1
Scatterplot (Unit 1)
The correlation coefficient is basically a scatterplot compressed into one number. If the dots cluster tightly along an upward line, r is close to +1; a loose, shapeless cloud gives an r near 0. Practice matching r values to scatterplot pictures, because the exam does exactly that.
Linear Relationship (Unit 1)
r only measures linear relationships. Two variables can be strongly related in a curve (like arousal and performance in the Yerkes-Dodson law) and still produce an r near zero. An r of 0 means no linear relationship, not necessarily no relationship at all.
Control Group (Unit 1)
Correlational studies have no control group and no manipulation, which is exactly why they can't establish cause and effect. When a question asks how to turn a correlational finding into a causal claim, the answer is to run an experiment with random assignment and a control group.
Cross-Sectional Study (Unit 1)
Cross-sectional studies are usually correlational. They compare different groups at one moment in time, so any relationship they find is described with a correlation coefficient and carries the same can't-prove-causation limitation.
Multiple-choice questions test whether you can interpret r values, like identifying that r = 0 means no linear relationship between the variables, or recognizing why a coefficient might be misleading in a study on sleep deprivation and academic performance (think third variables or a non-linear pattern). The College Board has also used correlation in free-response questions. The 2022 SAQ described Dr. Germanotta collecting data on the number of witnesses to a crime and how many people helped, then asked about her findings. You needed to recognize that as correlational research and interpret a negative correlation (more witnesses, less helping, which is the bystander effect). Expect to do three things with this term: judge strength and direction from a number, match numbers to scatterplots, and explain why correlation does not equal causation.
A strong correlation coefficient feels like proof that one variable causes the other, but it isn't. Ice cream sales and drowning deaths correlate strongly, yet hot weather (a third variable) drives both. Correlation tells you two variables move together; causation requires an experiment where researchers manipulate the independent variable and use random assignment. On the exam, claiming causation from correlational data is one of the most common ways to lose FRQ points.
The correlation coefficient (r) ranges from -1 to +1, where the sign shows direction and the absolute value shows strength.
An r of -0.8 indicates a stronger relationship than an r of +0.5, because strength depends on distance from zero, not the sign.
An r of 0 means there is no linear relationship between the variables, though a non-linear relationship could still exist.
Correlation never proves causation; a third variable could be driving both, or the direction of influence could go either way.
Correlational research is used when experiments would be unethical or impossible, but only experiments with manipulation and random assignment can establish cause and effect.
On scatterplots, tightly clustered points along a line mean r is close to -1 or +1, while a scattered cloud means r is near 0.
It's a statistic, symbolized r, that measures the strength and direction of a linear relationship between two variables. It ranges from -1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive), and it's covered in Topics 1.2 and 1.5 of Unit 1.
No. Even an r of 0.95 can't establish causation, because a third variable might cause both, or the causal direction might be reversed. Only an experiment with manipulation, random assignment, and a control group can demonstrate cause and effect.
No, the sign has nothing to do with strength. An r of -0.8 is stronger than an r of +0.5. Negative just means the variables move in opposite directions, like the 2022 SAQ scenario where more witnesses to a crime meant fewer people helped.
It means there is no linear relationship between the two variables. Knowing one variable's value tells you nothing about the other. Watch out, though, because a curved (non-linear) relationship can still exist when r is 0.
A correlational study measures two existing variables and computes r, while an experiment manipulates an independent variable, uses random assignment, and measures a dependent variable. That manipulation is why experiments can claim causation and correlational studies can't.