We present a study of showers initiated by electrons, pions, kaons, and protons with momenta from 15 GeV to 150 GeV in the highly granular CALICE scintillator-tungsten analogue hadronic calorimeter. The data were recorded at the CERN Super Proton Synchrotron in 2011. The analysis includes measurements of the calorimeter response to each particle type as well as measurements of the energy resolution and studies of the longitudinal and radial shower development for selected particles. The results are compared to Geant4 simulations (version 9.6.p02). In the study of the energy resolution we include previously published data with beam momenta from 1 GeV to 10 GeV recorded at the CERN Proton Synchrotron in 2010. KEYWORDS: Calorimeter methods; Detector modelling and simulations I (interaction of radiation with matter, interaction of photons with matter, interaction of hadrons with matter, etc); Particle identification methods.