Partial Correlation

Q: Is partial correlation free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

Q: What is the difference between partial and semi-partial correlation?

Partial r removes the control variable from both X and Y. Semi-partial r removes it from only one (usually the predictor X), making the semi-partial r directly comparable to standardised regression betas.

Q: How many control variables can I use?

StatRyx supports multiple control variables simultaneously. The partial correlation removes the joint influence of all specified covariates.

Q: How do I report a partial correlation in APA 7?

Name the control variable, give r with its degrees of freedom (n − 2 − number of controls), the p-value, and the zero-order r for comparison: "Controlling for age, exercise and depression remained negatively correlated, r(117) = −.38, p < .001 (zero-order r = −.52)."

Q: Is partial correlation the same as a regression coefficient?

They are closely related but not the same. The standardised regression coefficient and the partial correlation have the same sign and significance test, but the partial correlation is on the familiar −1 to 1 scale of r, which makes it easier to compare with zero-order correlations.

Measure the relationship between two variables after statistically removing the influence of one or more control variables.

Partial Correlation measures the relationship between two variables after removing the variance shared with one or more control variables (covariates). This is essential when a third variable confounds the observed relationship between two variables. For example, the correlation between exercise and mental health may be confounded by age; partial correlation removes age's influence from both variables before computing the correlation.

Semi-partial (part) correlation removes the control variable's influence from only one of the two variables of interest, making it useful for understanding unique predictive contributions in regression.

StatRyx computes both partial r and semi-partial r with 95% CIs and p-values, and reports the reduction in the zero-order correlation after controlling for the specified covariates.

A partial correlation is the correlation between X and Y after the linear influence of one or more control variables has been removed from both. Compare it with the ordinary (zero-order) correlation: if it shrinks towards zero, the control variable accounts for much of the relationship; if it stays similar, the relationship holds independently of it. It is interpreted on the same scale as Pearson's r.

When to use the Partial Correlation

You want to know whether the relationship between two variables holds after controlling for a third variable
You are checking whether an observed correlation is spurious (driven by a common cause)
You want to compute the unique predictive contribution of one variable in a regression model
You want to show that a relationship is not just an artefact of age, gender or another demographic
You have a correlation matrix and want the relationships net of a common confound

When not to use it

You want to predict an outcome from multiple predictors simultaneously — use Multiple Linear Regression instead
Your variables are not continuous or normally distributed — use Partial Spearman correlation or robust alternatives instead
You want to know whether a third variable explains how X affects Y — use Mediation Analysis instead

Worked example

Relationship	Zero-order r	Partial r	Controlled for	p
Exercise – Depression	−.52	−.38	Age	< .001

How to report it (APA 7)

After controlling for age, the partial correlation between exercise frequency and depression scores was significant, r(117) = −.38, p < .001 (zero-order r = −.52). This indicates that the relationship between exercise and depression is partially, but not fully, explained by age.

Frequently asked questions

Is partial correlation free on StatRyx?