Flight Instructor with student in traffic pattern of PWT non-towered airport reported an inbound aircraft announced they were entering the pattern for same runway but actually turned toward the opposite direction runway; resulting in an NMAC. Flight Instructor took evasive action.

Narrative

Our aircraft was using the left traffic pattern for Runway 20. The winds were reporting light and variable on the AWOS. The wind socks were showing winds favoring Runway 02 but kept transitioning. All aircraft were using 20 for takeoffs and landings. During our crosswind turn for 20 we heard Aircraft Y call they were setting up for the 45 for left downwind 20 and made the statement the winds were favoring Runway 02. We called that current active runway was 20. We turned downwind and made a radio call of our location in the traffic pattern. As we continued flying downwind I was watching Aircraft Y location on ForeFlight. It appeared they were setting up for a left base entry instead of a 45 for Runway 20. As we continued to fly downwind they were turning for a right downwind for Runway 02. This set us up for a head on collision in the downwind leg. I saw Aircraft Y keep a left turn and prevented me from banking right to comply with 91.113. I had to grab the controls from my student and do a hard left bank and hope Aircraft Y saw us. Both aircraft continued a left bank preventing a mid air collision from occurring. The problem occurred due to Aircraft Y making a statement on CTAF that they setting up for 20 but instead flew for the opposite traffic pattern of what they said they were doing. To prevent a re-occurrence of the events Aircraft Y PIC should undergo review of traffic pattern and radio communication procedures. PWT should also have ATC facilities for tower and ground.