The accurate assessment of the condition of transformer oil-paper insulation system is crucial for ensuring the reliable operation of power transformer. However, the information obtained from different chemical and electrical diagnostic tests performed on a transformer may have varying degree of significance for evaluating the overall insulation condition of the transformer. This paper investigates any correlations among different transformer oil characteristic tests and exploits the significance of individual oil characteristic test for the evaluation of transformer insulation conditions. Such investigation and exploitation will facilitate the proper weighting of various transformer oil tests in assessing transformer insulation condition. Numeric results obtained by applying multivariate analysis on a real oil test dataset are also provided in this paper.