Free Beta (Type II Error Rate) Calculator for Multiple Regression

The following formulas are involved in the calculation of beta (Type II error rate) values for multiple regression:

	Beta function:
	Cohen's f² effect size for an F-test: where R² is the squared multiple correlation.
	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, λ is the noncentrality parameter, F is the Fisher F-value, and I is the 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.

The following references can be used to cite this beta (type ii error rate) calculator for multiple regression:

	Soper, D.S. (2012) "Beta (Type II Error Rate) Calculator for Multiple Regression (Online Software)", http://www.danielsoper.com/statcalc3.
	Cohen, J. (1988) "Statistical Power Analysis for the Behavioral Sciences (2nd Edition)", Lawrence Earlbaum Associates, Hillsdale, NJ.
	Cohen, J., Cohen, P., West, S.G., and Aiken, L.S. (2003) "Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd edition)", Lawrence Earlbaum Associates, Mahwah, NJ.

The following statistics calculators are related to this beta (type II error rate) calculator for multiple regression, and may be useful for your research:

	A-priori Sample Size Calculator for Multiple Regression
	Adjusted R-square Calculator (Population R-square)
	Confidence Interval Calculator for an f-square Effect Size
	Critical F-value Calculator
	Effect Size Calculator for Multiple Regression
	F-Value and p-Value Calculator for Multiple Regression
	Post-hoc Statistical Power Calculator for Multiple Regression
	R-square Calculator (from an f-square Effect Size)
	R-square Confidence Interval Calculator
	Regression Coefficient Confidence Interval Calculator
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