Calculating Required Sample Size

Select the Quick
tab of the t-Test for Zero Correlation: Sample Size Calculation
Results dialog box to access options to interactively view the results
of sample size calculations and generate plots of required sample size
as a function of quantities that affect sample size 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 Sample Size Charts.

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

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

Start Rho. In the Start Rho box, enter the starting value of rho used in the N vs. Rho sample size chart.

End Rho. In the End Rho box, enter the final value of rho used in the N vs. Rho sample size chart.

Start Alpha. In the Start Alpha box, enter the starting value of alpha used in the N vs. Alpha sample size chart.

End Alpha. In the End Alpha box, enter the final value of alpha used in the N vs. Alpha sample size chart.

No. of Steps. In the No. of Steps box, enter the number of steps, or intervals, to plot on the X-axis in the charts specified in the Sample Size Charts group 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).

Sample Size Charts. Use the buttons under Sample Size Charts to produce charts of required N as a function of power goal, population correlation, or type I error rate. Note that parameters given in the X-Axis Graphing Parameters box control the range of values plotted on the X-axis and the number of steps plotted.

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

N vs. Rho. Click the N vs. Rho button to produce a plot of sample size (N) versus population correlation (ρ).

N vs. Alpha. Click the N vs. Alpha button to produce a plot of sample size (N) vs. type I error rate.