  In this paper we present a detailed analysis of the Electroweak Precision
Observables (EWPO) in composite Higgs models based on the coset $SO(5)/SO(4)$.
In our study we include both the fermionic top partners and the spin-1
resonances and consider their possible interplay as well. In order to achieve
calculability we use the assumptions of i) partial Ultra Violet Completion
(PUVC) following arXiv:1109.1570 and, ii) absence of sizeable effects from
physics above the cut-off. Apart from the EWPO, we also take into account the
constraints from the top quark, $Z$ and the Higgs boson masses whenever they
can be predicted in terms of the model parameters. After presenting our
analytic results (often, in certain limits) and discussing their symmetry
properties, we also perform detailed fits of the model parameters following the
Bayesian approach. We show the posterior probability distributions of the
parameters in various scenarios and provide with analytic understanding
whenever possible. We find that in certain cases the EWPO allow the
compositeness scale to lie well below $1$ TeV. Moreover, fermionic top partners
of mass around $1$ TeV and spin-1 resonances of mass around $2-3$ TeV are
consistent with the precision data.
