C172 Pilot reported NMAC with another aircraft in the traffic pattern. Pilot took evasive action to avoid a collision.

Narrative

Coming in on a practice ILS approach in visual conditions and eyes out the window. Announced a 10 mile straight in on the practice ILS XX; 5.5 mile final; then 3 mile final. Aircraft in the pattern took off; flew their left crosswind; then left downwind. I expected them to extend their downwind for me to come straight in. Watching them on ADSB; I could see where they were on their downwind. I announced a 3 mile final for Runway XX. Within 5-10 seconds; they started to turn left base; then announced their position. They were turning right in front of my flight path; maybe 100 feet below me. I went full power; started an immediate climb; and right turn to the west to offset the runway. Went on CTAF and announced a radio check; with no response. Tried again with no response. Tried one last time and got a response of 'loud and clear'. I asked them on frequency if they saw me on final before their left base; and if they heard any of my radio calls when on the practice ILS. They told me they didn't hear any of my calls; and didn't see me on their ADSB.