In a non-expanding universe, surface brightness is independent of distance or redshift, while in an expanding universe it decreases rapidly with both. Similarly, for objects of the same luminosity, the angular radius of an object in a non-expanding universe declines with redshift, while in an expanding universe this radius increases for redshifts z > 1.25. The author and colleagues have previously shown that data for the surface brightness of disc galaxies are compatible with a static universe with redshift linearly proportional to distance at all z [static Euclidian universe (SEU) hypothesis]. In this paper, we examine the more conventional hypothesis that the universe is expanding, but that the actual radii of galaxies of a given luminosity increase with time (decrease with z), as others have proposed. We show that the radii data for both disc and elliptical galaxies are incompatible with any of the published size-evolution predictions based on an expanding universe. We find that all the physical mechanisms proposed for size evolution, such as galaxy mergers, lead to predictions that are in quantitative contradiction with either the radius data or other data sets, such as the observed rate of galaxy mergers. In addition, we find that when the effect of telescope resolution is taken into account, the r-z relationships for disc and elliptical galaxies are identical. Both are excellently fit by SEU predictions. An overall comparison of cosmological models requires examining all available data sets, but for this data set there is a clear contradiction of predictions based on an expanding universe hypothesis.