The Decline and Fall of 

Type II Error Rates

Steve Verrill

Mark Durst

United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

Research

Paper

FPL–RP–628
August 2005

Verrill, Steve; Durst, Mark. 2005. The decline and fall of Type II error 

rates. Research Paper FPL-RP-628. Madison, WI: U.S. Department of 

Agriculture, Forest Service, Forest Products Laboratory. 11 p.

A limited number of free copies of this publication are available to the 

public from the Forest Products Laboratory, One Gifford Pinchot Drive, 

Madison, WI 53726–2398. This publication is also available online at 

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Abstract

For general linear models with normally distributed 

random errors, the probability of a Type II error decreases 

exponentially as a function of sample size. This potentially 

rapid decline reemphasizes the importance of performing 

power calculations. 

Keywords: power, sample size, linear models, experimental 

design, noncentral F, normal tail, Mills’ ratio, asymptotic 

relative efficiency, Hodges-Lehmann efficiency, Pitman 

efficiency, minimum detectable difference.
  	
 	 
    	

  	
 	


 	  
 	



	
 
  	



	 
 

  
 



 	



	 	 
 

     
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