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Below you will find a complete set of details for 5 different references / citations that are related to the computation of beta (type II error rate) values for hierarchical multiple regression studies.

Reference for Citing the Online Calculator

- Soper, D.S. (2020). Beta (Type II Error Rate) Calculator for Hierarchical Multiple Regression [Software]. Available from http://www.danielsoper.com/statcalc

References from the Scientific Literature

- Abramowitz, M. and Stegun, I.A., eds. (1965). Handbook of Mathematical Functions. New York, NY: Dover.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd Edition). Hillsdale, NJ: Lawrence Earlbaum Associates.
- Cohen, J., Cohen, P., West, S.G., and Aiken, L.S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd edition). Mahwah, NJ: Lawrence Earlbaum Associates.
- Raudenbush, S. and Bryk, A. (2002). Hierarchical Linear Models (Second Edition). Thousand Oaks, CA: Sage Publications.

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