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Allocation to groups: Examples of Lord's paradox.

Daniel B Wright1

  • 1University of Nevada, Las Vegas, Nevada, USA.

The British Journal of Educational Psychology
|July 14, 2019
PubMed
Summary
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Researchers should choose between analysis of covariance (ANCOVA) and gain score models based on how initial scores affect group assignment. ANCOVA is preferred when initial scores influence group allocation, preventing bias in educational effectiveness studies.

Area of Science:

  • Developmental psychology
  • Educational psychology
  • Quantitative methods

Background:

  • Analysis of change over time is common in developmental and educational psychology.
  • Analysis of covariance (ANCOVA) and gain score models are frequently used for two-group, two-time-point data.
  • These methods can yield divergent results, a phenomenon known as Lord's paradox.

Purpose of the Study:

  • To guide researchers and students in selecting appropriate analytical methods for studying group changes.
  • To investigate how the relationship between initial scores and group assignment impacts analytical choices.
  • To highlight potential biases in educational effectiveness measures, particularly for underperforming student groups.

Main Methods:

  • Exploration of Lord's paradox using examples from sports and educational settings.
Keywords:
ANCOVALord's paradoxeducator equityvalue-added models

Related Experiment Videos

  • Simulation study to compare ANCOVA and gain score models under different conditions.
  • Application of regression toward the mean to explain findings.

    • Main Results:

    • The choice between ANCOVA and gain score models depends on whether the initial score influences group allocation.
    • ANCOVA is recommended when the covariate (initial score) affects group assignment.
    • The gain score model may be suitable when the covariate does not influence group assignment.

    Conclusions:

    • The relationship between covariates and group allocation is a critical factor in choosing analytical methods.
    • Complex or unknown relationships may necessitate specific assumptions for method selection.
    • Accurate analysis requires careful consideration of how initial measurements influence group formation to avoid biased outcomes, especially in educational research.