The paper presents a method for inferring quartet relationships among taxa under the coalescent model, using techniques from algebraic statistics. The method quantifies uncertainty through a nonparametric bootstrap and is assessed using simulated data. It is then applied to larger taxon samples, demonstrating its utility with datasets for Sistrurus rattlesnakes and soybeans. The method is implemented in the software SVDquartets, which is available for download. The authors compare their method to existing approaches, highlighting its computational efficiency and ability to handle both unlinked SNP and multi-locus data. The results show that the SVD score accurately differentiates between valid and non-valid splits, and the method performs well across various simulation conditions. The method is also shown to be effective in inferring species phylogenies in larger taxon sets, with applications to rattlesnake and soybean datasets.The paper presents a method for inferring quartet relationships among taxa under the coalescent model, using techniques from algebraic statistics. The method quantifies uncertainty through a nonparametric bootstrap and is assessed using simulated data. It is then applied to larger taxon samples, demonstrating its utility with datasets for Sistrurus rattlesnakes and soybeans. The method is implemented in the software SVDquartets, which is available for download. The authors compare their method to existing approaches, highlighting its computational efficiency and ability to handle both unlinked SNP and multi-locus data. The results show that the SVD score accurately differentiates between valid and non-valid splits, and the method performs well across various simulation conditions. The method is also shown to be effective in inferring species phylogenies in larger taxon sets, with applications to rattlesnake and soybean datasets.