A non-experimental, descriptive study was conducted to examine the criteria by which ad hoc labor arbitrators are selected in the petroleum refining industry. Three factors — arbitrator background, recognition, and arbitration practice — were examined to determine their relative importance to advocates selecting ad hoc labor arbitrators. The population of the study consisted of management and labor union advocates in the petroleum refining industry who routinely select ad hoc labor arbitrators. Participating management and union advocates completed a questionnaire used to gather respondents' evaluations of criteria considered in the selection of ad hoc arbitrators. Responses to statements designed for measuring relative importance of the criteria considered were recorded. Descriptive statistics, discriminant analysis, and tests of significance were used in the treatment of the data.