Relationships.
Made visible.
Build your intuition, one observation at a time.
What is
correlation?
Correlation describes the direction and strength of a relationship between variables.
A coefficient compresses a pattern into a number from −1 to +1. Its sign gives the direction. Its magnitude describes the strength of the type of association being measured.
Values closer to zero may indicate weak negative or weak positive linear association. There are no universal cutoffs for “strong.”
Moving together.
As one variable rises, the other tends to rise too. A positive sign tells you the direction, not the cause.
01 / 04Moving apart.
As one variable rises, the other tends to fall. A negative relationship can be just as strong as a positive one.
02 / 04Look at the spread.
Points spread out around a trend when the association is weak. The meaning of “strong” depends on the research context.
03 / 04One unusual point.
An extreme observation may change Pearson r substantially. Investigate its source and show your sensitivity analysis.
04 / 04How close
is the connection?
Choose a coefficient and compare the spread. The same magnitude can point in either direction.
These are teaching examples, not universal strength thresholds. Domain knowledge, measurement quality and uncertainty matter.
Three ways to
see a relationship.
Choose the relationship you want to measure before choosing the method.
| Method | Measures | Data type | Relationship | Outlier sensitivity | Typical use |
|---|---|---|---|---|---|
| Pearson r | Standardized covariance | Numeric measurements | Linear | High | Linear association |
| Spearman ρ | Correlation of average ranks | Numeric or ordinal | Monotonic | Less sensitive, not immune | Ranked or skewed data; monotonic trends |
| Kendall τ-b | Pairwise rank agreement | Numeric or ordinal | Monotonic | Less sensitive, not immune | Concordance with tied observations |
Pearson, unpacked.
Center both variables, measure how their deviations move together, then scale by their spread.
- xᵢ, yᵢ
- The paired values for observation i
- x̄, ȳ
- The means of X and Y
- n
- The number of paired observations
- r
- Pearson’s linear correlation coefficient
Normality is not required to calculate Pearson r. The parametric p-value and Fisher interval shown in this lab do have sampling assumptions. Non-normal data alone does not automatically make one method best.
See the calculation with your own dataMove a point.
Change your perspective.
Drag the dots. Watch the number.
Every observation is part of the story.
Keyboard: Tab to a point, then use arrow keys to move it. “Random Pattern” uses a reproducible irregular pattern with zero sample correlation.
Can one point
change correlation?
Twenty observations tell one story. Add an extreme observation and see what happens to Pearson r.
This button changes a teaching dataset, not your uploaded data. Investigate unusual observations before excluding them.
The axes stay fixed so the effect is easy to compare.
Zero correlation.
An unmistakable
relationship.
Pearson correlation measures linear association. A low Pearson correlation does not necessarily mean there is no relationship.
Here, Y = X². The two arms of the curve cancel in the linear coefficient, even though X determines Y exactly.
Explore the U-shapeCorrelation
≠ causation.
Temperature can influence both ice cream sales and swimming activity. Their association does not establish that either causes the other.
A shared influence is a potential confounding variable. Study design, temporal order and credible causal assumptions are needed to move beyond association.
One shared cause. Two related observations.