Neutrons stars are unique laboratories to discriminate between the various proposed equations of state of matter at and above nuclear density. One sub-class of neutron stars - those inside quiescent low-mass X-ray binaries (qLMXBs) - produce a thermal surface emission from which the neutron star radius (R_NS) can be measured, using the widely accepted observational scenario for qLMXBs, assuming unmagnetized H atmospheres. In a combined spectral analysis, this work first reproduces a previously published measurement of the rns, assumed to be the same for all neutron stars, using a slightly expanded data set. The radius measured is R_NS = 9.4 +/-1.2 km. On the basis of spectral analysis alone, this measured value is not affected by imposing an assumption of causality in the core. However, the assumptions underlying this R_NS measurement would be falsified by the observation of any neutron star with a mass >2.6 Msun, since radii <11 km would be rejected if causality is assumed, which would exclude most of the R_NS parameter space obtained in this analysis. Finally, this work directly tests a selection of dense matter equations of states: WFF1, AP4, MPA1, PAL1, MS0, and thr
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