What is the test for arbitration in a personal injury matter?

Pursuant to Code of Civil Procedure section 1281.2, a trial court shall order arbitration of a controversy if an agreement to arbitrate the controversy exists, with certain exceptions inapplicable here. California has a strong public policy in favor of arbitration, but a party cannot be compelled to arbitrate a dispute that [s]he has not agreed to resolve by arbitration.' (Buckner v. Tamarin (2002) 98 Cal.App.4th 140, 142.)