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 which , 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 \propto ( 1 + z ) ^ { c } with c \approx - 0.8 \pm 0.4 which is found to arise mainly from a power-size correlation of the form l \propto P ^ { \beta } ( \beta \approx - 0.13 \pm 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 \approx 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 , though 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 non-parametric 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 can not 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 ( \Omega _ { 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 \Omega _ { 0 } \approx 0.35 with 1 \sigma ranges including values between \sim 0.25 and 1.0 ; the c \approx 0 subsamples yield values of \Omega _ { 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 .