Enter Survey Data
Use commas, spaces, or new lines between values. Both variables must contain the same number of responses.
Example Data Table
This sample uses survey satisfaction and loyalty scores to demonstrate a positive relationship.
| Respondent | Satisfaction Score | Loyalty Score |
|---|---|---|
| 1 | 2 | 1 |
| 2 | 3 | 2 |
| 3 | 4 | 3 |
| 4 | 4 | 4 |
| 5 | 5 | 4 |
| 6 | 6 | 5 |
| 7 | 6 | 6 |
| 8 | 7 | 7 |
| 9 | 8 | 8 |
| 10 | 9 | 9 |
Formula Used
1) Pearson Correlation
r = Σ[(xi − x̄)(yi − ȳ)] ÷ √{Σ(xi − x̄)2 × Σ(yi − ȳ)2}
2) Spearman Rank Correlation
The calculator converts raw values into average ranks and then applies the Pearson formula to those ranks.
When no ties exist: ρ = 1 − [6Σdi2 ÷ n(n2 − 1)]
3) Significance Test
t = r × √[(n − 2) ÷ (1 − r2)] with degrees of freedom n − 2. The p-value is based on the two-tailed t distribution.
4) Confidence Interval
Fisher transformation: z = atanh(r), standard error = 1 ÷ √(n − 3), then convert the interval back with tanh(z).
How to Use This Calculator
- Enter a survey name and labels for both variables.
- Choose Auto, Pearson, or Spearman based on your data type.
- Select the response scale and desired confidence level.
- Paste variable values into the two text areas.
- Keep both variables aligned by respondent order.
- Click Calculate Correlation to show results above the form.
- Review correlation strength, p-value, confidence interval, and regression trend.
- Use the export buttons to download CSV or PDF output.
FAQs
1) When should I use Pearson correlation?
Use Pearson when survey variables behave like continuous numeric measures and the relationship is roughly linear. It works well for averaged composite scores and interval-style survey scales.
2) When should I use Spearman correlation?
Use Spearman for ordinal or Likert-style responses, monotonic relationships, tied ranks, or data with non-normal patterns. It is often safer for raw survey item scores.
3) What does a positive correlation mean?
A positive value means both variables tend to rise together. For example, higher satisfaction scores may appear alongside higher loyalty scores.
4) What does a negative correlation mean?
A negative value means one variable tends to increase while the other decreases. This may appear when higher stress scores align with lower engagement scores.
5) Why is the p-value important?
The p-value helps test whether the observed relationship is likely due to random sampling noise. A smaller p-value suggests stronger statistical evidence of a real association.
6) What does R² show here?
R² is the squared correlation. It estimates the proportion of shared variation between the two variables, giving an easy summary of relationship strength.
7) Can I paste values from a spreadsheet?
Yes. Paste values separated by commas, spaces, or line breaks. Keep the same respondent order in both fields so each pair stays matched correctly.
8) Does this calculator handle tied ranks?
Yes. The Spearman option assigns average ranks for tied values, which makes it suitable for repeated Likert scores and many practical survey datasets.