Academic journal article Memory & Cognition

On the Interpretation of Removable Interactions: A Survey of the Field 33 Years after Loftus

Academic journal article Memory & Cognition

On the Interpretation of Removable Interactions: A Survey of the Field 33 Years after Loftus

Article excerpt

Abstract In a classic 1978 Memory & Cognition article, Geoff Loftus explained why noncrossover interactions are removable. These removable interactions are tied to the scale of measurement for the dependent variable and therefore do not allow unambiguous conclusions about latent psychological processes. In the present article, we present concrete examples of how this insight helps prevent experimental psychologists from drawing incorrect conclusions about the effects of forgetting and aging. In addition, we extend the Loftus classification scheme for interactions to include those on the cusp between removable and nonremovable. Finally, we use various methods (i.e., a study of citation histories, a questionnaire for psychology students and faculty members, an analysis of statistical textbooks, and a review of articles published in the 2008 issue of Psychology and Aging) to show that experimental psychologists have remained generally unaware of the concept of removable interactions. We conclude that there is more to interactions in a 2 × 2 design than meets the eye.

Keywords Transformations . Measurement scale . Statistics in psychology . Literature review

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Few statistical concepts appear to be as straightforward as an interaction in a 2 × 2 design. Most statistical textbooks inform undergraduate psychology students that an interaction is indicated when "the lines are not parallel." Thus, all psychologists are familiar with the concept of an interaction, and they often report and interpret interactions obtained in their own experiments. It is easy to conclude that experimental psychologists know what an interaction is, and how it should be interpreted. Unfortunately, there is more to an interaction than meets the eye.

More than three decades ago, Geoff Loftus published a Memory & Cognition article in which he summarized results from measurement theory (e.g., Krantz & Tversky, 1971; Luce & Tukey, 1964) and demonstrated that interactions are not created equal: Some interactions-the ones that cross over-are "nonremovable," whereas the others are "removable" (Loftus, 1978; see also Anderson, 1961, 1963; Bogartz, 1976). A nonremovable interaction can never be undone by a monotonic transformation of the measurement scale, and it is therefore also known as qualitative, cross-over, disordinal, nontransformable, orderbased, model-independent, or interpretable (Cox, 1984; De González & Cox, 2007; Neter, Wasserman, & Kutner, 1990). In contrast, a removable interaction can always be undone by a monotonic transformation of the measurement scale; such an interaction is also known as quantitative, ordinal, transformable, model-dependent, or uninterpretable.

Given the prominence of interactions in psychological research, it is important for experimental psychologists to be familiar with the Loftus (1978) article and realize that the only interactions that are nonremovable are the ones that cross over. Our personal experience, however, has led us to conjecture that experimental psychologists have forgotten about the difference between nonremovable and removable interactions. When told about the existence of removable interactions and the role of scale transformations, colleagues commonly respond, "But why would I want to transform my measurement scale at all?" Therefore, the first goal of the present article is to answer this question and to reiterate the main message from Loftus (1978). The second goal is to introduce a classification scheme for interactions that refines the one proposed by Loftus (1978). The third goal is to demonstrate through various means (i.e., a study of citation histories for the Loftus article, a questionnaire for faculty and graduate students, an analysis of statistical textbooks, and a review of the literature) that, 33 years after the Loftus (1978) article, experimental psychologists are-to their peril-generally unaware of the fact that many interactions are removable. …

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