In this letter, the impact of two phase shifting designs, namely random phase shifting and coherent phase shifting, on the performance of intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) is studied. Analytical results are developed to show that the two designs achieve different tradeoffs between reliability and complexity. Simulation results are provided to compare IRS-NOMA to conventional relaying and IRS assisted orthogonal multiple access, and also to verify the accuracy of the obtained analytical results.