Dual-Centered ANCOVA Overcomes Bias in ANCOVA with More Statistical Power than Difference-Score Analyses

• In Event: Regression Toward the Mean, Lord’s Paradox, and Modeling or Forecasting Change in Longitudinal Analyses

Abstract

Research for optimizing child development requires valid causal explanations of between-person differences in within-person changes. Difference scores and residualized change scores are the two fundamental approaches in analyzing change in longitudinal studies but can produce contradictory results, as shown by Lord’s (1967) paradox. The inconsistency between the two analyses of change is due to a violation of one of the assumptions of ANCOVA, namely independence of covariate(s) and treatment conditions (Huitema, 2011). The current study introduces a new dual-centered ANCOVA to remove any pretest mean difference between the treatment and the comparison group when ANCOVA’s assumption of independence between covariate and treatment is violated. We leveraged three examples to show the pattern of inconsistency in analyses of simple change scores and ANCOVA-type residualized scores. Then we introduce dual-centered ANCOVA to remove the pretest differences and get consistent results from the two approaches, i.e., difference-score analyses and ANCOVA.
Method. Example 1: Parent-youth discussions about sexual risks and subsequent unprotected sexual behaviors (N = 4753). Example 2: Disciplinary reasoning and subsequent child aggression (N = 2467). Example 3: Hospitalization and subsequent physical health in mothers (N = 3831). The first example used the Adolescent to Adult Health data and the other examples used the Fragile Families Child Well-Being longitudinal data. For all the examples, treatment was based on Time 1 data, and pretest and posttest outcome scores on Time 1 and Time 2 data.
Results. For all three examples, ANCOVA-type analyses made the treatments appear to be harmful. Parent-youth discussions of sexual costs predicted more unprotected sex, parental use of disciplinary reasoning with 5-year-olds predicted more child aggression at 9 years old, and hospitalizations led to worse physical health in mothers. In contrast, analyses of simple gain scores indicated that all treatments were effective in improving these outcomes. After using dual-centered ANCOVA to equalize pretest differences between the treatment group and the comparison group, results using the two approaches became consistent with each other and with the original difference score approach.
We plan to add more covariates to the reasoning example to learn whether the two estimates come closer together after controlling for relevant confounds.
Discussions. Although dual-centered ANCOVA satisfies a crucial assumption of ANCOVA by removing the mean pretest difference between the treatment and comparison groups, its results may still be biased. The results are less biased only when analyses of simple gain scores are less biased than traditional ANCOVA. Several statisticians have shown that ANCOVA-type longitudinal analyses are biased, however (Berry & Willoughby, 2017; Hamaker et al., 2015; Hoffman, 2015), which could explain why they make all three treatments look harmful. In any case, dual-centered ANCOVA has several strengths: The analysis 1) estimates pure within-person changes; 2) has more statistical power than difference-score analyses; 3) can be used to control for Pretest X Covariate interactions; and 4) is simple. For making causal inferences in longitudinal studies, dual-centered ANCOVA provides more statistical power than traditional difference-score analyses and overcomes biases in traditional ANCOVA when pre-test group means differ.

Authors

• Hua Lin, Oklahoma State University - Stillwater
  Presenting Author

• Robert E Larzelere, Oklahoma State University - Stillwater
  Non-Presenting Author