Sample Size Calculation For Correlation Study

Sample Size Formula:

\[ n = \left[ \frac{Z_{\alpha/2} + Z_{\beta}}{0.5 \times \ln\left(\frac{1+r}{1-r}\right)} \right]^2 + 3 \]

Z-score for Alpha (Z_α/2):

(e.g., 1.96 for α=0.05)

Z-score for Power (Z_β):

(e.g., 0.84 for 80% power)

Expected Correlation (r):

(-0.99 to 0.99)

Required Sample Size (n):

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1. What is Sample Size Calculation For Correlation Study?

This calculator determines the minimum sample size required to detect a correlation coefficient of specified magnitude with given statistical power and significance level. It's essential for planning correlation studies in research.

2. How Does the Calculator Work?

The calculator uses the sample size formula for correlation:

\[ n = \left[ \frac{Z_{\alpha/2} + Z_{\beta}}{0.5 \times \ln\left(\frac{1+r}{1-r}\right)} \right]^2 + 3 \]

Where:

\( Z_{\alpha/2} \) — Z-score for significance level (two-tailed)
\( Z_{\beta} \) — Z-score for statistical power
\( r \) — Expected correlation coefficient
\( n \) — Required sample size

Explanation: This formula calculates the minimum number of participants needed to detect a correlation of magnitude r with specified power and significance level, accounting for the Fisher z-transformation of correlation coefficients.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect meaningful effects while avoiding unnecessary resource expenditure. Underpowered studies may miss true effects, while overpowered studies waste resources.

4. Using the Calculator

Tips: Enter Z-scores corresponding to your desired alpha level and power. Common values: Z_α/2=1.96 (α=0.05), Z_β=0.84 (80% power). The expected correlation should be between -0.99 and 0.99.

5. Frequently Asked Questions (FAQ)

Q1: What are common Z-score values?
A: Z_α/2=1.96 for α=0.05, Z_β=0.84 for 80% power, Z_β=1.28 for 90% power.

Q2: How do I estimate the expected correlation?
A: Use pilot data, previous literature, or consider what correlation would be clinically meaningful in your field.

Q3: Why add 3 to the final result?
A: The +3 correction improves accuracy, especially for small sample sizes, based on Fisher's work on correlation sampling distributions.

Q4: What if my correlation is negative?
A: The formula works for both positive and negative correlations. The absolute value determines the required sample size.

Q5: When is this formula appropriate?
A: For Pearson correlation coefficients with bivariate normal data. For other correlation measures (Spearman, Kendall), different formulas apply.