Understand the hypothesis test
Read the test as a model-based comparison
Pearson Correlation Significance Test. The observed effect is scaled by its null-model uncertainty and located on a reference distribution selected before looking at the result.
1State H₀, the effect, and direction2Calculate the statistic under H₀3Report p-value with effect and interval
Test statistic and reference model
For ρ₀=0, t=r√[(n−2)/(1−r²)]; nonzero nulls use Fisher z.
Statistical association does not establish linear adequacy, causation, or practical importance.
Responsible interpretation
A p-value is not the probability that the null is true, the chance the result occurred ‘by luck,’ or a measure of effect size, importance, replication, bias, or causation.
Required assumption: Pairs must be independent with a defensible linear bivariate model and no dominating influential points.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the pearson correlation significance test calculator works
For ρ₀=0, t=r√[(n−2)/(1−r²)]; nonzero nulls use Fisher z.
Statistical association does not establish linear adequacy, causation, or practical importance.
Worked example
Pearson Correlation Significance Test example
A correlation of 0.6 across 20 independent pairs can be tested against zero.
For ρ₀=0, t=r√[(n−2)/(1−r²)]; nonzero nulls use Fisher z.
Supported inputs
Precision and limits
Model and design
Pairs must be independent with a defensible linear bivariate model and no dominating influential points.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Statistical association does not establish linear adequacy, causation, or practical importance.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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