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Partial Correlation Calculator

Calculate the correlation between two variables controlling for a third.

About Partial Correlation Calculator

Partial correlation removes the variance both variables share with the control. A large drop from the raw correlation indicates confounding by that third variable. Spurious correlations often collapse once an obvious confounder is controlled, which is exactly what this calculation reveals.

Formula

Partial Correlation

r_xy·z = (r_xy − r_xz r_yz) ÷ √((1 − r²_xz)(1 − r²_yz))

partial correlation
Association remaining after removing the shared influence of a third variable

Worked example

With the default values below, Partial Correlation Calculator returns Partial Correlation of 0.449346. Change any input above and every figure here is recalculated in your browser.

Inputs used

Correlation between x and yaccepts -1–1
0.6
Correlation between x and the controlaccepts -1–1
0.5
Correlation between y and the controlaccepts -1–1
0.55
Sample sizeminimum 4
100

Results

Partial Correlation
0.449346
Change From the Raw Correlation
-0.150654
T Statistic
4.95383
Degrees of Freedom
97
Interpretation
The association persists after controlling for the third variable

Step by step

  1. 1Values used
  2. 2Partial Correlation
  3. 3Partial Correlation= 0.449346
  4. 4Change From the Raw Correlation= -0.150654
  5. 5T Statistic= 4.95383
  6. 6Degrees of Freedom= 97
  7. 7Interpretation= The association persists after controlling for the third variable

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Partial Correlation calculated?

r_xy·z = (r_xy − r_xz r_yz) ÷ √((1 − r²_xz)(1 − r²_yz)) Partial correlation removes the variance both variables share with the control. A large drop from the raw correlation indicates confounding by that third variable.

Why does Partial Correlation matter?

Spurious correlations often collapse once an obvious confounder is controlled, which is exactly what this calculation reveals.

What values do I need to enter?

This calculator takes 4 inputs: Correlation between x and y, Correlation between x and the control, Correlation between y and the control, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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