Large-scale data decipher children's scale errors: A meta-analytic approach using the zero-inflated Poisson models

Scale errors are intriguing phenomena in which a child tries to perform an object-specific action on a tiny object. Several viewpoints explaining the developmental mechanisms underlying scale errors exist; however, there is no unified account of how different factors interact and affect scale errors, and the statistical approaches used in the previous research do not adequately capture the structure of the data. By conducting a secondary analysis of aggregated datasets across nine different studies (n = 528) and using more appropriate statistical methods, this study provides a more accurate description of the development of scale errors. We implemented the zero-inflated Poisson (ZIP) regression that could directly handle the count data with a stack of zero observations and regarded developmental indices as continuous variables. The results suggested that the developmental trend of scale errors was well documented by an inverted U-shaped curve rather than a simple linear function, although nonlinearity captured different aspects of the scale errors between the laboratory and classroom data. We also found that repeated experiences with scale error tasks reduced the number of scale errors, whereas girls made more scale errors than boys. Furthermore, a model comparison approach revealed that predicate vocabulary size (e.g., adjectives or verbs), predicted developmental changes in scale errors better than noun vocabulary size, particularly in terms of the presence or absence of scale errors. The application of the ZIP model enables researchers to discern how different factors affect scale error production, thereby providing new insights into demystifying the mechanisms underlying these phenomena. A video abstract of this article can be viewed at https://youtu.be/1v1U6CjDZ1Q RESEARCH HIGHLIGHTS: We fit a large dataset by aggregating the existing scale error data to the zero-inflated Poisson (ZIP) model. Scale errors peaked along the different developmental indices, but the underlying statistical structure differed between the in-lab and classroom datasets. Repeated experiences with scale error tasks and the children's gender affected the number of scale errors produced per session. Predicate vocabulary size (e.g., adjectives or verbs) better predicts developmental changes in scale errors than noun vocabulary size.