Major, trace, and rare earth element analyses of volcanic glass are used separately or in combination for correlating Quaternary tephras, often by graphical or simple comparative methods. We have taken a statistical approach using discriminant function analysis (DFA) to assess the relative discriminating power of the different elements in volcanic glasses from several tectonovolcanic provinces. We found that major oxides are powerful discriminating variables for widespread tephras from the Taupo Volcanic Zone in New Zealand and here they can be more discriminating than trace elements. A wide selection of tephras from the western United States can also be distinguished on major oxides alone, particularly those from Cascade Range volcanoes. For tephras from large intracontinental calderas, such as Long Valley or Yellowstone, REE and trace elements are more effective at discriminating than major oxides. However, tephras erupted from the Long Valley area can be distinguished on major oxide composition by DFA, despite their similar chemistry. The selection and relative significance of different elements for discriminating tephras depends on the total data set being compared, as well as the source volcano and the individual eruptive events. Caution must be exercised in the nonstatistical selection of compositional data for characterizing tephras: DFA is a more powerful and objective tool for the comparison of tephra chemistry.