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

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Beta (Type II Error Rate) Calculator for Multiple Regression

This calculator will tell you the beta level for your study (i.e., the Type II error rate), given the observed probability level, the number of predictors, the observed R², and the sample size.

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

Number of predictors:	The total number of predictors in the model, not including the regression constant.
Observed R²:	The model R-square. Also known as the squared multiple correlation or the coefficient of determination.
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.
Sample size:	The total number of valid cases used in the analysis.

Formulas

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, ? 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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