For　the　problem　of　comparing　the　means　of　k　populations　with　unequal　population　variances,　a　new　generalized　test　variable　is　defined　and　the　generalized　p-value　based　on　this　generalized　test　variable　is　given.　It　is　shown　that　the　proposed　generalized　p-value　is　invariant　under　the　group　of　scale　transformations.　Numerical　results　show　that　the　proposed　generalized　p-value　test　performs　better　than　a　generalized　F-test.　(C)　2007　Elsevier　B.V.　All　rights　reserved.