Partial conductivities contributed by electron holes, oxygen ions, and protons were caluclated in $SrZr_{0.95}Y_{0.05}O_{2.975}$, using the reported formulae derived from the defect chemistry of HTPCs. Required parameters were obtained from the graphical analysis of total conductivity variation against partial pressure of water vapor and oxygen. Predicted overall conductivities showed a reasonable agreement with experimental measurements. The conductivity of the material showed a linear increase with square root of the water vapor pressure. This increase was due to proton conduction in an almost pure ionic conductivity. The calculation of partial conductivities at $800^{circ}C$ resulted in an almost pure ionic conductivity at $P_{02}=10^{-10}$ atm and a predominant hole conductivity at $P_{02}=10^{-10}$ atm. Pure proton conduction was not expected at this temperature, contrary to the earlier reports. Discussions were made in relation with reported thermodynamic data and defect structure of the material. It was shown that from the total conductivity dependence on water vapor pressure, the pure ionic conductivity at low oxygen partial pressures could be separated into protonic and oxygen ionic conductivity in $ZrO_2$-based HTPCs.