What does the Pearson r measure?

Pearson r measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 (perfect negative linear relationship) through 0 (no linear relationship) to +1 (perfect positive linear relationship).

How is the p-value calculated?

The test converts r to a t-statistic using t = r * sqrt((n-2) / (1 - r^2)) with n-2 degrees of freedom, then evaluates the two-tailed p-value from the t-distribution via the regularized incomplete beta function.

What are the assumptions for this test?

Both variables should be measured on an interval or ratio scale, the relationship should be linear, the observations should be independent, and ideally both variables should be approximately normally distributed (especially important for small samples).

r-squared (the coefficient of determination) is simply r multiplied by itself. It represents the proportion of variance in one variable that is explained by the linear relationship with the other variable, expressed as a value between 0 and 1.

What is considered a strong correlation?

As a rough guide: |r| 0.7 is strong — but the interpretation depends heavily on context. A small r can still be statistically significant with a large sample, while a large r may not be with few observations.

How many data points do I need?

You need at least 3 pairs (so that degrees of freedom n-2 >= 1). In practice, the test has low power with fewer than 10 observations. Both variables must have the same number of values.

Pearson Correlation Test

Name: Pearson Correlation Test
Availability: InStock
Author: Nham Vu

Enter two equal-length numeric datasets and instantly get the Pearson r, r-squared, t-statistic, degrees of freedom, and two-tailed p-value.

Enter Your Data

X Variable

Y Variable

Significance Level (alpha)

Load Example

Enter two equal-length datasets and click Calculate

Pearson r

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r-squared

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variance explained

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t-statistic

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p-value (2-tail)

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Scatter Plot

Data Points

#	X	Y	x - x̄	y - ȳ

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