Partial Correlation
Computes the partial correlation between two variables while controlling for the effect of a third. It's the tool against spurious correlations: ice cream sales correlate with drownings, but only because both rise in hot weather — controlling for temperature, the partial correlation drops to near zero. It removes the influence of the control variable from both and measures the direct association that remains. The tool returns the partial coefficient and its significance test. Enter the three paired series.
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Partial Correlation
Computes the partial correlation between two variables while controlling for the effect of a third. It's the tool against spurious correlations: ice cream sales correlate with drownings, but only because both rise in hot weather — controlling for temperature, the partial correlation drops to near zero. It removes the influence of the control variable from both and measures the direct association that remains. The tool returns the partial coefficient and its significance test. Enter the three paired series.
The correlation left after removing the third factor
Many strong correlations are illusions created by a hidden variable. The classic example: ice cream sales rise together with drowning cases, but neither causes the other — both merely respond to hot weather. Partial correlation is the tool that unmasks this kind of relationship, measuring the association between two variables after discounting the influence of a third.
The calculation starts from the three simple correlations between the pairs of variables and combines them in a formula that mathematically removes the control variable's effect from both. What remains is the direct correlation between the first two, free of the confounding introduced by the third. If the original correlation was spurious, that partial value plummets to near zero.
Enter the three paired series: the two variables of interest and the control variable. The tool returns the partial correlation coefficient and its significance test, with degrees of freedom reduced to reflect the control. It's a basic instrument for investigating causal relationships in observational data, where confounding variables are always lurking.
Related Tools
CI for Correlation (Fisher z Transform)
Computes the confidence interval for a correlation coefficient using the Fisher z transformation. The sampling distribution of r is skewed, especially near −1 or +1, which prevents applying the usual symmetric margin. Fisher solved this with a transformation that makes the distribution approximately normal; you build the interval on that scale and then map back to r. The result is an asymmetric interval, narrower on the side near the extremes. Enter the coefficient r and the sample size.
Welch's t-test
Computes the Welch's t-test statistic, the two-sample t-test version that does NOT assume equal variances. Unlike the classic Student's t-test, it doesn't pool the variances into a single value, which makes it more reliable when the two groups have different spreads — the default recommendation in modern statistics. The degrees of freedom come from the Welch-Satterthwaite equation, usually fractional. Enter the mean, standard deviation and size of each of the two groups.
Paired t-Test
Computes the paired t-test, used when you measure the same subjects twice — before and after a treatment, or by two methods. It works with the differences of each pair and tests whether the mean difference is compatible with zero. By removing the variability between subjects, it's usually far more powerful than comparing two independent groups. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. Enter the two paired series.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.