Lord’s Paradox

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Lords Paradox. Analysis of Covariance vs. Analysis of Difference Scores. Lord, F. M. (1967). A paradox in the interpretation of group comparisons. Psychological Bulletin , 68 (5). 304-305. Inconsistency in significance testing. - PowerPoint PPT Presentation


  • Lords ParadoxAnalysis of Covariance vs. Analysis of Difference ScoresLord, F. M. (1967). A paradox in the interpretation of group comparisons. PsychologicalBulletin, 68 (5). 304-305.

  • Inconsistency in significance testing

    In analyzing how subjects change, analysis of covariance, and analysis of difference scores yield different results

    The same data sets, analyzed for the same effects, using different techniques yielded qualitatively different results

  • Lords exampleA test of sex differences in the Freshman 15Analysis of difference scores for males and females shows no differenceAnalysis of covariance shows a significant differenceSo, what is going on?

  • -Distributions on top = initial weight distributions-Distributions on side = final weight distributions-Ovals = scatter plots of male and female weights

  • with the data usually available for such studies, there simply is no logical or statistical procedure that can be counted on to make proper allowances for uncontrolled pre-existing conditions between groups

    -Frederic Lord

  • Different questions = Different answers

    ANCOVA asks how can one variable predict variation in another (in our example how can weight at the beginning be used to predict weight at the end)Analysis of difference scores asks how do initial scores differ from final scoresPike, G. R. (2004). Lords paradox and the assessment of change during college. Journal of College Student Development, 45 (3). 348-353.

  • Take Home MessageWhen evaluating differences within individuals, there may not be a consistently best wayThink of the question that you want to askThink of what question the statistical tools can askBe careful in interpreting your results

  • Thanks!