THE FREQUENCY RESPONSE ANALYSIS (FRA) TEST HASBEEN RECOGNIZED AS ONE OF THE SENSITIVE TOOLS AVAILABLE FORDETECTING ELECTRICAL AND MECHANICAL FAULTS INSIDE POWERTRANSFORMERS. HOWEVER, THERE IS STILL NO UNIVERSALLY SYSTEMATICINTERPRETATION TECHNIQUE FOR THESE TESTS. MANY RESEARCH EFFORTSHAVE EMPLOYED DIFFERENT Statistical CRITERIA IN ORDER TO AID THEINTERPRETATIVE CAPABILITY OF THE FRA, BUT IT IS SHOWED THAT THEMethods USED SO FAR, ARE BASED ON PARAMETRIC STATISTICS WHICHNEED A SET OF ASSUMPTIONS ABOUT THE NORMALITY, RANDOMNESS ANDStatistical INDEPENDENCE OF FRA DATA. THEREFORE, THIS PAPER AIMSTO PROPOSE SOME NONPARAMETRIC Statistical Methods WHICH AREBASED ON EXPLICITLY WEAKER ASSUMPTIONS THAN SUCH CLASSICALPARAMETRIC Methods. THE PROPOSED Statistical Methods AREAPPLIED TO THE EXPERIMENTAL FRA MEASUREMENTS OBTAINED FROMTWO TEST OBJECTS: A THREE PHASE, TWO WINDING DISTRIBUTIONTRANSFORMER (35/0.4 KV, 100 KVA) TO STUDY THE WINDING INTER-TURNFAULT AS AN ELECTRICAL FAULT, AND A TWO WINDING TRANSFORMER (1.2MVA, 10 KV) FOR THE STUDY OF RADIAL DEFORMATION AS A MECHANICALFAULT. IT WAS FOUND THROUGH THIS RESEARCH WORK THAT THE USEDMethods NAMELY, WILCOXON SIGNED RANK TEST AND FRIEDMAN TESTWHICH ARE PROPOSED FOR THE FIRST TIME, CAN EFFECTIVELY REFLECT THEDIFFERENCES BETWEEN COMPARED FRA DATA AND DIAGNOSE THE FAULT.