In previous attempts to measure cosmological parameters from the angular size-redshift (theta-z) relation of double-lobed radio sources, the observed data have generally been consistent with a static Euclidean universe rather than with standard Friedmann models, and past authors have disagreed significantly as to what effects are responsible for this observation. These results and different interpretations may be due largely to a variety of selection effects and differences in the sample definitions destroying the integrity of the data sets, and inconsistencies in the analysis undermining the results. Using the VLA FIRST survey, we investigate the theta-z relation for a new sample of double-lobed quasars. We define a set of 103 sources, carefully addressing the various potential problems that, we believe, have compromised past work,. including a robust definition of size and the completeness and homogeneity of the sample, and further devise a self-consistent method to assure accurate morphological classification and account for finite resolution effects in the analysis. Before focusing on cosmological constraints, we investigate the possible impact of correlations among the intrinsic properties of these sources over the entire assumed range of allowed cosmological parameter values. For all cases, we find apparent size evolution of the form l proportional to(1 + z)(c), with c approximate to -0.8 +/- 0.4, which is found to arise mainly from a power-size correlation of the form l proportional to P-beta (beta approximate to -0.13 +/- 0.06) coupled with a power-redshift correlation. Intrinsic size evolution is consistent with zero. We also find that in all cases, a subsample with c approximate to 0 can be defined, whose theta-z relation should therefore arise primarily from cosmological effects. These results are found to be independent of orientation effects, although other evidence indicates that orientation effects are present and consistent with predictions of the unified scheme for radio-loud active galactic nuclei. The above results are all confirmed by nonparametric analysis. Contrary to past work, we find that the observed theta-z relation for our sample is more consistent with standard Friedmann models than with a static Euclidean universe. Though the current data cannot distinguish with high significance between various Friedmann models, significant constraints on the cosmological parameters within a given model are obtained. In particular, we find that a flat, matter-dominated universe (theta(0) = 1), a flat universe with a cosmological constant, and an open universe all provide comparably good fits to the data, with the latter two models both yielding Ohm(0) approximate to 0.35 with 1 sigma ranges including values between similar to 0.25 and 1.0; the c approximate to 0 subsamples yield values of Ohm(0), near unity in these models, though with even greater error ranges. We also examine the values of H-0 implied by the data, using plausible assumptions about the intrinsic source sizes, and find these to be consistent with the currently accepted range of values. We determine the sample size needed to improve significantly the results and outline future strategies for such work.
