t-Test for Zero Correlation: Power Calculation Results - Quick Tab

Select the Quick tab of the t-Test for Zero Correlation: Power Calculation Results dialog box to access options to interactively view the results of power calculations and generate plots of power as a function of quantities that affect power in practice.

X-Axis Graphing Parameters

The entries in the boxes under X-Axis Graphing Parameters establish the start value, end value, and number of steps on the X-axis for the graphs specified under Power Charts.

Start N

In the Start N box, enter the starting value of N used in the Power vs. N power chart.

End N

In the End N box, enter the final value of N used in the Power vs. N power chart.

Start Rho

In the Start Rho box, enter the starting value of rho used in the Power vs. Rho power chart.

End Rho

In the End Rho box, enter the final value of rho used in the Power vs. Rho power chart.

Start Alpha

In the Start Alpha box, enter the starting value of alpha used in the Power vs. Alpha power chart.

End Alpha

In the End Alpha box, enter the final value of alpha used in the Power vs. Alpha power chart.

No. of Steps.

In the No. of Steps box, enter the number of steps, or intervals, plotted on the X-axis in the power charts specified in the Power Charts box.

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).

Power Charts

Use the buttons under Power Charts to produce charts of power as a function of variables known to affect it. Note that the parameters specified under X-Axis Graphing Parameters control the range of values plotted on the X-axis and the number of steps plotted.

Power vs. N.

Click the Power vs. N button to produce a plot of power versus sample size N.

Power vs. Rho.

Click the Power vs. Rho button to produce a plot of power versus population correlation (ρ).

Power vs. Alpha.

Click the Power vs. Alpha button to produce a plot of power vs. type I error rate (α).