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The analysis of large experimental datasets frequently reveals significantinteractions that are difficult to interpret within the theoretical frameworkguiding the research. Some of these interactions actually arise from thepresence of unspecified nonlinear main effects and statistically dependentcovariates in the statistical model. Importantly, such nonlinear main effectsmay be compatible (or, at least, not incompatible) with the current theoreticalframework. In the present literature this issue has only been studied in termsof correlated (linearly dependent) covariates. Here we generalize to nonlinearmain effects (i.e., main effects of arbitrary shape) and dependent covariates.We propose a novel nonparametric method to test for ambiguous interactionswhere present parametric methods fail. We illustrate the method with a set ofsimulations and with reanalyses (a) of effects of parental education on theirchildren's educational expectations and (b) of effects of word properties onfixation locations during reading of natural sentences, specifically of effectsof length and morphological complexity of the word to be fixated next. Theresolution of such ambiguities facilitates theoretical progress.

On the Ambiguity of Interaction and Nonlinear Main Effects in a Regime of Dependent Covariates