This dissertation is mainly about the use of efficient statistical tests to study the properties of powerful extragalactic radio sources. Most of the analysis is based on subsets of a sample of 166 bright (3CR) sources selected at 178 MHz. The first chapter is introductory and it is followed by three on the misalignment and symmetry of double radio sources. The properties of nuclear components in extragalactic sources are discussed in the next chapter, using statistical tests which make efficient use of upper limits, often the only available information on the flux density from the nuclear component. Multifrequency observations of four 3CR sources are presented in the next chapter. The penultimate chapter is about the analysis of correlations involving more than two variables. The Spearman partial rank correlation coefficient is shown to be the most powerful test available which is based on non-parametric statistics. It is therefore used to study the dependences of the properties of sources on their size at constant redshift, and the results are interpreted in terms of source evolution. Correlations of source properties with luminosity and redshift are then examined.