Sample Size for Correlation Studies When Normality Assumption Violated

Aims: Assessing the correlation between two variables is very important in observational and experimental researches. “How many sample size was required?” is one of the preliminary questions for correlation studies. Although achieving normality is rare the available techniques calculated the sample size based on fisher transformation statistics that supposed the bivariate normal distribution. This study conducted to find the sample size of correlation studies when the distribution of population is not bivriate normal.
Methodology: A Simulation study was used to compared the required sample size of the correlation test for ρ= 0.1, 0.2 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. Samples are drawn from bivariat normal, skewed, highly skewed, and heavy tailed distributions. The bias, variance, Mean Square Error (MSE), and the rejection rate of the fisher test for 10000 sample correlation coefficient were calculated. To achieving the nominal power the sample size was increased gradually.
Results: Both the mean Bias and Mean Square Error of Sample correlation increased when the bivariate distribution is not normal. The correlation test is robust against minor and major departures from bivariate normal assumption when the sample size of study was sufficiently large. To find the significance correlation between two variables with nominal power the required sample size depending on ρ and population distribution approximately 10 to 30 percent increased.
Conclusion: Departure from normality affected both accuracy and precision of sample correlation. Normality is not an ignorable assumption for correlation studies and it is important to have information about population distribution to determine the sample size when designing a study.