Psychonomic Bulletin & Review

, Volume 21, Issue 6, pp 1415–1430

Buy three but get only two: The smallest effect in a 2 × 2 ANOVA is always uninterpretable

  • Leonel Garcia-Marques
  • Teresa Garcia-Marques
  • Markus Brauer
Theoretical Review

DOI: 10.3758/s13423-014-0640-3

Cite this article as:
Garcia-Marques, L., Garcia-Marques, T. & Brauer, M. Psychon Bull Rev (2014) 21: 1415. doi:10.3758/s13423-014-0640-3

Abstract

Loftus (Memory & Cognition 6:312–319, 1978) distinguished between interpretable and uninterpretable interactions. Uninterpretable interactions are ambiguous, because they may be due to two additive main effects (no interaction) and a nonlinear relationship between the (latent) outcome variable and its indicator. Interpretable interactions can only be due to the presence of a true interactive effect in the outcome variable, regardless of the relationship that it establishes with its indicator. In the present article, we first show that same problem can arise when an unmeasured mediator has a nonlinear effect on the measured outcome variable. Then we integrate Loftus’s arguments with a seemingly contradictory approach to interactions suggested by Rosnow and Rosenthal (Psychological Bulletin 105:143–146, 1989). We show that entire data patterns, not just interaction effects alone, produce interpretable or noninterpretable interactions. Next, we show that the same problem of interpretability can apply to main effects. Lastly, we give concrete advice on what researchers can do to generate data patterns that provide unambiguous evidence for hypothesized interactions.

Keywords

Statistics Statistical inference 

Copyright information

© Psychonomic Society, Inc. 2014

Authors and Affiliations

  • Leonel Garcia-Marques
    • 1
  • Teresa Garcia-Marques
    • 2
  • Markus Brauer
    • 3
  1. 1.Faculdade de PsicologiaUniversidade de Lisboa, Alameda da UniversidadeLisboaPortugal
  2. 2.ISPA-University InstituteLisbonPortugal
  3. 3.University of Wisconsin–MadisonMadisonUSA

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