Partial Correlation
Partial Correlation Coefficient · Also known as: partial r, controlled correlation, Kısmi Korelasyon (Partial Correlation)
Partial correlation measures the linear relationship between two continuous variables after removing the shared influence of one or more control variables. The technique was formalised by R. A. Fisher in 1924 and is the standard approach whenever a researcher suspects that a third variable inflates or suppresses the observed association between two variables of interest.
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When to use it
Use partial correlation when you have two continuous focal variables and one or more continuous covariates whose influence you want to hold constant. All variables should be approximately normally distributed and linearly related to one another. The minimum recommended sample size is 30, and the choice of control variables must be theoretically justified before analysis — post-hoc selection of covariates inflates the false-positive rate. If the data are ordinal or strongly non-normal, consider rank-based (Spearman) partial correlation as an alternative.
Strengths & limitations
- Directly isolates the unique relationship between two variables by partialling out confounders, reducing the risk of spurious conclusions.
- Produces an effect size (partial r) that is easy to interpret and directly comparable across studies.
- Can handle multiple simultaneous control variables, giving a cleaner picture than a series of subgroup analyses.
- Assumes linearity; a nonlinear relationship between a covariate and either focal variable will not be fully removed.
- Controlling for variables measured with error (attenuation bias) can over- or under-correct the partial r.
- Does not establish causal direction — the choice of which variable to treat as outcome versus predictor is substantive, not statistical.
Frequently asked
How is partial correlation different from zero-order (Pearson) correlation?
A zero-order Pearson correlation reports the total linear association between two variables, which can include variance attributable to third variables. Partial correlation removes the portion of variance in both focal variables that is linearly shared with the specified covariates, leaving only the unique association between them.
What is the difference between partial and semi-partial (part) correlation?
Partial correlation removes the covariate's influence from both focal variables. Semi-partial (part) correlation removes it from only one of the two — typically the predictor — leaving the outcome variance intact. Semi-partial r is commonly reported in multiple regression as a measure of unique predictor contribution relative to the total outcome variance.
Can I use partial correlation with ordinal or non-normal data?
The standard parametric partial correlation assumes continuous, approximately normally distributed variables. For ordinal data or clearly non-normal distributions, a rank-based alternative (Spearman partial correlation) is more appropriate. In pingouin, you can specify method='spearman' in the partial_corr function.
How many control variables can I include?
Technically you can include multiple covariates, but each additional control variable costs one degree of freedom (df = n − 2 − k). With small samples, controlling for many variables dramatically reduces power and makes the partial r unstable. A minimum of roughly 20–30 cases per controlled variable is a reasonable rule of thumb.
Sources
- Fisher, R.A. (1924). The Distribution of the Partial Correlation Coefficient. Metron, 3, 329–332. link ↗
- Kim, S. (2015). ppcor: An R Package for a Fast Calculation to Semi-Partial Correlation Coefficients. Communications for Statistical Applications and Methods, 22(6), 665–674. DOI: 10.5351/CSAM.2015.22.6.665 ↗
How to cite this page
ScholarGate. (2026, June 1). Partial Correlation Coefficient. ScholarGate. https://scholargate.app/en/statistics/partial-correlation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Pearson CorrelationStatistics↔ compare
- Spearman CorrelationStatistics↔ compare