1. What is a P-value for Correlation?

The p-value for a correlation coefficient tests the null hypothesis that there is no correlation between two variables in the population. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Pearson correlation coefficient (-1 to 1)
• \( n \) — Sample size (number of observations)
• \( \text{tdist} \) — Student's t-distribution cumulative distribution function

Explanation: The formula converts the correlation coefficient to a t-statistic and calculates the two-tailed probability.

3. Interpretation of Results

Details:

• p ≤ 0.05: Significant correlation (reject null hypothesis)
• 0.05 < p ≤ 0.10: Marginally significant correlation
• p > 0.10: No significant correlation (fail to reject null hypothesis)

4. Using the Calculator

Tips: Enter the correlation coefficient (-1 to 1) and sample size (minimum 3). The calculator will compute the two-tailed p-value.

5. Frequently Asked Questions (FAQ)

Q1: What does the p-value mean?
A: The p-value is the probability of observing a correlation as extreme as the one calculated if there were actually no correlation in the population.

Q2: Why two-tailed p-value?
A: A two-tailed test is standard for correlation as we typically don't know in advance whether the correlation will be positive or negative.

Q3: What sample size is needed?
A: Larger samples provide more reliable results. Minimum n=3 is required mathematically, but n≥30 is recommended for stable estimates.

Q4: What are assumptions of this test?
A: Assumes both variables are normally distributed and the relationship is linear. For non-normal data, consider Spearman's correlation.

Q5: How accurate is this calculator?
A: The calculator provides a good approximation, though for critical applications use specialized statistical software.