Calculator Input
Example Data Table
| Observation | Study Hours (X) | Test Score (Y) |
|---|---|---|
| 1 | 2 | 54 |
| 2 | 3 | 58 |
| 3 | 4 | 63 |
| 4 | 5 | 68 |
| 5 | 6 | 72 |
| 6 | 7 | 78 |
This sample shows a positive relationship between study time and score.
Formula Used
Pearson correlation coefficient:
r = Σ[(x − x̄)(y − ȳ)] / √(Σ[(x − x̄)²] × Σ[(y − ȳ)²])
R² = r²
Pearson correlation measures linear association between two numeric variables. The coefficient ranges from −1 to +1.
The calculator also reports covariance, standard deviations, t statistic, degrees of freedom, and p-value for significance testing.
How to Use This Calculator
- Enter paired data in separate X and Y lists, or paste paired rows.
- Choose the delimiter if you use the paired values area.
- Set the significance level and decimal precision you want.
- Click Calculate Correlation to show the result above the form.
- Review the summary metrics, detailed table, and interpretation.
- Use the CSV or PDF buttons to export the result.
Frequently Asked Questions
1. What does Pearson correlation measure?
It measures the strength and direction of a linear relationship between two numeric variables using paired observations.
2. What values can r take?
The coefficient ranges from −1 to +1. Values near ±1 show stronger linear relationships, while values near 0 suggest weak linear association.
3. When should I avoid Pearson correlation?
Avoid it when data are strongly non-linear, categorical, heavily skewed, or dominated by outliers that distort the linear pattern.
4. What is the difference between r and R²?
r shows direction and strength. R² shows the proportion of variance in one variable explained by the linear relationship.
5. Why does the calculator show a p-value?
The p-value helps test whether the observed correlation is statistically significant, given your sample size and chosen hypothesis style.
6. Can I paste spreadsheet data?
Yes. Paste two columns into the paired values box, or paste separate columns into the X and Y text areas.
7. Does correlation prove causation?
No. Correlation only describes association. Other variables, reverse effects, or coincidence may explain the observed relationship.