Meta-analysis is a widely used method to evaluate evidence of associations by combining the results of multiple scientific studies. Although meta-analysis is one of the most robust tools in modern data science, it cannot provide information about associative relationships at the composition levels. Here, we develop a mathematical method to elucidate associative relationships at the composition levels by defining individual scientific studies as quantified incidences (QIs). Application of the QI method to all publicly available bigdata on fruits elucidated that fruit acids are the etiological components for anti-obesity effects. Animal experiments were carried out subsequently in this study, demonstrating that malic acid, among fruit acids, exerts anti-obesity effects putatively by decreasing quantities of fatty acids and NAD+. This work not only provides a novel mathematical method for big-data analysis but also provides an explanation for the paradox of how fruits contain large quantities of simple sugars but bestow anti-obesity effects.