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The data presented here support the research article titled “Disentangling the Controls on Fossil Bone Geochemistry Using Partial Redundancy Analysis”, submitted to Applied Geochemistry. The dataset includes trace element concentrations measured in the outer 3 mm of the cortical bone of fossil dinosaur specimens from the Upper Cretaceous Nemegt and Djadokhta formations (Gobi Desert, Mongolia). These data were used to investigate the relative influence of the local diagenetic environment, bone morphology, and skeletal element type on fossil bone geochemistry using partial redundancy analysis (pRDA). The dataset is organized into three main folders: “Data”, “Plots and Figures”, and “Tables”. The “Data” folder contains CSV files with trace element concentrations (ppm), PAAS-normalized element concentrations, detection limits, and metadata for individual measurement spots used in the analyses. The “Plots and Figures” folder contains images of the femur of specimen ZPAL MgD-I/30, including a cross-polarized photomicrograph of sample TS030 used in this study. This folder also contains two subfolders: - “RDA biplots”, which includes biplots for all models used in the analysis, including additional biplots showing the distribution of measurement spots in RDA space that are not included in the manuscript. - “Element plots”, which includes figures illustrating PAAS-normalized enrichment trends in bones of varying cortical thickness (in 0.6 mm intervals), the ratio of PAAS-normalized rare earth element (REEY) concentrations between the internal and external portions of the sampled bones, and boxplots showing relative Ca contents for different skeletal element types, Zn/REE, Sr/REE, Ba/REE and U/REE ratios in bones of different thickness, and differences in Ce anomaly (Ce/Ce*) between the studied localities. The “Tables” folder includes the tables used in the manuscript, including the list of samples analyzed in the study and two tables presenting the loadings of elements and elemental ratios on the RDA axes.