The influence of Y content on the grain-scale twinning behavior in extruded Mg-xY (x=0.5, 1, 5, wt.%) sheets under uniaxial tension and compression along the extruded direction was statistically investigated. An automatic twin variant analysis was employed, based on large data sets obtained by electron backscatter diffraction (EBSD), including 2691 grains with 977 twins. The tension twinning (TTW) dominance and prevailing anomalous twinning behavior (Schmid factor (m) <0) under both tension and compression were found. The anomalous twinning behavior was more pronounced as Y content increased under tensile loading, indicating a promoted stochasticity of twin variant selection for more concentrated Mg-Y alloys. However, the trend for the Y-content dependent anomalous twinning behavior was opposite in compression. The fractions of the anomalous TTWs were found to be well correlated with the maximum Schmid factor (m_max) values of basal slip and prismatic slip in the corresponding parent grains for compression and tension, respectively, indicating that twinning and dislocation slip might be closely related in the present Mg-Y alloys.