# Pearson Correlation Probability Calculator - Quick Tab

Power Analysis

The Quick tab of the Pearson Correlation Probability Calculator contains options to compute the cumulative probability and percentage points of r, the sample Pearson correlation coefficient, assuming a bivariate normal population distribution. Additionally, you can calculate a value of r, the population correlation coefficient, that corresponds to a particular value at a particular percentage point.

1 - Cumulative p. Select the 1 - Cumulative p box to show calculations in terms of 1 - Cumulative p, i.e., the probability of obtaining a value greater than the observed r. This can be useful when using the probability calculator to obtain upper rejection points for a hypothesis test, or in computing power.

Parameters. The options in this group box represent four quantities related to the distribution of r. Three of these quantities (Observed r, rho, Cum. p) can each be calculated as a function of the remaining three quantities, depending on the currently selected alternative in the Compute group box (see below). For example, if p is selected in the Compute group box, STATISTICA computes Cum. p for the current values of Observed r, N, and rho after the Compute button is clicked.

Observed r. Enter the value of the observed correlation coefficient r in the Observed r field if r is one of the input variables in the calculation. If the result of the calculation is a value of r, it will appear in this field.

rho. Enter the population correlation coefficient, r, in the rho field.

Sample Size (N). Enter N, the sample size in the Sample Size (N) field.

Cum. p. Enter the value of p in the Cum. p field if p is one of the input variables in the calculation. If the p option button is selected in the Compute group box, then the cumulative probability function (cdf) is evaluated at the Observed r, N, and rho currently displayed. Cum. p can also be used as the input variable for a calculation. If the 1 - Cumulative p box is checked, the label on this field switches to 1 - Cum. p, and calculations are altered accordingly.

Computational Algorithm. Most programs that include methods for power analysis of tests on correlations do not provide exact probability calculations. The Power Analysis and Interval Estimation 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 r and that the variance of the Fisher transform of r is 1/(N - 3).

Compute. Use the option buttons in the Compute group box to specify which quantity is to be the result of the calculation. When the Compute button is clicked, this quantity is computed as a function of the other four quantities in the Parameters group box, and the result is displayed in the appropriate field.

r. Select the r option button to compute a value of r as a function of rho, N, and Cum. p. (or 1 - Cum. p.)

p (or 1 - p). Select the p (1 - p) option button to compute a value of Cum. p (or 1 - Cum. p) as a function of r, rho, and N.

rho. Select the rho option button to compute a value of rho as a function of r, N, and Cum. p (or 1 - Cum. p).