title: Sample size planning for multiple correlation: reply to Shieh (2013).
abstract: BACKGROUND
  Bonett and Wright (2011) proposed a simple and accurate sample size planning formula for estimating a squared multiple correlation with desired relative precision. Shieh (2013) incorrectly evaluated the accuracy of the Bonett-Wright formula.
  
  
  METHODS
  To address a criticism of Shieh that the Bonett-Wright formula was not examined under a wider range of conditions, the accuracy of the Bonett-Wright sample size formula is evaluated under the additional conditions proposed by Shieh. A simple 2-step sample size formula for desired absolute precision is proposed and its accuracy is evaluated under the conditions proposed by Shieh.
  
  
  RESULTS
  The analyses indicate that the Bonett-Wright sample size formula for relative prediction and the new 2-step sample size formula for absolute precision are remarkably accurate.
  
  
  CONCLUSIONS
  Simple sample size planning formulas for a squared multiple correlation are important tools in designing a multiple regression analysis where the primary goal is to obtain an acceptably accurate estimate of the squared multiple correlation. The computationally intensive and simulation-based methods proposed by Shieh are not necessary.
authors: University of California.
authors: Douglas
authors: D
authors: Bonett
authors: Thomas
authors: T
authors: Wright
mesh_terms: D016001:Confidence Intervals; D015999:Multivariate Analysis; D012044:Regression Analysis; D018401:Sample Size