1. What is Critical r for Pearson Correlation?

The critical r value is the minimum correlation coefficient needed for statistical significance at a given confidence level. It helps determine whether an observed Pearson correlation is statistically significant.

2. How Does the Calculator Work?

The calculator uses the critical r formula:

Where:

• \( r_{crit} \) — Critical correlation coefficient
• \( t_{crit} \) — Critical t-value from t-distribution
• \( n \) — Sample size

Explanation: The formula converts a t-critical value to its corresponding r-critical value for Pearson correlation tests.

3. Importance of Critical r

Details: Critical r values are essential for hypothesis testing in correlation analysis. They help researchers determine if an observed correlation is statistically significant or likely due to chance.

4. Using the Calculator

Tips: Enter the critical t-value (from t-distribution tables) and sample size (n ≥ 3). The calculator will compute the corresponding critical r value.

5. Frequently Asked Questions (FAQ)

Q1: How do I find the t_crit value?
A: t_crit comes from t-distribution tables based on your desired confidence level and degrees of freedom (n-2).

Q2: What sample size should I use?
A: Use your actual sample size (n ≥ 3). Larger samples require smaller r values to reach significance.

Q3: How is this different from p-value?
A: Critical r provides a threshold value, while p-value gives the exact probability of observing your correlation by chance.

Q4: Can I use this for Spearman correlation?
A: This formula is specifically for Pearson correlation. Spearman correlation has different critical values.

Q5: What's a typical critical r value?
A: For α=0.05 and n=30, critical r is about ±0.361. Values vary with sample size and confidence level.