What is the test for federal habeas corpus relief under AEDPA?

Constitution or laws of the United States. 28 U.S.C. 2254(a); Williams v. Taylor, 529 U.S. 362, 375 n. 7 (2000). Federal habeas corpus relief is not available for any claim decided on the merits in state court proceedings unless the state court's adjudication of the claim:

28 U.S.C. 2254(d). Although "AEDPA does not require a federal habeas court to adopt any one methodology," there are certain principles which guide its application. Lockyer v. Andrade, 538 U.S. 63, 71 (2003)