Noncentrality Interval Estimation and the Evaluation of Statistical Models

Select the Quick tab of the t-Test for Zero Correlation: Interval Estimation dialog box to access options to calculate exact and approximate confidence intervals for the population correlation. These confidence intervals will commonly be employed in situations where the t-test on a single correlation is calculated. The exact confidence interval can, in fact, be used in lieu of the (two-tailed) hypothesis test procedure, since it excludes zero if and only if the hypothesis test (at the same level of type I error) fails to reject.

Observed R. In the Observed R box, enter the value of the observed correlation. If you are attempting to calculate the confidence interval, based on a reported value of a t-statistic or its probability level, you can reconstruct the value of r, using the probability distribution calculator.

Sample Size (N). In the Sample Size (N) box, enter the sample size (N) for the experimental group used in the study.

Conf. Level. In the Conf. Level box, enter the confidence level for the confidence interval calculation.

Computational Algorithm. Most programs that include methods for power analysis of tests on correlations do not provide exact probability calculations. The Power Analysis module allows you to choose from three algorithms:

Exact. Select the Exact option button to obtain exact calculations. These calculations take substantially longer to compute than the approximations given below, but the calculation is not prohibitively time-consuming for the sample sizes typically employed in research studies.

Fisher Z Refined. Select the Fisher Z Refined option button to employ an approximation based on the Fisher transformation, but using refined series approximation formulae for the mean and variance (Fouladi, 1991).

Fisher Z Crude. Select the Fisher Z Crude option button to use the traditional (somewhat crude) approximation, based on the Fisher transformation, assuming that the mean of the Fisher transform of r is the Fisher transform of ρ, and that the variance of the Fisher transform of r is 1/(N - 3).