In line with open-source genetics, we report a novel linear regression technique for genome-wide association studies (GWAS), called Open GWAS algoriTHm (OATH). When individual-level data are not available, OATH can not only completely reproduce reported results from an experimental model, but also recover underreported results from other alternative models with a different combination of nuisance parameters using naïve summary statistics (NSS). OATH can also reliably evaluate all reported results in-depth (e.g., p-value variance analysis), as demonstrated for 42 Arabidopsis phenotypes under three magnesium (Mg) conditions. In addition, OATH can be used for consortium-driven genome-wide association meta-analyses (GWAMA), and can greatly improve the flexibility of GWAMA. A prototype of OATH is available in the Genetic Analysis Repository (https://github.com/gc5k/GEAR).