The private pilot was test flying an airplane following a number three cylinder change. On initial climb, the engine began to vibrate, backfire and lose power. The airplane crashed on a highway median located about one mile from the airport center. A post-crash inspection of the engine revealed a piece of exhaust valve lodged in the number one piston head. Another valve fragment was found inside the muffler. The pilot reported that the number three cylinder change was the result of a previously failed number three exhaust valve and subsequent internal damage to the number three cylinder. An assumption was made that the fragments from the failed valve had exited the engine via the exhaust system. A local mechanic changed the cylinder, but did not complete the repair due to a lack of time. The pilot finished the repair, test ran the engine, and flew the airplane on the accident flight. The engine was not certified airworthy prior to the flight.