A model independent analysis of the electroweak precision data is performed which extends Previous work along the same lines by including, together with the leptonic observables at the Z pole, the hadronic observables as well GAMMA(T), GAMMA(h) and GAMMA(b). This is done by adding to the previously defined epsilon1, epsilon2 and epsilon3 a new parameter epsilon(b) which describes the top mass dependence of the Z --> bbBAR vertex. The data are then analysed by formulating a hierarchy of simple and general assumptions, without ever having to specify the value of the top mass m(t). In particular, by allowing arbitrary new physics effects in vacuum polarization functions (possibly distorting, e.g., the m(t)-dependence of the p-parameter) but assuming negligible modifications of all vertices, we obtain the limit m(t) < 207 GeV at 95% C.L. for alpha(s)(m(Z)) = 0.118+/-0.007. As a very relevant particular example, the comparison of the data with the Standard Model is illustrated: all the epsilons are consistent with the Standard Model predictions, with the central values of epsilon3 and epsilon(b) being respectively slightly lower and slightly higher than expected.