The present work considers the semiconducting properties of In-doped TiO2 in terms of the Jonker formalism applied for both electrical conductivity and thermoelectric power data determined simultaneously in equilibrium with the gas phase of controlled oxygen activity. It is shown that the electrical properties of In-doped TiO2 annealed in oxidizing conditions [p(O2) > 10 Pa] can be described by the Jonker formalism very well. However, annealing of In-doped TiO2 in strongly reducing conditions [p(O2) < 10(-10) Pa], imposed by the gas phase involving hydrogen, results in a deviation of the experimental data from the Jonker's theoretical model derived for the Maxwell-Boltzmann statistics. This departure is considered in terms of the effect of hydrogen on the formation of structural domains, which are expected to be entirely different from those of oxidized TiO2 in terms of its electronic properties. It is argued that In-doped TiO2 annealed in the gas phase involving hydrogen exhibits a high concentration of donor-type ionic defects, which lead to the formation of high concentration of electrons. The related semiconducting properties are inconsistent with the model of classical semiconductor where the electrons are described by the Maxwell-Boltzmann statistics. It is concluded that strong interactions within the electron gas lead, in consequence, to the behavior resembling correlated transport of electrons. The obtained results suggest that indium incorporation into the rutile structure of TiO2 results in the formation of structural properties that exhibit extraordinary charge transport.