Data Input
More Options
Results
| n | — |
|---|---|
| Method | — |
| Reported r | — |
| Absolute |r| | — |
| Mean(X) | — |
| Mean(Y) | — |
| SD(X) | — |
| SD(Y) | — |
| Cov/ρ base | — |
| t statistic | — |
| df | — |
| p-value | — |
| CI for r | — |
| Strength | — |
Example Data Table
| # | X | Y |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 2 |
| 3 | 3 | 3 |
| 4 | 4 | 5 |
| 5 | 6 | 7 |
| 6 | 8 | 9 |
Formula Used
For Pearson:
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √(Σ(xᵢ − x̄)² · Σ(yᵢ − ȳ)²)
For Spearman, compute ranks R(x), R(y) with average ties, then apply Pearson to ranks.
Absolute value |r| represents association strength without direction.
Significance uses t = r √((n − 2)/(1 − r²)) (approximation for Spearman), with df = n − 2. Confidence intervals use Fisher’s z transform.
How to Use This Calculator
- Paste or type X and Y columns into the boxes.
- Or select a CSV containing two numeric columns or headers.
- Choose a method, tail, and confidence level in More Options.
- Optionally winsorize to cap extreme values before analysis.
- Click Calculate, then export results or cleaned data.
Strength Guide
| |r| | Interpretation |
|---|---|
| 0.00–0.19 | Very weak |
| 0.20–0.39 | Weak |
| 0.40–0.59 | Moderate |
| 0.60–0.79 | Strong |
| 0.80–1.00 | Very strong |
Additional Reference Data
1) CI Half‑Width vs Sample Size (r = 0.50, 95%)
| n | CI Low | CI High | Half‑width |
|---|---|---|---|
| 10 | -0.189 | 0.859 | 0.359 |
| 20 | 0.074 | 0.772 | 0.272 |
| 30 | 0.170 | 0.729 | 0.229 |
| 50 | 0.257 | 0.683 | 0.183 |
| 100 | 0.337 | 0.634 | 0.134 |
| 200 | 0.388 | 0.597 | 0.097 |
2) Approximate Minimum n for p < 0.05 (Two‑tailed)
| |r| | Minimum n |
|---|---|
| 0.20 | ~97 |
| 0.30 | ~43 |
| 0.40 | ~25 |
| 0.50 | ~16 |
3) Winsorization Effect on |r| (Illustrative Outlier Example)
| Winsorization per tail | |r| |
|---|---|
| 0% | 0.717 |
| 5% | 0.717 |
| 10% | 0.717 |
| 15% | 0.717 |
| 20% | 0.973 |
4) Pearson vs Spearman on Monotonic Non‑linear Data
| Method | Correlation |
|---|---|
| Pearson | 0.9746 |
| Spearman | 1.0000 |
Frequently Asked Questions
1) What does absolute correlation mean?
Absolute correlation, |r|, measures association strength without direction. Values near 1 indicate strong relationships, while values near 0 indicate weak relationships. It helps compare magnitude across positive and negative associations consistently.
2) When should I prefer Spearman over Pearson?
Use Spearman for monotonic but nonlinear relationships, ordinal data, or when outliers or non-normality may distort Pearson. Spearman ranks the data first, reducing sensitivity to extreme values and scale differences between variables.
3) How many pairs do I need?
More is better. With fewer than ten pairs, estimates and p-values are unstable. Many studies target at least 20–30 pairs for reasonable precision, and larger samples are required for smaller effects.
4) Should I use one-tailed or two-tailed tests?
Two-tailed tests are standard when any nonzero association is plausible. One-tailed tests require a justified directional hypothesis in advance. Avoid switching tails after seeing data; doing so inflates false-positive risk.
5) How do outliers affect correlation?
Outliers can inflate or deflate Pearson dramatically. Consider diagnostics, robust alternatives, or winsorization to limit extreme influence. Always investigate whether outliers reflect real phenomena or data-entry or measurement issues.
6) Does a high |r| imply causation?
No. Correlation quantifies association, not cause. Confounding, reverse causation, or shared drivers can produce high |r|. Establishing causality requires design, experiments, instruments, or strong analytical controls beyond correlation alone.