Liberals and conservatives both express political animosity and favouritism. However, less is known about whether the same or different factors contribute to this phenomenon among liberals and conservatives. We test three different relationships that could emerge among cognitive ability, cognitive reflection and political group-based attitudes. Analysing two nationally representative surveys of US Americans (N = 9035) containing a measure of cognitive ability, we find evidence that compared to people lower in cognitive ability, people higher in cognitive ability express more animosity towards ideologically discordant groups and more favouritism towards ideologically concordant groups. This pattern was particularly pronounced among liberals. In a registered report study, we then test whether the same is true of cognitive reflection in another large dataset (N = 3498). In contrast to cognitive ability, we find no relationship between cognitive reflection, political animosity and favouritism. Together, these studies provide a comprehensive test of how cognitive ability and cognitive reflection are related to political animosity and favouritism for liberals and conservatives in the United States.