Pilot reported taking evasive action during departure from a non-towered airport to avoid a near midair collision with a landing aircraft that turned the wrong way over the active runway.

Narrative

While taxiing back to Runway 24 at PAN for departure; I was monitoring CTAF. Multiple aircraft were at the airport and in the vicinity. I noted 1 in the pattern; and 3 approaching the pattern from various distances and direction; I was forming a mental picture. One aircraft; Aircraft Y; was approaching from the south for Runway 24 which is preferred and was the runway in use. Aircraft Y had announced that he planned to enter right downwind for Runway 24. I had announced I was taxiing to Runway 24 for runup. As I completed my runup; I turned landing; taxi; and strobe lights on and announced that I was taking Runway 24 for departure to the west. Aircraft Y announced he was turning right base for Runway 24. I checked final was clear and began my takeoff roll. Just as I lifted off the runway; Aircraft Y announced turning final for Runway 24.PAN has a noise abatement procedure to turn right 30 degrees after departure. I started that turn early to avoid houses. As I was in the right turn; Aircraft Y appeared from behind the nose of my aircraft; just below and to my left; short final for Runway 6. On the video I could see that I immediately reacted to avoid a collision with a right turn; but due to closure rates this would have been inadequate. I also immediately warned on CTAF 'aircraft on short final; you're wrong way! wrong way!' and then warned 'traffic in Payson; caution; there's a wrong direction aircraft over the runway'. The pilot of the other aircraft announced he was turning to the left away from the runway; which would have put him into conflict with the right-hand traffic pattern of Runway 24. Later analysis on FlightAware showed he turned to the south; his right; away from the pattern. He also confessed he got turned around and apologized.Had I not turned early for the noise abatement; and had I not been light that day (no passengers); I'm convinced we would have collided head-on and I'd have never seen him. The event was captured by my GoPro; which is also connected to cockpit audio. I am equipped with WAAS GPS and ADS-B in and out and did not receive a traffic alert. Upon reflection; a clue might have been; coming from the south; that he did not announce that he would be crossing midfield to enter downwind. Additionally; I will now be more cautious to either visually or through ADS-B traffic confirm aircraft are where they say they are and consider that there could be aircraft not talking or on the wrong frequency.