Evaluating the Significance Test When the Correlation Coefficient is Different from Zero in the Test of Hypothesis

Sample size and correlation coefficient of populations are the most important factors which influence the statistical significance of the sample correlation coefficient. It is observed that for evaluating the hypothesis when the observed value of the correlation coefficient's r is different from zero, Fisher's Z transformation may be incorrect for small samples especially when population correlation coefficient ρ has big values. In this study, a simulation program has been generated for to illustrate how the bias in the Fisher transformation of the correlation coefficient affects estimate precision when sample size is small and ρ has big value. By the simulation results, 90 and 95% confidence intervals of correlation coefficients have been created and tabled. As a result, it is suggested that especially when ρ is greater than 0.2 and sample sizes of 18 or less, Tables 1 and 2 can be used for the significance test in correlations.