An investigation of the properties of double radio sources using the Spearman partial rank correlation coefficient

The methods available for analysing correlations between two variables in the presence of a third are reviewed, and it is concluded that the Spearman partial rank correlation coefficient makes the most efficient use of the available data. This is therefore used to study the correlations of the properties of double radio sources with size and redshift z, and with z and luminosity P. Results for a sample of 3CR sources show that larger sources are more diffuse, but their spectral indices are not steeper. If all sources have similar expansion speeds, these results provide information about how sources evolve, since then larger sources are older ones. Spectral index is fundamentally related to z, and only part of this correlation arises because spectra are curved. The values of ‘compactness’ (the fraction of the emission, excluding any nuclear component, from double radio sources which originates from their hot spots) measured by Jenkins & McEllin are fundamentally related to P, but this result requires confirmation because some of their values may be in error. Results for a sample of 3CR and 4C quasars rule out (at the 2σ level) cosmological evolution of physical size which is stronger than $${(1+z)}^{-1.3}$$. The possibility of determining the density parameter Ω of the Universe from the relation between z, P and physical size is considered, and the extension of the Spearman partial rank correlation coefficient to correlations involving more than three parameters is discussed.