The A Priori Procedure (APP) for Estimating Regression Coefficients in Linear Models

Authors

  • Tingting Tong
    Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA
  • David Trafimow
    Department of Psychology, New Mexico State University, Las Cruces, NM, USA
  • Tonghui Wang
    Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA
  • Cong Wang
    Department of Mathematics, University of Nebraska, Omaha, NE, USA
  • Liqun Hu
    Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA
  • Xiangfei Chen
    Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA

Abstract

Regression coefficients are crucial in the sciences, as researchers use them to determine which independent variables best explain the dependent variable. However, researchers obtain regression coefficients from data samples and wish to generalize to populations; without reason to believe that sample regression coefficients are good estimates of corresponding population regression coefficients, their usefulness would be curtailed. In turn, larger sample sizes provide better estimates than do smaller ones. There is much recent literature on the a priori procedure (APP) that was designed for the general purpose of determining the sample sizes needed to obtain sample statistics that are good estimates of corresponding population parameters. We provide an extension of the APP to regression coefficients, which works for standardized or unstandardized regression coefficients. A simulation study and real data example support the mathematical derivations. Also, we include a free and user-friendly computer program to aid researchers in making the calculations.