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See paper for full list of authors - 26 pages, 4 captioned figures, 2 tables, Author from page 20 to page 23 ; Angular correlations between unidentified charged trigger particles and various species of charged associated particles (unidentified particles, pions, kaons, protons and antiprotons) are measured by the ALICE detector in p-Pb collisions at a nucleon--nucleon centre-of-mass energy of 5.02 TeV in the transverse-momentum range 0.3 < p_T < 4 GeV/c. The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range |eta_lab|<0.8. Fourier coefficients are extracted from the long-range correlations projected onto the azimuthal angle difference and studied as a function of $\pt$ and in intervals of event multiplicity. In high-multiplicity events, the second-order coefficient for protons, v_2^p, is observed to be smaller than that for pions, v_2^pi, up to about p_T = 2 GeV/c. To reduce correlations due to jets, the per-trigger yield measured in low-multiplicity events is subtracted from that in high-multiplicity events. A two-ridge structure is obtained for all particle species. The Fourier decomposition of this structure shows that the second-order coefficients for pions and kaons are similar. The v_2^p is found to be smaller at low p_T and larger at higher p_T than v_2^pi, with a crossing occurring at about 2 GeV. This is qualitatively similar to the elliptic-flow pattern observed in heavy-ion collisions. A mass ordering effect at low transverse momenta is consistent with expectations from hydrodynamic model calculations assuming a collectively expanding system.
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