Critical thinkingArticle: Kievit, Frankenhuis, Waldorp, & Borsboom (2013)Simpson's paradox in psychological science: a practical guideIntroduction Simpson’s paradox: the direction of an association at the population-level may be reversed within the subgroups comprising that population.Simpson showed that a statistical relation observed in a population could be reversed within all of the subgroups that make up that population. Simpson’s paradox is a counter-intuitive feature of aggregated data, which may arise when (causal) inferences are drawn across different explanatory levels. (like population to subgroup or subgroup to individual).Simpson’s paradox is conceptually and analytically related to many statistical challenges and techniques.The underlying shared theme of these techniques is that they are concerned with the nature of (causal) inference. The challenge is what inferences are warranted based on the data we observe. One can only be sure that a group-level finding generalizes to individuals when the data are ergodic, which is a very strict requirement.Since this requirement is unlikely to hold in many data sets, extreme caution is warranted in generalizing across levels.The dimensions that appear in a covariance structure analysis describe patterns of variation between people, not variation within individuals over time.A person X may have a position on five dimensions compared to other people in a given population, but this...