Sample Size Calculation, Two Correlations, Z-Test

Sample Size calculation for two independent correlations via Z-Test with option for charts of sample size vs. population one rho value, sample size vs. alpha level, and sample size vs. power.

General

Element Name Description
Power Goal Specifies Power Goal for the Sample Size calculation (acceptable range 0.65 to 0.9999).
Rho1 Population number one correlation coefficient (acceptable range -0.9999 to 0.9999).
Rho2 Population number two correlation coefficient (acceptable range -0.9999 to 0.9999).
Sample One Size Sample size of group one for the sample size calculation (acceptable range 3 to 150000).
Sample Two Size Sample size of group two for the sample size calculation (acceptable range 3 to 150000).
Alpha Level Alpha level (Type I error rate for Z-statistic) (acceptable range 0.0001 to 0.25).
Hypothesis type Hypothesis type selection:

 Two-tailed (Rho1=Rho2, population one rho = population two rho);

 One-tailed (Rho1<=Rho2, population one rho <= population two rho);

 One-tailed (Rho1>=Rho2, population one rho >= population two rho).
Computational Method Computational method selection:

 Fisher Z Refined, employ an approximation based on the Fisher transformation, but using refined series approximation formulae for the mean and variance;

 Fisher Z Crude, use the traditional (somewhat cruder) approximation assuming the mean of the Fisher transform of r is the Fisher transform of r and the variance of the Fisher transform of r is 1/(N-3).
N to Vary Find sample size for one or both groups:

 Equal N (vary N1 and N2 simultaneously and equally);

 Vary N1 (Vary N1 while holding N2 constant at the value specified under Sample Two Size above);

 Vary N2 (Vary N2 while holding N1 constant at the value specified under Sample One Size above). This option also applies to any charts that are produced.
Detail of computed results reported Output level of detail selection:

 Sample Size Calculation produces Sample size Calculation Spreadsheet;

 Smpl Size Calc plus Charts option produces, in addition, Sample Size vs. Population One Rho, Sample Size vs. Alpha Level, and Sample Size vs. Power charts.

Chart Parameters

Element Name Description
Number of Steps. (For charts only) Number of individual steps for which to calculate Sample Size between the starting and ending parameter values for Sample Size Charts (Min 4, Max 100).
Starting Power. (For charts only) Initial power value for calculation of Sample Size vs. Power chart (acceptable range 0.05 to 0.99).
Ending Power. (For charts only) Final Power value for calculation of Sample Size vs. Power chart (acceptable range 0.1 to 0.999).
Starting Correlation (Rho). (For charts only) Initial population one correlation value for calculation of Sample Size vs. Population One Rho chart (acceptable range -0.9999 to 0.9999).
Ending Correlation (Rho). (For charts only) Final population one correlation value for calculation of Sample Size vs. Population One Rho chart (acceptable range -0.9999 to 0.9999).
Starting Alpha. (For charts only) Initial alpha value for calculation of Sample Size vs. Alpha Level chart (acceptable range 0.0001 to 0.2499).
Ending Alpha. (For charts only) Final alpha value for calculation of Sample Size vs. Alpha Level chart (acceptable range 0.0002 to 0.25).