Correlation Significance Test
Computes the significance test for the Pearson correlation coefficient, answering whether the observed correlation between two variables is real or could have arisen by chance. A correlation of 0.5 in a sample of 6 points is unimpressive; the same correlation in 600 points is very strong. The test converts r into a t value, with n−2 degrees of freedom, and returns the p-value. The tool computes r, the t statistic and the two-sided p-value. Enter the two series of paired values.
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Correlation Significance Test
Computes the significance test for the Pearson correlation coefficient, answering whether the observed correlation between two variables is real or could have arisen by chance. A correlation of 0.5 in a sample of 6 points is unimpressive; the same correlation in 600 points is very strong. The test converts r into a t value, with n−2 degrees of freedom, and returns the p-value. The tool computes r, the t statistic and the two-sided p-value. Enter the two series of paired values.
Is this correlation real or just luck?
Computing a correlation coefficient is easy; knowing whether it means anything is what matters. An r of 0.5 from five points may be pure coincidence, while the same 0.5 from five hundred points is solid evidence of a relationship. The correlation significance test separates the signal from the noise, taking the sample size into account.
The mechanics transform the coefficient r into a t statistic, through a formula that weighs r against the amount of data. Under the hypothesis of no correlation in the population, that statistic follows a t distribution with n minus two degrees of freedom. The larger the r in magnitude and the larger the sample, the larger the t, and the more unlikely the observed correlation arose by chance.
Enter the two series of paired values. The tool computes the Pearson coefficient, the t statistic, the degrees of freedom and the two-sided p-value. A reminder that's always worth repeating: a significant correlation isn't causation, and the test only assesses a linear relationship — a strong curved association can go unnoticed behind an r near zero.
Related Tools
Point-Biserial Correlation
Computes the point-biserial correlation coefficient, which measures the association between a continuous variable and a dichotomous (two-group) variable. It is, in fact, the Pearson correlation applied to the case where one variable takes only two values — so it ranges from −1 to +1 and carries the same interpretation. It shows up often in psychometrics, to assess how well a test item (right/wrong) discriminates between high- and low-scoring students. Enter the continuous values of each of the two groups.
D'Agostino-Pearson Normality Test (K²)
Computes the D'Agostino-Pearson omnibus normality test, which combines two clues of non-normality into a single verdict: skewness (do the data lean to one side?) and kurtosis (are the tails too heavy or too light?). Each becomes a standardized z score, and the sum of their squares, the K² statistic, follows a chi-square with 2 degrees of freedom. It's more informative than looking at skewness and kurtosis separately. Enter the sample (at least 8 values).
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.
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.