General aviation pilot reported an NMAC with an aircraft while maneuvering to land. Pilot took evasive action to avoid a collision.

Narrative

A training flight was conducted under VMC conditions on Day 0 in a Super Decathlon with a private pilot acting as PIC in the front seat and CFI in the back seat. The flight departed just after XA:00 local time from ZZZ; leaving the pattern to the south to conduct simulated emergencies and simulated off field landings. Approximately 10 minutes into the flight while turning right base to final at approximately 1200' AGL for a chosen farm field to make a simulated landing; a yellow Cub was seen at the 10 or 11 o'clock position 100'-200' away and ~20 feet below the Super Decathlon. The Cub appeared to be in a left bank and moving away from the Super Decathlon. The pilot of the Super Decathlon noted the close traffic over intercom; increased power to full throttle; and increased the rate of right bank in order to avoid the Cub. Due to the poor visibility from the backseat and the immediate increase in bank angle hiding the Cub from view under the belly of the Super Decathlon; the CFI did not make visual contact with the Cub at any point. After moving away from the point of near miss; the Super Decathlon climbed to a higher altitude and left the area to continue the flight without issue.Shortly prior to departing ZZZ; a yellow Cub has been observed departing the field and leaving the pattern without making any traffic calls on CTAF. The CFI had been observing ADS-B traffic on an EFB in the plane sporadically during the flight; but did not observe the Cub at any point on ForeFlight. It is hypothesized that the Cub; not having had an electrical system at the time of its construction; may not have had accommodations for COMM radio or ADS-B.The PIC in the front seat of the Super Decathlon lost situational awareness and failed to clear for traffic while focused on the simulated engine out. Due to the tandem seating of the Super Decathlon obstructing the view of the CFI in the back seat; extra care should be taken to clear for traffic before maneuvers. Task saturation and tunnel vision were also contributing factors.It is possible that the view of the Cub was obstructed by the cowl of the Super Decathlon for most of the maneuver; contributing to the failure of the Super Decathlon pilot to see and avoid. The high wing Cub may have been unaware of the presence of the Super Decathlon entirely due to its configuration and the fact that the Super Decathlon was approaching the Cub from behind and above.Flight following was not obtained at any time during the flight. At the time of the event; the Super Decathlon was monitoring the CTAF frequency for ZZZ. Flight following may have added to situational awareness in the Super Decathlon.No communications were exchanged between either aircraft during or after the event; and the tail number of the Cub is unknown.