ABSTRACT We present a new, cosmologically model-independent, statistical analysis of the Pantheon$+$ Type Ia Supernovae spectroscopic data set, improving a standard methodology adopted by Lane et al. We use the Tripp equation for supernova standardization alone, thereby avoiding any potential correlation in the stretch and colour distributions. We compare the standard homogeneous cosmological model, i.e. spatially flat $\Lambda$ cold dark matter ($\Lambda$CDM), and the timescape cosmology which invokes backreaction of inhomogeneities. Timescape, while statistically homogeneous and isotropic, departs from average Friedmann–Lemaître–Robertson–Walker evolution, and replaces dark energy by kinetic gravitational energy and its gradients, in explaining independent cosmological observations. When considering the entire Pantheon$+$ sample, we find very strong evidence ($\ln B\gt 5$) in favour of timescape over $\Lambda$CDM. Furthermore, even restricting the sample to redshifts beyond any conventional scale of statistical homogeneity, $z \gt 0.075$, timescape is preferred over $\Lambda$CDM with $\ln B\gt 1$. These results provide evidence for a need to revisit the foundations of theoretical and observational cosmology.