AN E145 CREW; ON APCH TO SDF; MISINTERPRETED A SPD ASSIGNMENT AS A HEADING VECTOR; DEVIATING FROM ASSIGNED COURSE.

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DSNDING INTO SDF WITH APCH CTLR. CLRNC WAS DSND TO 4000 FT; SPD 190 KTS ON DOWNWIND VECTOR. WE GOT A TURN TO BASE 270 DEG HDG. WE WERE GETTING VECTORED TO ILS RWY 17 AT SDF. INBOUND COURSE FOR RWY WAS 168 DEGS. DURING BASE VECTOR WE GOT A CLRNC TO DSND TO 3500 FT SPD 180 KTS; WHICH MY FO READ BACK AS HE WAS PNF. I ENTERED 3500 FT IN THE ALT ALERTER AND ASKED IF IT WAS HEADING 180 DEGS; WHICH HE ACKNOWLEDGED. I BEGAN THE TURN AND DSCNT. DURING THE TURN THE APCH CTLR ASKED IF WE HAD BEGUN OUR TURN IN. WE SAID YES 3500 FT HEADING 180 DEGS. WE WERE TOLD TO TURN BACK HEADING 270 DEGS WHICH WE DID. ESTABLISHED ON 270 DEG HDG WE TOLD THE CTLR THAT WE SCREWED UP THE INSTRUCTIONS. HE THEN CLRED US FOR VISUAL APCH. THIS CLRNC WAS GIVEN AT A PERFECT TIME IN THE APCH VECTOR WHERE A 180 DEG HDG WAS A WORKABLE VECTOR FOR FINAL AT A TIME WHEN ONE WOULD EXPECT A TURN IN; AND JUST AFTER A SPD REDUCTION TO 190 KTS. THE EVENTS LEADING UP TO MY TURN INTO ARPT DID NOT LEAD ME TO BELIEVE THAT MY 180 DEG HDG WAS IN ERROR BECAUSE IT ALL FIT INTO PARAMETERS FOR A FINAL VECTOR.