Correlation calculator
Paste two columns from Excel: one row per person, one column per variable (for example, motivation score and performance score). Pick Pearson or Spearman to get the coefficient, whether it’s significant and how to report it.
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How it’s calculated
Pearson (r) measures linear relationship: r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² × Σ(y − ȳ)²).
Spearman (rho) applies the same formula to the ranks of the data (ties get the average rank). Use it for ordinal scales like Likert, or when data aren’t normal.
The two-tailed p-value comes from t = r × √((n − 2) / (1 − r²)) with n − 2 degrees of freedom, as in SPSS.
How to read the result
- The coefficient goes from −1 to 1. Positive: when one rises, so does the other. Negative: when one rises, the other falls. Near 0: no linear relationship.
- A common scale: under 0.20 very weak, 0.20 to 0.39 weak, 0.40 to 0.59 moderate, 0.60 to 0.79 strong and 0.80 or more very strong.
- If p is below 0.05, the correlation is statistically significant: it’s unlikely to come from chance alone.
- Correlation isn’t causation. Two variables moving together doesn’t prove one causes the other.
Frequently asked questions
- Pearson or Spearman?
- Use Pearson if both variables are numeric and roughly normal. Use Spearman with Likert scales, ranks or data with extreme values. For questionnaire-based theses, Spearman is most common.
- How much data do I need?
- At least 3, but with fewer than 30 the result isn’t very stable. With small samples only large correlations come out significant.
- Does it match SPSS?
- Yes: it uses the same formulas and t test, so r, rho and p match SPSS “Bivariate Correlations”.
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