相关性P值计算器

计算相关系数的统计显著性P值。

t-Statistic

4.5260

自由度28
0.4225

t-Statistic vs Correlation Coefficient (r)

公式

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.

计算示例

Correlation r = 0.65 from a sample of n = 30.

  1. 01t = 0.65 × sqrt(28) / sqrt(1 - 0.4225)
  2. 02t = 0.65 × 5.292 / sqrt(0.5775)
  3. 03t = 3.440 / 0.7599 = 4.527
  4. 04With df = 28, this is highly significant (p < 0.001)

常见问题

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.

学习

Understanding the Normal Distribution

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