Correlation P-Value Calculator
Calculate the t-statistic for testing whether a correlation coefficient is significantly different from zero.
t-Statistic
4.5260
t-Statistic vs Correlation Coefficient (r)
Formula
## Testing Correlation Significance To determine whether an observed correlation is statistically significant, calculate the t-statistic and compare to the t-distribution. ### Formula **t = r × sqrt(n-2) / sqrt(1-r²)** with df = n - 2. If |t| exceeds the critical value (e.g., ~2.048 for alpha=0.05, df=28), the correlation is statistically significant.
Exemplo Resolvido
Correlation r = 0.65 from a sample of n = 30.
- 01t = 0.65 × sqrt(28) / sqrt(1 - 0.4225)
- 02t = 0.65 × 5.292 / sqrt(0.5775)
- 03t = 3.440 / 0.7599 = 4.527
- 04With df = 28, this is highly significant (p < 0.001)
Perguntas Frequentes
What does a significant correlation mean?
It means the observed correlation is unlikely to have occurred by chance if the true correlation is zero. It does NOT mean the correlation is strong or practically important. With large n, even tiny correlations can be significant.
What is the critical value of r for significance?
It depends on n and alpha. For alpha=0.05: n=10 requires |r| > 0.632, n=30 requires |r| > 0.361, n=100 requires |r| > 0.197. Larger samples need smaller r to be significant.
Does significance imply causation?
No. A significant correlation only establishes a linear association. Causation requires experimental manipulation, time ordering, and ruling out confounding variables.
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