Table 4.

Minimum and Maximum Length for 95% CI for Pearson Correlation Coefficient (0.1–0.9 by 0.1)

Sample size (n)	Minimum	Maximum
10	0.35	1.25
20	0.20	0.88
30	0.15	0.71
40	0.13	0.62
50	0.11	0.55
60	0.10	0.50
70	0.09	0.47
80	0.09	0.44
90	0.08	0.41

Note: The 95% CI for the correlation coefficient was obtained by using Fisher’s Z transformation (3). First, compute a 95% CI for the parameter $\frac{1}{2}\ln \frac{1+\rho }{1-\rho }$ using the formula $\frac{1}{2}\ln \frac{1+r}{1-r}\pm \frac{1.96}{\sqrt{n-3}}$, where r is the sample correlation coefficient and n is the sample size.

Denote the limits for the 95% CI for this interval as (L_z, U_z). Then the limits of the 95% CI for the original scale (L_ρ, U_ρ) can be calculated by using the conversion formulas below: $L_{\rho }=\frac{e^{2L_z}-1}{e^{2L_z}+1}\text{and}{U}_{\rho }=\frac{e^{2U_z}-1}{e^{2U_z}+1}$