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The complexity of eye-movement control during reading allows measurement of many dependent variables, the most prominent ones being fixation durations and their locations in words. In current practice, either variable may serve as dependent variable or covariate for the other in linear mixed models (LMMs) featuring also psycholinguistic covariates of word recognition and sentence comprehension. Rather than analyzing fixation location and duration with separate LMMs, we propose linking the two according to their sequential dependency. Specifically, we include predicted fixation location (estimated in the first LMM from psycholinguistic covariates) and its associated residual fixation location as covariates in the second, fixation-duration LMM. This linked LMM affords a distinction between direct and indirect effects (mediated through fixation location) of psycholinguistic covariates on fixation durations. Results confirm the robustness of distributed processing in the perceptual span. They also offer a resolution of the paradox of the inverted optimal viewing position (IOVP) effect (i.e., longer fixation durations in the center than at the beginning and end of words) although the opposite (i.e., an OVP effect) is predicted from default assumptions of psycholinguistic processing efficiency: The IOVP effect in fixation durations is due to the residual fixation-location covariate, presumably driven primarily by saccadic error, and the OVP effect (at least the left part of it) is uncovered with the predicted fixation-location covariate, capturing the indirect effects of psycholinguistic covariates. We expect that linked LMMs will be useful for the analysis of other dynamically related multiple outcomes, a conundrum of most psychonomic research.
False positives and other statistical errors in standard analyses of eye movements in reading
(2017)
In research on eye movements in reading, it is common to analyze a number of canonical dependent measures to study how the effects of a manipulation unfold over time. Although this gives rise to the well-known multiple comparisons problem, i.e. an inflated probability that the null hypothesis is incorrectly rejected (Type I error), it is accepted standard practice not to apply any correction procedures. Instead, there appears to be a widespread belief that corrections are not necessary because the increase in false positives is too small to matter. To our knowledge, no formal argument has ever been presented to justify this assumption. Here, we report a computational investigation of this issue using Monte Carlo simulations. Our results show that, contrary to conventional wisdom, false positives are increased to unacceptable levels when no corrections are applied. Our simulations also show that counter-measures like the Bonferroni correction keep false positives in check while reducing statistical power only moderately. Hence, there is little reason why such corrections should not be made a standard requirement. Further, we discuss three statistical illusions that can arise when statistical power is low, and we show how power can be improved to prevent these illusions. In sum, our work renders a detailed picture of the various types of statistical errors than can occur in studies of reading behavior and we provide concrete guidance about how these errors can be avoided. (C) 2016 Elsevier Inc. All rights reserved.