What is the test for vacating an award from an arbitrator based on error in law?

"Under certain circumstances an award based on an error in law may be set aside on the ground that it was in excess of the arbitrator's powers. (Code Civ.Proc., 1286.2, subd. (d); ⁴ Abbott v. California State Auto. Assn. (1977) 68 Cal.App.3d 763, 770 [137 Cal.Rptr. 580].) A trial court, however, is limited in its authority to vacate the award of an arbitrator, even in the event of an error of fact or law. The mere fact that an arbitrator reached an erroneous conclusion based on an error of law which does not appear on the face of the the record will not invalidate the award; on the other hand, where the error appears on the face of the award and causes substantial injustice the award may be vacated. [Citations.]" (Id. at p. 1090, 213 Cal.Rptr. 62.)