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Sample size and multiple regression analysis.

S E Maxwell1

  • 1Department of Psychology, University of Notre Dame, 118 Haggar Hall, Notre Dame, Indiana 46556, USA. smaxwell@nd.edu

Psychological Methods
|February 24, 2001
PubMed
Summary
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Calculating effect sizes in multiple regression is complex, often leading to persistent rules of thumb for sample size. This study offers new methods and simulations to address this, aiming for more reliable research findings.

Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Rules of thumb for sample size persist in multiple regression despite available calculation methods.
  • Difficulty in determining a priori effect size values contributes to the reliance on heuristics.
  • Underpowered studies, often resulting from persistent rules of thumb, can lead to contradictory research findings.

Purpose of the Study:

  • To present various methods for calculating effect sizes in multiple regression.
  • To introduce a novel method for effect size calculation based on predictor variable exchangeability.
  • To provide insights into why rules of thumb for sample size persist and their consequences.

Main Methods:

  • Review and presentation of multiple perspectives for calculating effect sizes in multiple regression.

Related Experiment Videos

  • Introduction of a new effect size calculation method leveraging an exchangeability structure among predictors.
  • Simulation studies to investigate the persistence of sample size rules of thumb and their impact.

    • Main Results:

    • No single method for effect size calculation is universally superior; a combination is often most valuable.
    • Simulations offer a second explanation for the persistence of sample size rules of thumb.
    • Underpowered studies yield a body of literature with seemingly contradictory results.

    Conclusions:

    • Effective sample size calculation in multiple regression requires considering multiple effect size perspectives.
    • A new method based on predictor exchangeability offers an additional approach to effect size estimation.
    • Addressing the challenges in a priori effect size determination is crucial for advancing robust scientific literature.