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Two implicit generalizations are often made from group-level studies in cognitive experimental psychology and their common statistical analysis in the general linear model: (1) Group-level phenomena are assumed to be present in every participant with variations between participants being often treated as random error in data analyses; (2) phenomena are assumed to be stable over time. In this preregistered study, we investigated the validity of these generalizations in the commonly used parity judgment task. In the proposed Ironman paradigm, the intraindividual presence and stability of three popular numerical cognition effects were tested in 10 participants on 30 days: the SNARC (Spatial-Numerical Association of Response Codes, i.e., faster left-/right-sided responses to small/large magnitude numbers, respectively; Dehaene, Bossini, & Giraux, 1993), MARC (Linguistic Markedness of Response Codes; i.e., faster left-/right-sided responses to odd/even numbers, respectively; Nuerk, Iversen, & Willmes, 2004), and Odd (i.e., faster responses to even numbers; Hines, 1990) effects. We replicated the group-level effects; however, they were reliably present in only four to five (SNARC), six (MARC) or five (Odd) of 10 participants. Fluctuations seemed unsystematic, although the SNARC effect decreased over time along with reaction times. No correlation between the SNARC and MARC effects and sleep duration, tiredness, daytime, and consumption of stimulants were detected in most participants. These results challenge the frequent generalizations from group-level phenomena to individual participants and from single sessions to typical behavior. The innovative Ironman paradigm combined with bootstrap analyses permits unique insights into the intraindividual presence and stability of cognitive phenomena., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest with the content of this article., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)