Correlation in statistics is a measure of how strongly two variables move together — whether they rise and fall in sync, move in opposite directions, or have no relationship at all. If you've ever wondered "as one thing goes up, does the other go up too?", correlation is the number that answers it. Most people Googling this are staring at two columns of data — hours studied and exam scores, maybe, or age and blood pressure — and trying to figure out if there's a real link between them.
Key Takeaways
- Correlation measures the strength and direction of a linear relationship between two numeric variables, expressed as a coefficient (r) between −1 and +1.
- A positive correlation means both variables increase together; a negative correlation means one rises as the other falls; a value near 0 means no linear relationship.
- Correlation does NOT prove causation — two variables can move together because of a hidden third factor, or by coincidence.
- Pearson's r is the most common correlation coefficient for continuous data; Spearman's rho is used for ranked or non-normal data.
- In APA 7, a correlation is reported like this: r(48) = .62, p < .001.
What does correlation actually mean?
Correlation is a single number that summarises how two variables relate. Imagine plotting your data on a scatterplot with one variable on each axis. If the dots trend upward from left to right, you have a positive correlation — bigger values of one go with bigger values of the other. If the dots trend downward, you have a negative correlation. If the dots form a shapeless cloud, there's little to no correlation.
That number is called the correlation coefficient, written as r. It always falls between −1 and +1:
- +1 = a perfect positive relationship (every increase in X matches an increase in Y).
- 0 = no linear relationship at all.
- −1 = a perfect negative relationship (every increase in X matches a decrease in Y).
Real data almost never hits exactly −1, 0, or +1. Instead you'll see values like .34 or −.71, and the job is to interpret how strong that is.
How do I interpret the size of a correlation?
The sign tells you the direction; the number tells you the strength. A widely used rule of thumb from Jacob Cohen classifies the strength of a correlation like this:
| Value of r (absolute) | Strength | What it looks like |
|---|---|---|
| .00 – .09 | Negligible | Basically a random cloud of points |
| .10 – .29 | Small / weak | A faint trend you'd struggle to see |
| .30 – .49 | Medium / moderate | A visible but loose upward or downward slope |
| .50 – 1.0 | Large / strong | A clear, tight line through the points |
So r = .62 is a strong positive correlation, while r = −.18 is a weak negative one. These bands are guidelines, not laws — in some fields (like medicine), even a small correlation can matter clinically.
When should I use correlation?
Use correlation when you have two continuous (numeric) variables and you want to know whether they are related — but you are not claiming one causes the other. Good examples:
- Does sleep duration relate to reported stress?
- Is there a link between daily screen time and anxiety scores?
- Do temperature and ice cream sales rise together?
If instead you want to predict one variable from another or model a cause-and-effect relationship, you'd move on to regression. And if one of your variables is a category (like treatment vs. control group) rather than a number, correlation isn't the right tool — you'd likely want a t-test or ANOVA instead. If you're unsure which test your data calls for, StatRyx picks the correct analysis for you based on your variable types.
Pearson vs. Spearman: which correlation do I need?
The two most common correlation coefficients answer slightly different questions:
| Pearson's r | Spearman's rho (rₛ) | |
|---|---|---|
| Measures | Linear relationship | Monotonic (rank-order) relationship |
| Data type | Continuous, roughly normal | Ordinal, or non-normal continuous |
| Sensitive to outliers? | Yes, quite | Less so (uses ranks) |
| Use when | Both variables are numeric and roughly bell-shaped | Data is skewed, ranked, or has outliers |
As a practical default: reach for Pearson when your data is continuous and reasonably normally distributed, and switch to Spearman when your data is ranked, skewed, or has extreme outliers. StatRyx checks your data's distribution automatically and flags when Spearman is the safer choice.
A worked example with real numbers
Let's walk through a real analysis. Suppose you collect data from 50 university students, recording each student's weekly study hours and their final exam score (out of 100).
You run a Pearson correlation and get:
r(48) = .62, p < .001
Here's what every piece means:
- .62 is the correlation coefficient — a strong positive relationship. As study hours go up, exam scores tend to go up too.
- (48) is the degrees of freedom, calculated as N − 2 (50 students − 2 = 48). It reflects your sample size.
- p < .001 is the p-value. It tells you the probability of seeing a correlation this strong if there were no real relationship in the population. Because .001 is far below the standard .05 threshold, the correlation is statistically significant — it's very unlikely to be a fluke.
You can also square the correlation to get r² = .38, meaning study hours explain about 38% of the variation in exam scores. The rest is down to other factors — sleep, prior knowledge, test anxiety, and so on.
Interpretation in plain English: Students who studied more tended to score higher, and this relationship was strong and statistically significant. However, correlation alone doesn't prove that studying causes higher scores — motivated students might both study more and understand the material better.
Why doesn't correlation prove causation?
A strong correlation tells you two variables move together — it does not tell you that one causes the other. There are three reasons a correlation can appear:
- X causes Y (studying raises scores).
- Y causes X (or the direction runs the other way).
- A third variable (Z) drives both — for example, conscientiousness could cause both more studying and higher scores.
The classic illustration: ice cream sales and drowning deaths are strongly correlated, but neither causes the other — hot weather drives both. Whenever you report a correlation, resist writing "X causes Y." Establishing causation requires an experiment with random assignment, not just observed co-movement.
How do I report correlation in APA 7?
APA 7 has strict formatting for correlations. The test statistic r and the p-value are italicised, and you drop the leading zero on values that can't exceed 1 (so .62, not 0.62):
A Pearson correlation revealed a strong positive relationship between weekly study hours and exam scores, r(48) = .62, p < .001.
Include the degrees of freedom in parentheses, and where your field expects it, report a 95% confidence interval and the effect size (r² or the correlation itself, since r is already an effect size). StatRyx generates this full APA 7 sentence — coefficient, degrees of freedom, p-value, and CI — automatically, so you can paste it straight into your results section.
Stop calculating this by hand — run it free in StatRyx → Try StatRyx
Frequently Asked Questions
What is a good correlation coefficient?
There's no universal "good" value — it depends on context. Using Cohen's gu