Tamanho amostra correlação
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The sample size calculator for correlation estimates the minimum number of observations needed to detect a statistically significant correlation with adequate power. It uses the formula ((z_a + z_b)/0.5·ln((1+r)/(1−r)))² +3, where 'r' is the expected correlation coefficient, and 'z_a' and 'z_b' are critical values for significance (alpha) and power (1-beta) levels.
The calculation incorporates Fisher's z-transformation, which normalizes the correlation for analysis. The formula adjusts the sample size based on effect magnitude (r) and error tolerance (alpha and beta). It is ideal for planned studies aiming to validate the statistical validity of a relationship between two variables.
When using this tool, it's crucial to define 'r' accurately and set appropriate significance thresholds. Underestimating 'r' may overburden the sample size, while overestimating reduces result reliability. Review existing scientific literature for reference values before applying this calculator.
Frequently asked questions
Why is Fisher's z-transformation used in this calculation?
Fisher's z-transformation standardizes correlation coefficients, making them more stable for statistical analysis. This reduces biases in smaller samples and improves the accuracy of sample size estimates.
What alpha and beta levels are recommended?
Common thresholds are alpha = 0.05 (5% risk of error) and beta = 0.20 (80% power). Adjustments depend on the study context and acceptable error margins in the field.
What if the actual correlation is lower than expected?
If the true correlation is smaller than the assumed 'r' value, the calculated sample size will be insufficient. Increase the sample size or revise the hypothesis to ensure validity.
Is this formula suitable for small samples?
The formula assumes moderate to large samples. For very small samples (n < 10), non-parametric methods like Spearman correlation may be more appropriate.