Free A-priori Sample Size Calculator for Hierarchical Multiple Regression

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A-priori Sample Size Calculator for Hierarchical Multiple Regression

This calculator will tell you the minimum sample size required for a hierarchical multiple regression analysis; i.e., the minimum sample size required for a significance test of the addition of a set of independent variables B to the model, over and above another set of independent variables A. The value returned by the calculator is the minimum sample size required to detect an effect of the specified size, probability level, and power level for the addition of set B to the model.

Please supply the necessary parameter values, and then click 'Calculate'.

Anticipated effect size for set B:	Cohen's f-square effect size. By convention, effect sizes of 0.02, 0.15, and 0.35 are considered small, medium, and large, respectively.
Desired statistical power level:	By convention, this value should be greater than or equal to 0.80.
Number of predictors in set A:	The number of independent variables that comprise set A.
Number of predictors in set B:	The number of independent variables that comprise set B.
Probability level:	Also known as the p-value, alpha level, or type I error rate. By convention, this value should be less than or equal to 0.05 to claim statistical significance.

Formulas

The following formulas are involved in the calculation of a-priori sample size values for hierarchical multiple regression:

	Beta function:
	Effect size for hierarchical multiple regression: where R²_A is the variance accounted for by a set of one or more independent variables A, and R²_AB is the combined variance accounted for by A and another set of one or more independent variables B.
	Error function:
	F-distribution cumulative distribution function (CDF): where d₁ and d₂ are the degrees of freedom, and I is the regularized lower incomplete beta function.
	Lower incomplete beta function:
	Noncentral F-distribution cumulative distribution function (CDF): where d₁ and d₂ are the numerator and denominator degrees of freedom, ? is the noncentrality parameter, F is the Fisher F-value, and I is the regularized lower incomplete beta function.
	Noncentral F-distribution noncentrality parameter: where f² is the effect size and n is the sample size.
	Normal distribution cumulative distribution function (CDF): where µ is the mean, σ is the standard deviation, and erf is the error function.
	Regularized lower incomplete beta function: where the numerator is the lower incomplete beta function, and the denominator is the beta function.

References

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