This paper considers the power and size properties of some well known nonparametric linear rank tests for location and scale as well as the Kolmogorov-Smirnov omnibus test and proposed alternatives to it. Independence between some classes of linear rank tests is established facilitating their joint application. Monte Carlo study confirms the asymptotic power properties of the linear rank tests but raises concerns about their application in more general and practically relevant circumstances. It also indicates that the new omnibus tests constitute viable alternatives with superior properties to the Kolmogorov-Smirnov test in certain circumstances.