Correlation Coefficient Calculator
Calculate Pearson, Spearman and Kendall correlation from paired data, with significance testing, confidence intervals and a scatter plot showing what the number is actually measuring.
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Three coefficients measuring different things
Pearson measures how close the relationship is to a straight line, and it is the one people mean by "correlation". Spearman correlates the ranks instead of the values, so it detects any consistently increasing or decreasing relationship whether or not it is straight, and it is barely affected by outliers. Kendall's tau counts how many pairs of observations agree in their ordering, which makes it the most robust of the three and the least familiar. When Pearson and Spearman disagree substantially, the relationship is either curved or dominated by a few extreme points.
The number hides the shape
Anscombe's quartet is four datasets with identical means, variances and Pearson correlations that look completely different when plotted: one is a clean linear relationship, one is a perfect parabola, one is a straight line with a single outlier, and one is a vertical cluster with one distant point. Any correlation reported without looking at the scatter plot is a number of unknown meaning, which is why the plot is drawn here rather than offered as an option.
Correlation is not causation and not the whole story
Beyond the familiar warning, a correlation near zero does not mean no relationship. Pearson correlation of a perfect symmetric parabola is exactly zero, because the linear component cancels. The coefficient measures linear association specifically, and a strong non linear relationship can produce any Pearson value at all including zero.
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Frequently Asked Questions
What is the difference between Pearson and Spearman?
Pearson measures how close the data is to a straight line. Spearman does the same on the ranks, so it detects any consistently increasing or decreasing relationship regardless of shape and is much less affected by outliers. A large gap between them means the relationship is curved or a few points dominate.
What counts as a strong correlation?
It depends entirely on the field. In physics 0.9 might be disappointing and in social science 0.3 can be a notable finding. The r squared value is more interpretable: it gives the proportion of variance in one variable that the other accounts for.
Can a correlation of zero mean no relationship?
No. Pearson correlation of a perfect symmetric parabola is exactly zero, because it measures linear association only. A strong curved relationship can produce any Pearson value including zero, which is why the scatter plot matters.
What is Kendall's tau?
A coefficient based on counting how many pairs of observations agree in their ordering versus how many disagree. It is the most robust of the three and has a direct interpretation as a probability of concordance, but it is smaller in magnitude than Spearman for the same data, so the two are not comparable.
How many points do I need?
Correlation from fewer than about ten pairs is very unstable, and even a strong looking coefficient can arise by chance. The confidence interval shown here widens dramatically at small sample sizes, which is a more honest picture than the point estimate alone.
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How to Use
Paste paired x and y values to get all three correlation coefficients.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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